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<li><a class="reference internal" href="#">pymatgen.analysis.elasticity package</a><ul>
<li><a class="reference internal" href="#submodules">Submodules</a></li>
<li><a class="reference internal" href="#module-pymatgen.analysis.elasticity.elastic">pymatgen.analysis.elasticity.elastic module</a><ul>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ComplianceTensor"><code class="docutils literal notranslate"><span class="pre">ComplianceTensor</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor"><code class="docutils literal notranslate"><span class="pre">ElasticTensor</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.agne_diffusive_thermalcond"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.agne_diffusive_thermalcond()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.cahill_thermalcond"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.cahill_thermalcond()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.clarke_thermalcond"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.clarke_thermalcond()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.compliance_tensor"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.compliance_tensor</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.debye_temperature"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.debye_temperature()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.directional_elastic_mod"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.directional_elastic_mod()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.directional_poisson_ratio"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.directional_poisson_ratio()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.from_independent_strains"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.from_independent_strains()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.from_pseudoinverse"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.from_pseudoinverse()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.g_reuss"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.g_reuss</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.g_voigt"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.g_voigt</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.g_vrh"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.g_vrh</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.get_structure_property_dict"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.get_structure_property_dict()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.green_kristoffel"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.green_kristoffel()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.homogeneous_poisson"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.homogeneous_poisson</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.k_reuss"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.k_reuss</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.k_voigt"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.k_voigt</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.k_vrh"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.k_vrh</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.long_v"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.long_v()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.property_dict"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.property_dict</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_ac"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.snyder_ac()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_opt"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.snyder_opt()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_total"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.snyder_total()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.trans_v"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.trans_v()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.universal_anisotropy"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.universal_anisotropy</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.y_mod"><code class="docutils literal notranslate"><span class="pre">ElasticTensor.y_mod</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.calculate_stress"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.calculate_stress()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.energy_density"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.energy_density()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.from_diff_fit"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.from_diff_fit()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_compliance_expansion"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_compliance_expansion()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_effective_ecs"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_effective_ecs()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_ggt"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_ggt()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_gruneisen_parameter"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_gruneisen_parameter()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_heat_capacity"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_heat_capacity()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_stability_criteria"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_stability_criteria()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_strain_from_stress"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_strain_from_stress()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_symmetric_wallace_tensor"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_symmetric_wallace_tensor()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_tgt"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_tgt()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_wallace_tensor"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_wallace_tensor()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_yield_stress"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.get_yield_stress()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.omega"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.omega()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.order"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.order</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.thermal_expansion_coeff"><code class="docutils literal notranslate"><span class="pre">ElasticTensorExpansion.thermal_expansion_coeff()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor"><code class="docutils literal notranslate"><span class="pre">NthOrderElasticTensor</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.GPa_to_eV_A3"><code class="docutils literal notranslate"><span class="pre">NthOrderElasticTensor.GPa_to_eV_A3</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.calculate_stress"><code class="docutils literal notranslate"><span class="pre">NthOrderElasticTensor.calculate_stress()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.energy_density"><code class="docutils literal notranslate"><span class="pre">NthOrderElasticTensor.energy_density()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.from_diff_fit"><code class="docutils literal notranslate"><span class="pre">NthOrderElasticTensor.from_diff_fit()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.order"><code class="docutils literal notranslate"><span class="pre">NthOrderElasticTensor.order</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.symbol"><code class="docutils literal notranslate"><span class="pre">NthOrderElasticTensor.symbol</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.diff_fit"><code class="docutils literal notranslate"><span class="pre">diff_fit()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.find_eq_stress"><code class="docutils literal notranslate"><span class="pre">find_eq_stress()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.generate_pseudo"><code class="docutils literal notranslate"><span class="pre">generate_pseudo()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.get_diff_coeff"><code class="docutils literal notranslate"><span class="pre">get_diff_coeff()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.get_strain_state_dict"><code class="docutils literal notranslate"><span class="pre">get_strain_state_dict()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.get_symbol_list"><code class="docutils literal notranslate"><span class="pre">get_symbol_list()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.raise_if_unphysical"><code class="docutils literal notranslate"><span class="pre">raise_if_unphysical()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.subs"><code class="docutils literal notranslate"><span class="pre">subs()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#module-pymatgen.analysis.elasticity.strain">pymatgen.analysis.elasticity.strain module</a><ul>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Deformation"><code class="docutils literal