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#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Python GetFEM++ interface
#
# Copyright (C) 2016-2020 Yves Renard, Farshid Dabaghi.
#
# This file is a part of GetFEM++
#
# GetFEM++ is free software; you can redistribute it and/or modify it
# under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation; either version 2.1 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
# License for more details.
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
#
############################################################################
""" This program performs a test for several implementations of
small strain isotropic plasticity in GetFEM++
$Id: test_small_strain_plasticity.py 5189 2015-12-15 10:24:07Z renard $
"""
import os
import sys
import matplotlib.pyplot as plt
import numpy as np
import getfem as gf
option = 3 # 1 : without hardening, im_data and plastic multiplier
# 2 : without hardening, with im_data and plastic multiplier
# 3 : with kinematic and isotropic hardening,
# with plastic multiplier
# 4 : with kinematic and isotropic hardening, with im_data,
# without plastic multiplier
# 5 : Souza-Auricchio model with plastic multiplier (not working)
load_type = 1 # 1 : vertical
# 2 : horizontal
constraint_at_np1 = False
trapezoidal = False # Trapezoidal or generalized mid-point (for option 2
# only for the moment ..., except when using the predefined
# brick : always the generalized trapezoidal rule)
bi_material = False
test_tangent_matrix = False
do_export = 2 # 0 : no export,
# 1 : export_solution only,
# 2 : export for graphical post-treatment.
use_small_strain_pl_brick = True; # Use the (new) small strain plasticity brick
resultspath = './exported_solutions'
# Physical parameters
lambda_top = 84605. # Iron
mu_top = 77839. # Iron
lambda_bottom = 121150. # Steel
mu_bottom = 80769. # Steel
sigma_y_top = 8000.
sigma_y_bottom = 7000.
Hk = mu_top/5.; Hi = Hk; # Kinematic and isotropic hardening parameters
# Numerical parameters
T = 10.
NT = 40
LX = 40.
LY = 20.
NX = 40
theta = 0.5; # Parameter for the generalized mid point scheme.
order = 2;
# Arguments from the command line if any
for i in range(1,len(sys.argv)):
a = sys.argv[i]
if (a[0:7] == 'option='):
option = int(a[7:]); print 'option set to %d from argv' % option; continue
if (a[0:10] == 'load_type='):
load_type = int(a[10:]); print 'load_type set to %d from argv' % load_type
continue
if (a[0:3] == 'NX='):
NX = int(a[3:]); print 'NX set to %d from argv' % NX; continue
if (a[0:3] == 'NT='):
NT = int(a[3:]); print 'NT set to %d from argv' % NT; continue
if (a[0:6] == 'order='):
order = int(a[6:]); print 'order set to %d from argv' % order; continue
if (a[0:3] == 'Hk='):
Hk = float(a[3:]); print 'Hk set to %g from argv' % Hk; continue
if (a[0:3] == 'Hi='):
Hi = float(a[3:]); print 'Hi set to %g from argv' % Hi; continue
if (a[0:6] == 'theta='):
theta = float(a[6:]); print 'theta set to %g from argv' % theta; continue
if (a[0:12] == 'resultspath='):
