1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
|
.. _use-case-chaboche:
The Chaboche mechanical model
=============================
Deterministic model
-------------------
The Chaboche mechanical law predicts the stress depending on the strain:
.. math::
\sigma = G(\epsilon,R,C,\gamma) = R + \frac{C}{\gamma} (1-\exp(-\gamma\epsilon))
where:
- :math:`\epsilon` is the strain,
- :math:`\sigma` is the stress (Pa),
- :math:`R`, :math:`C`, :math:`\gamma` are the parameters.
The variables have the following distributions and are supposed to be independent.
================ ===========================================================
Random var. Distribution
================ ===========================================================
:math:`R` Lognormal (:math:`\mu = 750` MPa, :math:`\sigma = 11` MPa)
:math:`C` Normal (:math:`\mu = 2750` MPa, :math:`\sigma = 250` MPa)
:math:`\gamma` Normal (:math:`\mu = 10`, :math:`\sigma = 2`)
:math:`\epsilon` Uniform(a=0, b=0.07).
================ ===========================================================
The model can be used in two different contexts:
- model calibration with observations where :math:`R`, :math:`C` and :math:`\gamma` are parameters,
- uncertainty propagation where :math:`R`, :math:`C` and :math:`\gamma` are random variables.
Thanks to
---------
- Antoine Dumas, Phimeca
References
----------
- J. Lemaitre and J. L. Chaboche (2002) "Mechanics of solid materials" Cambridge University Press.
API documentation
-----------------
.. currentmodule:: openturns.usecases.chaboche_model
.. autoclass:: ChabocheModel
:noindex:
Examples based on this use case
-------------------------------
.. minigallery:: openturns.usecases.chaboche_model.ChabocheModel
|