notranslate"><span class="pre">Deformation</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Deformation.apply_to_structure"><code class="docutils literal notranslate"><span class="pre">Deformation.apply_to_structure()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Deformation.from_index_amount"><code class="docutils literal notranslate"><span class="pre">Deformation.from_index_amount()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Deformation.get_perturbed_indices"><code class="docutils literal notranslate"><span class="pre">Deformation.get_perturbed_indices()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Deformation.green_lagrange_strain"><code class="docutils literal notranslate"><span class="pre">Deformation.green_lagrange_strain</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Deformation.is_independent"><code class="docutils literal notranslate"><span class="pre">Deformation.is_independent()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Deformation.symbol"><code class="docutils literal notranslate"><span class="pre">Deformation.symbol</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.DeformedStructureSet"><code class="docutils literal notranslate"><span class="pre">DeformedStructureSet</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Strain"><code class="docutils literal notranslate"><span class="pre">Strain</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Strain.from_deformation"><code class="docutils literal notranslate"><span class="pre">Strain.from_deformation()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Strain.from_index_amount"><code class="docutils literal notranslate"><span class="pre">Strain.from_index_amount()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Strain.get_deformation_matrix"><code class="docutils literal notranslate"><span class="pre">Strain.get_deformation_matrix()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Strain.symbol"><code class="docutils literal notranslate"><span class="pre">Strain.symbol</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Strain.von_mises_strain"><code class="docutils literal notranslate"><span class="pre">Strain.von_mises_strain</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.strain.convert_strain_to_deformation"><code class="docutils literal notranslate"><span class="pre">convert_strain_to_deformation()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#module-pymatgen.analysis.elasticity.stress">pymatgen.analysis.elasticity.stress module</a><ul>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.stress.Stress"><code class="docutils literal notranslate"><span class="pre">Stress</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.stress.Stress.dev_principal_invariants"><code class="docutils literal notranslate"><span class="pre">Stress.dev_principal_invariants</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.stress.Stress.deviator_stress"><code class="docutils literal notranslate"><span class="pre">Stress.deviator_stress</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.stress.Stress.mean_stress"><code class="docutils literal notranslate"><span class="pre">Stress.mean_stress</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.stress.Stress.piola_kirchoff_1"><code class="docutils literal notranslate"><span class="pre">Stress.piola_kirchoff_1()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.stress.Stress.piola_kirchoff_2"><code class="docutils literal notranslate"><span class="pre">Stress.piola_kirchoff_2()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.stress.Stress.symbol"><code class="docutils literal notranslate"><span class="pre">Stress.symbol</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.analysis.elasticity.stress.Stress.von_mises"><code class="docutils literal notranslate"><span class="pre">Stress.von_mises</span></code></a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
</div>
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<section id="module-pymatgen.analysis.elasticity">
<span id="pymatgen-analysis-elasticity-package"></span><h1>pymatgen.analysis.elasticity package<a class="headerlink" href="#module-pymatgen.analysis.elasticity" title="Link to this heading"></a></h1>
<p>Package for analyzing elastic tensors and properties.</p>
<section id="submodules">
<h2>Submodules<a class="headerlink" href="#submodules" title="Link to this heading"></a></h2>
</section>
<section id="module-pymatgen.analysis.elasticity.elastic">
<span id="pymatgen-analysis-elasticity-elastic-module"></span><h2>pymatgen.analysis.elasticity.elastic module<a class="headerlink" href="#module-pymatgen.analysis.elasticity.elastic" title="Link to this heading"></a></h2>
<p>This module provides a class used to describe the elastic tensor,
including methods used to fit the elastic tensor from linear response
stress-strain data.</p>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ComplianceTensor">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ComplianceTensor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s_array</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L524-L540"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ComplianceTensor" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="pymatgen.core.html#pymatgen.core.tensors.Tensor" title="pymatgen.core.tensors.Tensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code></a></p>
<p>This class represents the compliance tensor, and exists
primarily to keep the voigt-conversion scheme consistent
since the compliance tensor has a unique vscale.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>s_array</strong> (<em>np.ndarray</em>) – input array for tensor</p>
</dd>
</dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ElasticTensor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">input_array</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.0001</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L130-L521"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor" title="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">NthOrderElasticTensor</span></code></a></p>
<p>This class extends Tensor to describe the 3x3x3x3 second-order elastic tensor,
C_{ijkl}, with various methods for estimating other properties derived from the second
order elastic tensor (e.g. bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio)
in units of eV/A^3.</p>
<p>Create an ElasticTensor object. The constructor throws an error if the shape of
the input_matrix argument is not 3x3x3x3, i.e. in true tensor notation. Issues a
warning if the input_matrix argument does not satisfy standard symmetries. Note
that the constructor uses __new__ rather than __init__ according to the standard
method of subclassing numpy ndarrays.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input_array</strong> (<em>3x3x3x3 array-like</em>) – the 3x3x3x3 array-like representing the elastic tensor</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance for initial symmetry test of tensor</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.agne_diffusive_thermalcond">
<span class="sig-name descname"><span class="pre">agne_diffusive_thermalcond</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L122-L125"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.agne_diffusive_thermalcond" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.cahill_thermalcond">
<span class="sig-name descname"><span class="pre">cahill_thermalcond</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L122-L125"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.cahill_thermalcond" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.clarke_thermalcond">
<span class="sig-name descname"><span class="pre">clarke_thermalcond</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L122-L125"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.clarke_thermalcond" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.compliance_tensor">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">compliance_tensor</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.compliance_tensor" title="Link to this definition"></a></dt>
<dd><p>The Voigt notation compliance tensor, which is the matrix
inverse of the Voigt notation elastic tensor.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.debye_temperature">
<span class="sig-name descname"><span class="pre">debye_temperature</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L122-L125"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.debye_temperature" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.directional_elastic_mod">
<span class="sig-name descname"><span class="pre">directional_elastic_mod</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">float</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L223-L226"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.directional_elastic_mod" title="Link to this definition"></a></dt>
<dd><p>Calculate directional elastic modulus for a specific vector.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.directional_poisson_ratio">