resultspath=a[12:]; print 'resultspath set to %s from argv' % resultspath
continue
if (a[0:10] == 'do_export='):
do_export=int(a[10:]); print 'do_export set to %s from argv' % do_export
continue
print "Unknow argument '%s' from the command line, exiting" % a; exit(1);
NY = int(np.ceil(NX * LY / (2 * LX))*2)
DT = T/NT
gf.util('trace_level', 1);
if (do_export >= 2):
if (not os.path.exists(resultspath)):
os.makedirs(resultspath)
print('You can vizualize the optimization steps by launching')
print('mayavi2 -d %s/von_mises_1.vtk -f WarpVector -m Surface' %resultspath)
print('mayavi2 -d %s/plast_1.vtk -f WarpVector -m Surface' % resultspath)
if (load_type == 2 and option < 3):
print('Will not work with this load : will break the body')
exit(1)
if (load_type == 1):
f = np.array([0., -1150.]);
t = np.sin(2*np.pi*(np.arange(0, T+DT/2, DT))/20.);
else:
f = np.array([15000., 0.]);
t = np.sin(2*np.pi*(np.arange(0, T+DT/2, DT))/10.) + 0.1;
# Create the mesh
# m = gfMesh('triangles grid', [0:(LX/NX):LX], [0:(LY/NY):LY])
m = gf.Mesh('import','structured',
'GT="GT_PK(2,1)";SIZES=[%d,%d];NOISED=0;NSUBDIV=[%d,%d];'
% (LX, LY, NX, NY))
N = m.dim()
# Define used MeshIm
mim=gf.MeshIm(m, gf.Integ('IM_TRIANGLE(6)'))
# Define used MeshFem
mf_u=gf.MeshFem(m,2)
mf_u.set_fem(gf.Fem('FEM_PK(2,%d)' % order))
if (option == 1):
mf_sigma=gf.MeshFem(m,2,2)
mf_sigma.set_fem(gf.Fem('FEM_PK_DISCONTINUOUS(2,1)'))
# mf_xi = gf.MeshFem(m); mf_xi.set_fem(gf.Fem('FEM_PK(2,2)'));
mf_xi = gf.MeshFem(m); mf_xi.set_fem(gf.Fem('FEM_PK_DISCONTINUOUS(2,1)'))
mf_data=gf.MeshFem(m); mf_data.set_fem(gf.Fem('FEM_PK_DISCONTINUOUS(2,0)'))
mf_vm = gf.MeshFem(m); mf_vm.set_fem(gf.Fem('FEM_PK_DISCONTINUOUS(2,1)'))
# Find the boundary of the domain
P=m.pts()
pidleft=np.compress((abs(P[0,:])<1e-6), range(0, m.nbpts()))
pidright=np.compress((abs(P[0,:] - LX)<1e-6), range(0, m.nbpts()))
fleft = m.faces_from_pid(pidleft)
fright = m.faces_from_pid(pidright)
m.set_region(1, fleft)
m.set_region(2, fright)
# Decompose the mesh into two regions with different Lame coefficients
if (bi_material):
separation = LY/2.
else:
separation = 0
pidtop = np.compress((abs(P[1,:])>=separation-1E-6), range(0, m.nbpts()))
pidbottom = np.compress((abs(P[1,:])<=separation+1E-6), range(0, m.nbpts()))
cvidtop = m.cvid_from_pid(pidtop)
cvidbottom = m.cvid_from_pid(pidbottom)
CVtop = (mf_data.basic_dof_from_cvid(cvidtop))[0]
CVbottom = (mf_data.basic_dof_from_cvid(cvidbottom))[0]
# Definition of Lame coeff
cmu = np.zeros(mf_data.nbdof()); clambda = cmu.copy()
sigma_y = cmu.copy()
for i in CVbottom:
clambda[i] = lambda_bottom
cmu[i] = mu_bottom
sigma_y[i] = sigma_y_bottom
for i in CVtop:
clambda[i] = lambda_top
cmu[i] = mu_top
sigma_y[i] = sigma_y_top
# Create the model
md = gf.Model('real')
md.set_time_step(DT)
md.add_fem_variable('u', mf_u)
md.add_fem_data('Previous_u', mf_u);
md.add_initialized_fem_data('lambda', mf_data, clambda)
md.add_initialized_fem_data('mu', mf_data, cmu)
if (option == 1):
md.add_initialized_fem_data('sigma_y', mf_data, sigma_y*np.sqrt(2./3.))