<span class="sig-name descname"><span class="pre">directional_poisson_ratio</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ArrayLike</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">m</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ArrayLike</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-08</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">float</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L206-L221"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.directional_poisson_ratio" title="Link to this definition"></a></dt>
<dd><p>Calculates the poisson ratio for a specific direction
relative to a second, orthogonal direction.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>n</strong> (<em>3-d vector</em>) – principal direction</p></li>
<li><p><strong>m</strong> (<em>3-d vector</em>) – secondary direction orthogonal to n</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance for testing of orthogonality</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.from_independent_strains">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_independent_strains</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strains</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stresses</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eq_stress</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">vasp</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-10</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L489-L521"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.from_independent_strains" title="Link to this definition"></a></dt>
<dd><p>Constructs the elastic tensor least-squares fit of independent strains.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strains</strong> (<em>list</em><em> of </em><em>Strains</em>) – list of strain objects to fit</p></li>
<li><p><strong>stresses</strong> (<em>list</em><em> of </em><em>Stresses</em>) – list of stress objects to use in fit
corresponding to the list of strains</p></li>
<li><p><strong>eq_stress</strong> (<a class="reference internal" href="#pymatgen.analysis.elasticity.stress.Stress" title="pymatgen.analysis.elasticity.stress.Stress"><em>Stress</em></a>) – equilibrium stress to use in fitting</p></li>
<li><p><strong>vasp</strong> (<em>bool</em>) – flag for whether the stress tensor should be
converted based on vasp units/convention for stress</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance for removing near-zero elements of the
resulting tensor.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.from_pseudoinverse">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_pseudoinverse</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strains</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stresses</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L464-L487"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.from_pseudoinverse" title="Link to this definition"></a></dt>
<dd><p>Class method to fit an elastic tensor from stress/strain
data. Method uses Moore-Penrose pseudo-inverse to invert
the s = C*e equation with elastic tensor, stress, and
strain in voigt notation.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>stresses</strong> (<em>Nx3x3 array-like</em>) – list or array of stresses</p></li>
<li><p><strong>strains</strong> (<em>Nx3x3 array-like</em>) – list or array of strains</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.g_reuss">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">g_reuss</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.g_reuss" title="Link to this definition"></a></dt>
<dd><p>The G_r shear modulus (in eV/A^3).</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.g_voigt">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">g_voigt</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.g_voigt" title="Link to this definition"></a></dt>
<dd><p>The G_v shear modulus (in eV/A^3).</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.g_vrh">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">g_vrh</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.g_vrh" title="Link to this definition"></a></dt>
<dd><p>The G_vrh (Voigt-Reuss-Hill) average shear modulus (in eV/A^3).</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.get_structure_property_dict">
<span class="sig-name descname"><span class="pre">get_structure_property_dict</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">include_base_props</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ignore_errors</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">dict</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L427-L462"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.get_structure_property_dict" title="Link to this definition"></a></dt>
<dd><p>Get a dictionary of properties derived from the elastic tensor
and an associated structure.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – structure object for which to calculate
associated properties</p></li>
<li><p><strong>include_base_props</strong> (<em>bool</em>) – whether to include base properties,
like k_vrh, etc.</p></li>
<li><p><strong>ignore_errors</strong> (<em>bool</em>) – if set to true, will set problem properties
that depend on a physical tensor to None, defaults to False</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.green_kristoffel">
<span class="sig-name descname"><span class="pre">green_kristoffel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">u</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">float</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L407-L409"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.green_kristoffel" title="Link to this definition"></a></dt>
<dd><p>Get the Green-Kristoffel tensor for a second-order tensor.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.homogeneous_poisson">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">homogeneous_poisson</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.homogeneous_poisson" title="Link to this definition"></a></dt>
<dd><p>The homogeneous poisson ratio.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.k_reuss">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">k_reuss</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.k_reuss" title="Link to this definition"></a></dt>
<dd><p>The K_r bulk modulus (in eV/A^3).</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.k_voigt">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">k_voigt</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.k_voigt" title="Link to this definition"></a></dt>
<dd><p>The K_v bulk modulus (in eV/A^3).</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.k_vrh">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">k_vrh</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.k_vrh" title="Link to this definition"></a></dt>
<dd><p>The K_vrh (Voigt-Reuss-Hill) average bulk modulus (in eV/A^3).</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.long_v">
<span class="sig-name descname"><span class="pre">long_v</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L122-L125"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.long_v" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.property_dict">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">property_dict</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.property_dict" title="Link to this definition"></a></dt>
<dd><p>A dictionary of properties derived from the elastic tensor.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_ac">
<span class="sig-name descname"><span class="pre">snyder_ac</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L122-L125"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_ac" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_opt">
<span class="sig-name descname"><span class="pre">snyder_opt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L122-L125"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_opt" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_total">
<span class="sig-name descname"><span class="pre">snyder_total</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L122-L125"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.snyder_total" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.trans_v">
<span class="sig-name descname"><span class="pre">trans_v</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L122-L125"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.trans_v" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.universal_anisotropy">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">universal_anisotropy</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.universal_anisotropy" title="Link to this definition"></a></dt>
<dd><p>The universal anisotropy value.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensor.y_mod">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">y_mod</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensor.y_mod" title="Link to this definition"></a></dt>
<dd><p>Calculates Young’s modulus (in SI units) using the
Voigt-Reuss-Hill averages of bulk and shear moduli.</p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ElasticTensorExpansion</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">c_list</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L543-L836"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="pymatgen.core.html#pymatgen.core.tensors.TensorCollection" title="pymatgen.core.tensors.TensorCollection"><code class="xref py py-class docutils literal notranslate"><span class="pre">TensorCollection</span></code></a></p>
<p>This class is a sequence of elastic tensors corresponding
to an elastic tensor expansion, which can be used to
calculate stress and energy density and inherits all
of the list-based properties of TensorCollection
(e.g. symmetrization, voigt conversion, etc.).</p>
<p>Initialization method for ElasticTensorExpansion.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>c_list</strong> (<em>list</em><em> or </em><em>tuple</em>) – sequence of Tensor inputs or tensors from which
the elastic tensor expansion is constructed.</p>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.calculate_stress">
<span class="sig-name descname"><span class="pre">calculate_stress</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strain</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">float</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L579-L584"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.calculate_stress" title="Link to this definition"></a></dt>
<dd><p>Calculate’s a given elastic tensor’s contribution to the
stress using Einstein summation.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.energy_density">
<span class="sig-name descname"><span class="pre">energy_density</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strain</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">convert_GPa_to_eV</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L586-L588"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.energy_density" title="Link to this definition"></a></dt>
<dd><p>Calculate the elastic energy density due to a strain in eV/A^3 or GPa.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.from_diff_fit">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_diff_fit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strains</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stresses</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eq_stress</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L563-L569"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.from_diff_fit" title="Link to this definition"></a></dt>
<dd><p>Generate an elastic tensor expansion via the fitting function
defined below in diff_fit.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_compliance_expansion">
<span class="sig-name descname"><span class="pre">get_compliance_expansion</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L733-L754"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_compliance_expansion" title="Link to this definition"></a></dt>
<dd><p>Get a compliance tensor expansion from the elastic
tensor expansion.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_effective_ecs">
<span class="sig-name descname"><span class="pre">get_effective_ecs</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strain</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L766-L778"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_effective_ecs" title="Link to this definition"></a></dt>
<dd><p>Get the effective elastic constants
from the elastic tensor expansion.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strain</strong> (<a class="reference internal" href="#pymatgen.analysis.elasticity.strain.Strain" title="pymatgen.analysis.elasticity.strain.Strain"><em>Strain</em></a><em> or </em><em>3x3 array-like</em>) – strain condition
under which to calculate the effective constants</p></li>
<li><p><strong>order</strong> (<em>int</em>) – order of the ecs to be returned</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_ggt">
<span class="sig-name descname"><span class="pre">get_ggt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L590-L601"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_ggt" title="Link to this definition"></a></dt>
<dd><p>Get the Generalized Gruneisen tensor for a given
third-order elastic tensor expansion.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>n</strong> (<em>3x1 array-like</em>) – normal mode direction</p></li>
<li><p><strong>u</strong> (<em>3x1 array-like</em>) – polarization direction</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_gruneisen_parameter">
<span class="sig-name descname"><span class="pre">get_gruneisen_parameter</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">temperature</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">quad</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L641-L654"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_gruneisen_parameter" title="Link to this definition"></a></dt>
<dd><p>Get the single average gruneisen parameter from the TGT.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – Temperature in kelvin, if not specified
will return non-cv-normalized value</p></li>
<li><p><strong>structure</strong> (<em>float</em>) – Structure to be used in directional heat
capacity determination, only necessary if temperature
is specified</p></li>
<li><p><strong>quadct</strong> (<em>dict</em>) – quadrature for integration, should be
dictionary with “points” and “weights” keys defaults
to quadpy.sphere.Lebedev(19) as read from file</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_heat_capacity">
<span class="sig-name descname"><span class="pre">get_heat_capacity</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">temperature</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">n</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cutoff</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100.0</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L656-L677"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_heat_capacity" title="Link to this definition"></a></dt>
<dd><p>Get the directional heat capacity for a higher order tensor
expansion as a function of direction and polarization.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – Temperature in kelvin</p></li>
<li><p><strong>structure</strong> (<em>float</em>) – Structure to be used in directional heat
capacity determination</p></li>
<li><p><strong>n</strong> (<em>3x1 array-like</em>) – direction for Cv determination</p></li>
<li><p><strong>u</strong> (<em>3x1 array-like</em>) – polarization direction, note that
no attempt for verification of eigenvectors is made</p></li>
<li><p><strong>cutoff</strong> (<em>float</em>) – cutoff for scale of kt / (hbar * omega)
if lower than this value, returns 0</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_stability_criteria">
<span class="sig-name descname"><span class="pre">get_stability_criteria</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L810-L824"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_stability_criteria" title="Link to this definition"></a></dt>
<dd><p>Get the stability criteria from the symmetric
Wallace tensor from an input vector and stress
value.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>s</strong> (<em>float</em>) – Stress value at which to evaluate
the stability criteria</p></li>
<li><p><strong>n</strong> (<em>3x1 array-like</em>) – direction of the applied
stress</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_strain_from_stress">
<span class="sig-name descname"><span class="pre">get_strain_from_stress</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stress</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">float</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L756-L764"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_strain_from_stress" title="Link to this definition"></a></dt>
<dd><p>Get the strain from a stress state according to the compliance
expansion corresponding to the tensor expansion.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_symmetric_wallace_tensor">
<span class="sig-name descname"><span class="pre">get_symmetric_wallace_tensor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">tau</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L799-L808"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_symmetric_wallace_tensor" title="Link to this definition"></a></dt>
<dd><p>Get the symmetrized wallace tensor for determining
yield strength criteria.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>tau</strong> (<em>3x3 array-like</em>) – stress at which to evaluate
the wallace tensor.</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_tgt">
<span class="sig-name descname"><span class="pre">get_tgt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">temperature</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">quad</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L603-L639"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_tgt" title="Link to this definition"></a></dt>
<dd><p>Get the thermodynamic Gruneisen tensor (TGT) by via an
integration of the GGT weighted by the directional heat
capacity.</p>
<dl class="simple">
<dt>See refs:</dt><dd><p>R. N. Thurston and K. Brugger, Phys. Rev. 113, A1604 (1964).