else:
md.add_initialized_fem_data('sigma_y', mf_data, sigma_y)
md.add_Dirichlet_condition_with_multipliers(mim, 'u', mf_u, 1)
md.add_initialized_fem_data('VolumicData', mf_data, np.zeros(N*mf_data.nbdof()))
md.add_source_term_brick(mim, 'u', 'VolumicData', 2)
mim_data = gf.MeshImData(mim, -1, [N, N])
mim_data_scal = gf.MeshImData(mim, -1, 1)
if (option == 1):
if (use_small_strain_pl_brick):
md.add_fem_data('xi', mf_xi)
md.add_fem_data('Previous_xi', mf_xi)
md.add_initialized_data('theta', [theta])
md.add_im_data('Epn', mim_data)
md.add_small_strain_elastoplasticity_brick(mim, 'Prandtl Reuss',
'displacement only',
'u', 'xi', 'Epn', 'lambda',
'mu', 'sigma_y', 'theta',
'timestep');
else:
md.add_fem_data('sigma', mf_sigma);
md.add_elastoplasticity_brick(mim, 'VM', 'u', 'Previous_u', 'lambda', 'mu',
'sigma_y', 'sigma');
if (option == 2):
if (use_small_strain_pl_brick):
md.add_fem_variable('xi', mf_xi)
md.add_fem_data('Previous_xi', mf_xi)
md.add_initialized_data('theta', [theta])
md.add_im_data('Epn', mim_data)
md.add_small_strain_elastoplasticity_brick(mim, 'Prandtl Reuss',
'displacement and plastic multiplier',
'u', 'xi', 'Epn', 'lambda',
'mu', 'sigma_y', 'theta',
'timestep');
else:
md.add_fem_variable('xi', mf_xi)
md.add_initialized_data('theta', [theta])
md.add_initialized_data('r', [1e-8])
md.add_im_data('Epn', mim_data)
if (theta == 1.):
Etheta = '(Sym(Grad_u))';
Eptheta = '((Epn+2*mu*xi*Deviator('+Etheta+'))/(1+2*mu*xi))'
Epnp1 = Eptheta
sigma_np1 = ('(lambda*Trace(Sym(Grad_u)-'+Epnp1
+')*Id(meshdim) + 2*mu*(Sym(Grad_u)-'+Epnp1+'))')
sigma_theta = sigma_np1;
else:
En = '(Sym(Grad_Previous_u))'
Enp1 = '(Sym(Grad_u))'
Etheta = '(theta*'+Enp1+'+(1-theta)*'+En+')'
if (trapezoidal):
md.add_fem_data('Previous_xi', mf_xi)
Epnp1='((Epn+(1-theta)*2*mu*Previous_xi*(Deviator('+En+')-Epn) + 2*mu*theta*xi*Deviator('+Enp1+'))/(1+2*mu*theta*xi))'
Eptheta='(theta*'+Epnp1+'+(1-theta)*Epn)'
else:
Eptheta='((Epn+2*mu*theta*xi*Deviator('+Etheta+'))/(1+2*mu*theta*xi))'
Epnp1 = '(('+Eptheta+'-(1-theta)*Epn)/theta)'
sigma_np1 = ('(lambda*Trace(Sym(Grad_u)-'+Epnp1
+')*Id(meshdim) + 2*mu*(Sym(Grad_u)-'+Epnp1+'))')
sigma_theta = ('(lambda*Trace('+Etheta+'-'+Eptheta
+')*Id(meshdim) + 2*mu*('+Etheta+'-'+Eptheta+'))')
if (constraint_at_np1 or trapezoidal):
fbound = '(Norm(Deviator('+sigma_np1+'))-sqrt(2/3)*sigma_y)'
else:
fbound = '(Norm(Deviator('+sigma_theta+'))-sqrt(2/3)*sigma_y)'
expr = sigma_np1+':Grad_Test_u+(1/r)*(xi-pos_part(xi+r*'+fbound+'))*Test_xi'
# expr = sigma_np1+':Grad_Test_u+('+fbound+'+pos_part(-xi/r-'+fbound+
# '))*Test_xi'
md.add_nonlinear_term(mim, expr)
if (option == 3):
if (use_small_strain_pl_brick):
md.add_fem_variable('xi', mf_xi)
md.add_fem_data('Previous_xi', mf_xi)
md.add_initialized_data('theta', [theta])
md.add_im_data('Epn', mim_data)
md.add_im_data('alphan', mim_data_scal)
md.add_initialized_data('Hk', [Hk])
md.add_initialized_data('Hi', [Hi])
md.add_small_strain_elastoplasticity_brick(mim,
'Prandtl Reuss linear hardening',
'displacement and plastic multiplier',
'u', 'xi', 'Epn', 'alphan',
'lambda', 'mu', 'sigma_y',
'Hk', 'Hi', 'theta', 'timestep');
else:
md.add_fem_variable('xi', mf_xi)
md.add_initialized_data('theta', [theta])
md.add_initialized_data('r', [1e-8])
md.add_im_data('Epn', mim_data)
md.add_im_data('alphan', mim_data_scal)
md.add_initialized_data('Hk', [Hk])
md.add_initialized_data('Hi', [Hi])
if (theta == 1):
Etheta = '(Sym(Grad_u))'