K. Brugger Phys. Rev. 137, A1826 (1965).</p>
</dd>
</dl>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – Temperature in kelvin, if not specified
will return non-cv-normalized value</p></li>
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Structure to be used in directional heat
capacity determination, only necessary if temperature
is specified</p></li>
<li><p><strong>quadct</strong> (<em>dict</em>) – quadrature for integration, should be
dictionary with “points” and “weights” keys defaults
to quadpy.sphere.Lebedev(19) as read from file</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_wallace_tensor">
<span class="sig-name descname"><span class="pre">get_wallace_tensor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">tau</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L780-L797"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_wallace_tensor" title="Link to this definition"></a></dt>
<dd><p>Get the Wallace Tensor for determining yield strength
criteria.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>tau</strong> (<em>3x3 array-like</em>) – stress at which to evaluate
the wallace tensor</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_yield_stress">
<span class="sig-name descname"><span class="pre">get_yield_stress</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L826-L836"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.get_yield_stress" title="Link to this definition"></a></dt>
<dd><p>Get the yield stress for a given direction.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>n</strong> (<em>3x1 array-like</em>) – direction for which to find the
yield stress</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.omega">
<span class="sig-name descname"><span class="pre">omega</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">n</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L679-L695"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.omega" title="Link to this definition"></a></dt>
<dd><p>Find directional frequency contribution to the heat
capacity from direction and polarization.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Structure to be used in directional heat
capacity determination</p></li>
<li><p><strong>n</strong> (<em>3x1 array-like</em>) – direction for Cv determination</p></li>
<li><p><strong>u</strong> (<em>3x1 array-like</em>) – polarization direction, note that
no attempt for verification of eigenvectors is made</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.order">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">order</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">int</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.order" title="Link to this definition"></a></dt>
<dd><p>Order of the elastic tensor expansion, i.e. the order of the
highest included set of elastic constants.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.thermal_expansion_coeff">
<span class="sig-name descname"><span class="pre">thermal_expansion_coeff</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">temperature</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Literal</span><span class="p"><span class="pre">[</span></span><span class="s"><span class="pre">'dulong</span> <span class="pre">-</span> <span class="pre">petit'</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="s"><span class="pre">'debye'</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'debye'</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L697-L731"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.ElasticTensorExpansion.thermal_expansion_coeff" title="Link to this definition"></a></dt>
<dd><p>Get thermal expansion coefficient from third-order constants.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – Temperature in kelvin, if not specified
will return non-cv-normalized value</p></li>
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Structure to be used in directional heat
capacity determination, only necessary if temperature
is specified</p></li>
<li><p><strong>mode</strong> (<em>str</em>) – mode for finding average heat-capacity,
current supported modes are ‘debye’ and ‘dulong-petit’</p></li>
</ul>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NthOrderElasticTensor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">input_array</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">check_rank</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.0001</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L46-L113"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="pymatgen.core.html#pymatgen.core.tensors.Tensor" title="pymatgen.core.tensors.Tensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">Tensor</span></code></a></p>
<p>An object representing an nth-order tensor expansion
of the stress-strain constitutive equations.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input_array</strong> (<em>np.ndarray</em>) – input array for tensor</p></li>
<li><p><strong>check_rank</strong> (<em>int</em>) – rank of tensor to check</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance for initial symmetry test of tensor</p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.GPa_to_eV_A3">
<span class="sig-name descname"><span class="pre">GPa_to_eV_A3</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">0.006241509074460764</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.GPa_to_eV_A3" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.calculate_stress">
<span class="sig-name descname"><span class="pre">calculate_stress</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strain</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L74-L88"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.calculate_stress" title="Link to this definition"></a></dt>
<dd><p>Calculate’s a given elastic tensor’s contribution to the
stress using Einstein summation.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>strain</strong> (<em>3x3 array-like</em>) – matrix corresponding to strain</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.energy_density">
<span class="sig-name descname"><span class="pre">energy_density</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strain</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">convert_GPa_to_eV</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L90-L95"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.energy_density" title="Link to this definition"></a></dt>
<dd><p>Calculate the elastic energy density due to a strain.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.from_diff_fit">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_diff_fit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strains</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stresses</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eq_stress</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-10</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L97-L113"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.from_diff_fit" title="Link to this definition"></a></dt>
<dd><p>Takes a list of strains and stresses, and returns a list of coefficients for a
polynomial fit of the given order.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strains</strong> – a list of strain values</p></li>
<li><p><strong>stresses</strong> – the stress values</p></li>
<li><p><strong>eq_stress</strong> – The stress at which the material is assumed to be elastic.</p></li>
<li><p><strong>order</strong> – The order of the polynomial to fit. Defaults to 2</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance for the fit.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>the fitted elastic tensor</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor" title="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor">NthOrderElasticTensor</a></p>
</dd>
</dl>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.order">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">order</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.order" title="Link to this definition"></a></dt>
<dd><p>Order of the elastic tensor.</p>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.symbol">
<span class="sig-name descname"><span class="pre">symbol</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">'C'</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/elastic.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.NthOrderElasticTensor.symbol" title="Link to this definition"></a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.diff_fit">
<span class="sig-name descname"><span class="pre">diff_fit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strains</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stresses</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eq_stress</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-10</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L840-L897"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.diff_fit" title="Link to this definition"></a></dt>
<dd><p>nth order elastic constant fitting function based on
central-difference derivatives with respect to distinct
strain states. The algorithm is summarized as follows:</p>
<ol class="arabic simple">
<li><p>Identify distinct strain states as sets of indices
for which nonzero strain values exist, typically
[(0), (1), (2), (3), (4), (5), (0, 1) etc.]</p></li>
<li><p>For each strain state, find and sort strains and
stresses by strain value.</p></li>
<li><p>Find first, second .. nth derivatives of each stress
with respect to scalar variable corresponding to
the smallest perturbation in the strain.</p></li>
<li><p>Use the pseudo-inverse of a matrix-vector expression
corresponding to the parameterized stress-strain
relationship and multiply that matrix by the respective
calculated first or second derivatives from the
previous step.</p></li>
<li><p>Place the calculated nth-order elastic
constants appropriately.</p></li>
</ol>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>order</strong> (<em>int</em>) – order of the elastic tensor set to return</p></li>
<li><p><strong>strains</strong> (<em>nx3x3 array-like</em>) – Array of 3x3 strains
to use in fitting of ECs</p></li>
<li><p><strong>stresses</strong> (<em>nx3x3 array-like</em>) – Array of 3x3 stresses
to use in fitting ECs. These should be PK2 stresses.</p></li>
<li><p><strong>eq_stress</strong> (<em>3x3 array-like</em>) – stress corresponding to
equilibrium strain (i.e. “0” strain state).
If not specified, function will try to find
the state in the list of provided stresses
and strains. If not found, defaults to 0.</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – value for which strains below
are ignored in identifying strain states.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Set of tensors corresponding to nth order expansion of
the stress/strain relation</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.find_eq_stress">
<span class="sig-name descname"><span class="pre">find_eq_stress</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strains</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stresses</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-10</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L900-L924"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.find_eq_stress" title="Link to this definition"></a></dt>
<dd><p>Find stress corresponding to zero strain state in stress-strain list.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strains</strong> (<em>Nx3x3 array-like</em>) – array corresponding to strains</p></li>
<li><p><strong>stresses</strong> (<em>Nx3x3 array-like</em>) – array corresponding to stresses</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance to find zero strain state</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.generate_pseudo">
<span class="sig-name descname"><span class="pre">generate_pseudo</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strain_states</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L982-L1017"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.generate_pseudo" title="Link to this definition"></a></dt>
<dd><p>Generate the pseudo-inverse for a given set of strains.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strain_states</strong> (<em>6xN array like</em>) – a list of Voigt-notation strain-states,
i.e. perturbed indices of the strain as a function of the smallest
strain e.g. (0, 1, 0, 0, 1, 0)</p></li>
<li><p><strong>order</strong> (<em>int</em>) – order of pseudo-inverse to calculate</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><dl class="simple">
<dt>for each order tensor, these can be multiplied by the central</dt><dd><p>difference derivative of the stress with respect to the strain state</p>
</dd>
</dl>
<p>absent_syms: symbols of the tensor absent from the PI expression</p>
</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>pseudo_inverses</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.get_diff_coeff">
<span class="sig-name descname"><span class="pre">get_diff_coeff</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">hvec</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L1064-L1079"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.get_diff_coeff" title="Link to this definition"></a></dt>
<dd><p>Helper function to find difference coefficients of an
derivative on an arbitrary mesh.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>hvec</strong> (<em>1D array-like</em>) – sampling stencil</p></li>
<li><p><strong>n</strong> (<em>int</em>) – degree of derivative to find</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.get_strain_state_dict">
<span class="sig-name descname"><span class="pre">get_strain_state_dict</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strains</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stresses</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eq_stress</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">add_eq</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sort</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L927-L979"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.get_strain_state_dict" title="Link to this definition"></a></dt>
<dd><p>Create a dictionary of voigt notation stress-strain sets
keyed by “strain state”, i.e. a tuple corresponding to
the non-zero entries in ratios to the lowest nonzero value,
e.g. [0, 0.1, 0, 0.2, 0, 0] -> (0,1,0,2,0,0)
This allows strains to be collected in stencils as to
evaluate parameterized finite difference derivatives.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strains</strong> (<em>Nx3x3 array-like</em>) – strain matrices</p></li>
<li><p><strong>stresses</strong> (<em>Nx3x3 array-like</em>) – stress matrices</p></li>
<li><p><strong>eq_stress</strong> (<em>Nx3x3 array-like</em>) – equilibrium stress</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance for sorting strain states</p></li>
<li><p><strong>add_eq</strong> (<em>bool</em>) – Whether to add eq_strain to stress-strain sets for each strain state.