Eptheta = '((Epn+2*mu*xi*Deviator('+Etheta+'))/(1+(2*mu+Hk)*xi))'
Epnp1 = Eptheta
sigma_np1 = ('(lambda*Trace(Sym(Grad_u)-'+Epnp1
+')*Id(meshdim) + 2*mu*(Sym(Grad_u)-'+Epnp1+'))')
sigma_theta = sigma_np1
alpha_theta = ('(alphan+sqrt(2/3)*xi*(Norm(2*mu*Deviator('+Etheta
+')-(2*mu+Hk)*'+Eptheta+')))')
alpha_np1 = alpha_theta
else:
Etheta = '(Sym(theta*Grad_u+(1-theta)*Grad_Previous_u))'
Eptheta = '((Epn+2*mu*theta*xi*Deviator('+Etheta+'))/(1+(2*mu+Hk)*theta*xi))'
Epnp1 = '(('+Eptheta+' - (1-theta)*Epn)/theta)'
sigma_np1 = ('(lambda*Trace(Sym(Grad_u)-'+Epnp1
+')*Id(meshdim) + 2*mu*(Sym(Grad_u)-'+Epnp1+'))')
sigma_theta = ('(lambda*Trace('+Etheta+'-'+Eptheta
+')*Id(meshdim) + 2*mu*('+Etheta+'-'+Eptheta+'))')
alpha_theta = '(alphan+sqrt(2/3)*theta*xi*(Norm(2*mu*Deviator('+Etheta+')-(2*mu+Hk)*'+Eptheta+')))'
# alpha_np1 = '(('+alpha_theta+' - (1-theta)*alphan)/theta)'
alpha_np1 = ('(alphan+sqrt(2/3)*xi*(Norm(2*mu*Deviator('+Etheta
+')-(2*mu+Hk)*'+Eptheta+')))')
# alpha_theta = '(alphan+sqrt(2/3)*Norm('+Eptheta+'-Epn))' # do not work
# alpha_np1 = '(alphan+sqrt(2/3)*Norm('+Eptheta+'-Epn)/theta)' # do not work
# fbound = ('(Norm(Deviator('+sigma_theta+')-Hk*'+Eptheta
# +') - sigma_y - Hi*'+alpha_theta+')')
if (constraint_at_np1):
fbound = ('(Norm(2*mu*Deviator(Sym(Grad_u))-(2*mu+Hk)*'+Epnp1
+') - sqrt(2/3)*(sigma_y + Hi*'+alpha_np1+'))')
else:
fbound = ('(Norm(2*mu*Deviator('+Etheta+')-(2*mu+Hk)*'+Eptheta
+') - sqrt(2/3)*(sigma_y + Hi*'+alpha_theta+'))')
expr = (sigma_np1+':Grad_Test_u + (1/r)*(xi - pos_part(xi+r*'+fbound
+'))*Test_xi')
# expr = (sigma_np1+':Grad_Test_u + ('+fbound+' + pos_part(-xi/r-'+fbound
# +'))*Test_xi')
md.add_nonlinear_term(mim, expr)
if (option == 4):
if (use_small_strain_pl_brick):
md.add_fem_data('xi', mf_xi)
md.add_fem_data('Previous_xi', mf_xi)
md.add_initialized_data('theta', [theta])
md.add_im_data('Epn', mim_data)
md.add_im_data('alphan', mim_data_scal)
md.add_initialized_data('Hk', [Hk])
md.add_initialized_data('Hi', [Hi])
md.add_small_strain_elastoplasticity_brick(mim,
'Prandtl Reuss linear hardening',
'displacement only',
'u', 'xi', 'Epn','alphan',
'lambda', 'mu', 'sigma_y',
'Hk', 'Hi', 'theta', 'timestep');
else:
md.add_initialized_data('theta', [theta])
md.add_im_data('Epn', mim_data)
md.add_im_data('alphan', mim_data_scal)
md.add_initialized_data('Hk', [Hk])
md.add_initialized_data('Hi', [Hi])
Etheta = '(Sym(theta*Grad_u+(1-theta)*Grad_Previous_u))'
Btheta = '((2*mu)*Deviator('+Etheta+')-(2*mu+Hk)*Epn)'
alpha_theta = ('(max(alphan, (sqrt(3/2)*(2*mu+Hk)*alphan+Norm('+Btheta+
') - sqrt(2/3)*sigma_y)/(sqrt(3/2)*(2*mu+Hk)'+
'+sqrt(2/3)*Hi)))')
alpha_np1 = '(('+alpha_theta+' - (1-theta)*alphan)/theta)'
Eptheta= ('(Epn+(1/(2*mu+Hk))*pos_part(1-sqrt(2/3)*(sigma_y+Hi*'
+alpha_theta+')/(Norm('+Btheta+')+1e-25))*'+Btheta+')')
Epnp1 = '(('+Eptheta+' - (1-theta)*Epn)/theta)'
sigma_np1 = ('(lambda*Trace(Sym(Grad_u)-'+Epnp1
+')*Id(meshdim) + 2*mu*(Sym(Grad_u)-'+Epnp1+'))')
sigma_theta = ('(lambda*Trace('+Etheta+'-'+Eptheta
+')*Id(meshdim) + 2*mu*('+Etheta+'-'+Eptheta+'))')
expr = sigma_np1+':Grad_Test_u'
md.add_nonlinear_term(mim, expr)
if (option == 5):
md.add_fem_variable('xi', mf_xi)
md.add_fem_variable('delta', mf_xi)
md.add_initialized_data('theta', [theta])
md.add_initialized_data('r1', [1e-8])
md.add_initialized_data('r2', [1])
md.add_im_data('Epn', mim_data)
md.add_initialized_data('c1', [0])
md.add_initialized_data('c2', [Hk])
md.add_initialized_data('c3', [0.3])