Defaults to True.</p></li>
<li><p><strong>sort</strong> (<em>bool</em>) – flag for whether to sort strain states</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>strain state keys and dictionaries with stress-strain data corresponding to strain state</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dict</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.get_symbol_list">
<span class="sig-name descname"><span class="pre">get_symbol_list</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rank</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">6</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L1020-L1041"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.get_symbol_list" title="Link to this definition"></a></dt>
<dd><p>Get a symbolic representation of the Voigt-notation
tensor that places identical symbols for entries related
by index transposition, i.e. C_1121 = C_1211 etc.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>dim</strong> (<em>int</em>) – dimension of matrix/tensor, e.g. 6 for
voigt notation and 3 for standard</p></li>
<li><p><strong>rank</strong> (<em>int</em>) – rank of tensor, e.g. 3 for third-order ECs</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><dl class="simple">
<dt>tuple of arrays representing the distinct</dt><dd><p>indices and the tensor with equivalent indices assigned as above</p>
</dd>
</dl>
</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>tuple[np.array, np.array]</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.raise_if_unphysical">
<span class="sig-name descname"><span class="pre">raise_if_unphysical</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">func</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L116-L127"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.raise_if_unphysical" title="Link to this definition"></a></dt>
<dd><p>Wrapper for functions or properties that should raise an error
if tensor is unphysical.</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.elastic.subs">
<span class="sig-name descname"><span class="pre">subs</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">entry</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cmap</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/elastic.py#L1044-L1056"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.elastic.subs" title="Link to this definition"></a></dt>
<dd><p>Sympy substitution function, primarily for the purposes
of numpy vectorization.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>entry</strong> (<em>symbol</em><em> or </em><em>exp</em>) – sympy expr to undergo subs</p></li>
<li><p><strong>cmap</strong> (<em>dict</em>) – map for symbols to values to use in subs</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Evaluated expression with substitution</p>
</dd>
</dl>
</dd></dl>
</section>
<section id="module-pymatgen.analysis.elasticity.strain">
<span id="pymatgen-analysis-elasticity-strain-module"></span><h2>pymatgen.analysis.elasticity.strain module<a class="headerlink" href="#module-pymatgen.analysis.elasticity.strain" title="Link to this heading"></a></h2>
<p>This module provides classes and methods used to describe deformations and
strains, including applying those deformations to structure objects and
generating deformed structure sets for further calculations.</p>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Deformation">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Deformation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">deformation_gradient</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L38-L97"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Deformation" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="pymatgen.core.html#pymatgen.core.tensors.SquareTensor" title="pymatgen.core.tensors.SquareTensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareTensor</span></code></a></p>
<p>Subclass of SquareTensor that describes the deformation gradient tensor.</p>
<p>Create a Deformation object. Note that the constructor uses __new__ rather than
__init__ according to the standard method of subclassing numpy arrays.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>deformation_gradient</strong> (<em>3x3 array-like</em>) – the 3x3 array-like
representing the deformation gradient</p>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Deformation.apply_to_structure">
<span class="sig-name descname"><span class="pre">apply_to_structure</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L70-L82"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Deformation.apply_to_structure" title="Link to this definition"></a></dt>
<dd><p>Apply the deformation gradient to a structure.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>structure</strong> (<em>Structure object</em>) – the structure object to
be modified by the deformation</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Deformation.from_index_amount">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_index_amount</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">matrix_pos</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">amt</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L84-L97"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Deformation.from_index_amount" title="Link to this definition"></a></dt>
<dd><p>Factory method for constructing a Deformation object
from a matrix position and amount.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>matrix_pos</strong> (<em>tuple</em>) – tuple corresponding the matrix position to
have a perturbation added</p></li>
<li><p><strong>amt</strong> (<em>float</em>) – amount to add to the identity matrix at position
matrix_pos</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Deformation.get_perturbed_indices">
<span class="sig-name descname"><span class="pre">get_perturbed_indices</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-08</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L59-L63"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Deformation.get_perturbed_indices" title="Link to this definition"></a></dt>
<dd><p>Get indices of perturbed elements of the deformation gradient,
i.e. those that differ from the identity.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Deformation.green_lagrange_strain">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">green_lagrange_strain</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/strain.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Deformation.green_lagrange_strain" title="Link to this definition"></a></dt>
<dd><p>Calculate the Euler-Lagrange strain from the deformation gradient.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Deformation.is_independent">
<span class="sig-name descname"><span class="pre">is_independent</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-08</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L55-L57"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Deformation.is_independent" title="Link to this definition"></a></dt>
<dd><p>Check to determine whether the deformation is independent.</p>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Deformation.symbol">
<span class="sig-name descname"><span class="pre">symbol</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">'d'</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/strain.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Deformation.symbol" title="Link to this definition"></a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.DeformedStructureSet">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DeformedStructureSet</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm_strains</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">(-0.01,</span> <span class="pre">-0.005,</span> <span class="pre">0.005,</span> <span class="pre">0.01)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shear_strains</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">(-0.06,</span> <span class="pre">-0.03,</span> <span class="pre">0.03,</span> <span class="pre">0.06)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">symmetry</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L100-L153"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.DeformedStructureSet" title="Link to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></p>
<p>class that generates a set of independently deformed structures that
can be used to calculate linear stress-strain response.</p>
<p>Construct the deformed geometries of a structure. Generates m + n deformed structures
according to the supplied parameters.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – structure to undergo deformation</p></li>
<li><p><strong>norm_strains</strong> (<em>list</em><em> of </em><em>floats</em>) – strain values to apply
to each normal mode. Defaults to (-0.01, -0.005, 0.005, 0.01).</p></li>
<li><p><strong>shear_strains</strong> (<em>list</em><em> of </em><em>floats</em>) – strain values to apply
to each shear mode. Defaults to (-0.06, -0.03, 0.03, 0.06).</p></li>
<li><p><strong>symmetry</strong> (<em>bool</em>) – whether or not to use symmetry reduction.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Strain">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Strain</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strain_matrix</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L156-L237"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Strain" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="pymatgen.core.html#pymatgen.core.tensors.SquareTensor" title="pymatgen.core.tensors.SquareTensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareTensor</span></code></a></p>
<p>Subclass of SquareTensor that describes the Green-Lagrange strain tensor.</p>
<p>Create a Strain object. Note that the constructor uses __new__
rather than __init__ according to the standard method of
subclassing numpy ndarrays. Note also that the default constructor
does not include the deformation gradient.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>strain_matrix</strong> (<em>ArrayLike</em>) – 3x3 matrix or length-6 Voigt notation vector
representing the Green-Lagrange strain</p>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Strain.from_deformation">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_deformation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">deformation</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ArrayLike</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L187-L196"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Strain.from_deformation" title="Link to this definition"></a></dt>
<dd><p>Factory method that returns a Strain object from a deformation
gradient.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>deformation</strong> (<em>ArrayLike</em>) – 3x3 array defining the deformation</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Strain.from_index_amount">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_index_amount</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">idx</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">tuple</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">amount</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L198-L219"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Strain.from_index_amount" title="Link to this definition"></a></dt>
<dd><p>Like Deformation.from_index_amount, except generates
a strain from the zero 3x3 tensor or Voigt vector with
the amount specified in the index location. Ensures
symmetric strain.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>idx</strong> (<em>tuple</em><em> or </em><em>integer</em>) – index to be perturbed, can be Voigt or full-tensor notation</p></li>
<li><p><strong>amount</strong> (<em>float</em>) – amount to perturb selected index</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Strain.get_deformation_matrix">
<span class="sig-name descname"><span class="pre">get_deformation_matrix</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Literal</span><span class="p"><span class="pre">[</span></span><span class="s"><span class="pre">'upper'</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="s"><span class="pre">'lower'</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="s"><span class="pre">'symmetric'</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'upper'</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L221-L230"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Strain.get_deformation_matrix" title="Link to this definition"></a></dt>
<dd><p>Get the deformation matrix.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>shape</strong> (<em>'upper'</em><em> | </em><em>'lower'</em><em> | </em><em>'symmetric'</em>) – method for determining deformation
‘upper’ produces an upper triangular defo
‘lower’ produces a lower triangular defo
‘symmetric’ produces a symmetric defo</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Strain.symbol">
<span class="sig-name descname"><span class="pre">symbol</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">'e'</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/strain.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Strain.symbol" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.Strain.von_mises_strain">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">von_mises_strain</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/strain.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.Strain.von_mises_strain" title="Link to this definition"></a></dt>
<dd><p>Equivalent strain to Von Mises Stress.</p>
</dd></dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.strain.convert_strain_to_deformation">
<span class="sig-name descname"><span class="pre">convert_strain_to_deformation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strain</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Literal</span><span class="p"><span class="pre">[</span></span><span class="s"><span class="pre">'upper'</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="s"><span class="pre">'lower'</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="s"><span class="pre">'symmetric'</span></span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/strain.py#L240-L260"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.strain.convert_strain_to_deformation" title="Link to this definition"></a></dt>
<dd><p>This function converts a strain to a deformation gradient that will
produce that strain. Supports three methods:</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>strain</strong> (<em>3x3 array-like</em>) – strain matrix</p></li>
<li><p><strong>shape</strong> – (‘upper’ | ‘lower’ | ‘symmetric’): method for determining deformation
‘upper’ produces an upper triangular defo
‘lower’ produces a lower triangular defo
‘symmetric’ produces a symmetric defo</p></li>
</ul>
</dd>
</dl>
</dd></dl>
</section>
<section id="module-pymatgen.analysis.elasticity.stress">
<span id="pymatgen-analysis-elasticity-stress-module"></span><h2>pymatgen.analysis.elasticity.stress module<a class="headerlink" href="#module-pymatgen.analysis.elasticity.stress" title="Link to this heading"></a></h2>
<p>This module provides the Stress class used to create, manipulate, and
calculate relevant properties of the stress tensor.</p>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.stress.Stress">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Stress</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stress_matrix</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/stress.py#L28-L101"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.stress.Stress" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="pymatgen.core.html#pymatgen.core.tensors.SquareTensor" title="pymatgen.core.tensors.SquareTensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareTensor</span></code></a></p>
<p>This class extends SquareTensor as a representation of the
stress.</p>
<p>Create a Stress object. Note that the constructor uses __new__
rather than __init__ according to the standard method of
subclassing numpy ndarrays.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>stress_matrix</strong> (<em>3x3 array-like</em>) – the 3x3 array-like
representing the stress</p>
</dd>
</dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.stress.Stress.dev_principal_invariants">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">dev_principal_invariants</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/stress.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.stress.Stress.dev_principal_invariants" title="Link to this definition"></a></dt>
<dd><p>The principal invariants of the deviatoric stress tensor,
which is calculated by finding the coefficients of the characteristic
polynomial of the stress tensor minus the identity times the mean
stress.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.stress.Stress.deviator_stress">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">deviator_stress</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/stress.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.stress.Stress.deviator_stress" title="Link to this definition"></a></dt>
<dd><p>The deviatoric component of the stress.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.stress.Stress.mean_stress">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mean_stress</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/stress.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.stress.Stress.mean_stress" title="Link to this definition"></a></dt>
<dd><p>The mean stress.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.stress.Stress.piola_kirchoff_1">
<span class="sig-name descname"><span class="pre">piola_kirchoff_1</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">def_grad</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/stress.py#L79-L89"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.stress.Stress.piola_kirchoff_1" title="Link to this definition"></a></dt>
<dd><p>Calculates the first Piola-Kirchoff stress.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>def_grad</strong> (<em>3x3 array-like</em>) – deformation gradient tensor</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.stress.Stress.piola_kirchoff_2">
<span class="sig-name descname"><span class="pre">piola_kirchoff_2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">def_grad</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../analysis/elasticity/stress.py#L91-L101"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.stress.Stress.piola_kirchoff_2" title="Link to this definition"></a></dt>
<dd><p>Calculates the second Piola-Kirchoff stress.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>def_grad</strong> (<em>3x3 array-like</em>) – rate of deformation tensor</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.stress.Stress.symbol">
<span class="sig-name descname"><span class="pre">symbol</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">'s'</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/stress.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.stress.Stress.symbol" title="Link to this definition"></a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.analysis.elasticity.stress.Stress.von_mises">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">von_mises</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/analysis/elasticity/stress.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.analysis.elasticity.stress.Stress.von_mises" title="Link to this definition"></a></dt>
<dd><p>The von Mises stress.</p>
</dd></dl>
</dd></dl>
</section>
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