# Simplified model without c1 and for theta = 1 and delta as
# additional multiplier (not working ...)
Etheta = '(Sym(theta*Grad_u+(1-theta)*Grad_Previous_u))'
Btheta = '(Epn+theta*xi*2*mu*Deviator('+Etheta+'))'
Eptheta = '('+Btheta+'/(1+(2*mu+c2+delta)*theta*xi))'
# Eptheta = '('+Btheta+'*min(c3/(Norm(',Btheta,')+1e-5),'
# +'1/(1+2*mu*theta*xi)))')
Epnp1 = '(('+Eptheta+' - (1-theta)*Epn)/theta)'
sigma_np1 = ('(lambda*Trace(Sym(Grad_u)-'+Epnp1
+')*Id(meshdim) + 2*mu*(Sym(Grad_u)-'+Epnp1+'))')
sigma_theta = ('(lambda*Trace('+Etheta+'-'+Eptheta
+')*Id(meshdim) + 2*mu*('+Etheta+'-'+Eptheta+'))')
# fbound = ('(Norm(2*mu*Deviator('+Etheta+')-(2*mu+pos_part((Norm('+Btheta
# +')-c3)/(c3*theta*xi+1e-25)-2*mu))*'+Eptheta
# +')-sqrt(2/3)*sigma_y)')
fbound = ('(Norm(2*mu*Deviator('+Etheta+')-(2*mu+c2+delta)*'+Eptheta
+') - sqrt(2/3)*sigma_y)')
fbound_delta = '(Norm('+Eptheta+')-c3)'
# fbound = ('(Norm(2*mu*Deviator('+Etheta+')-(2*mu+c2)*'+Eptheta
# +') - sqrt(2/3)*sigma_y)')
expr = (sigma_np1+':Grad_Test_u + (1/r1)*(xi - pos_part(xi+r1*'+fbound
+'))*Test_xi-(1/r2)*(delta-pos_part(delta+r2*'+fbound_delta
+'))*Test_delta')
md.add_nonlinear_term(mim, expr)
if (False):
Etheta = '(Sym(theta*Grad_u+(1-theta)*Grad_Previous_u))'
Btheta = '(Epn+theta*xi*2*mu*Deviator('+Etheta+'))'
# Eptheta = ('(Print('+Btheta+')*min(c3/(max(Norm('+Btheta
# +'), c3/2)), pos_part(1-theta*xi*c1/(Norm('+Btheta
# +')+0.001))/(1+(2*mu+c2)*theta*xi)))')
# Eptheta = ('('+Btheta+'*min(c3/(max(Norm('+Btheta
# +'), c3/2)), 1/(1+(2*mu+c2)*theta*xi)))')
Eptheta = ('('+Btheta+'*min(c3/(Norm('+Btheta
+')+1e-10), 1/(1+(2*mu+c2)*theta*xi)))')
Epnp1 = '(('+Eptheta+' - (1-theta)*Epn)/theta)'
sigma_np1 = ('(lambda*Trace(Sym(Grad_u)-'+Epnp1
+')*Id(meshdim) + 2*mu*(Sym(Grad_u)-'+Epnp1+'))')
sigma_theta = ('(lambda*Trace('+Etheta+'-'+Eptheta
+')*Id(meshdim) + 2*mu*('+Etheta+'-'+Eptheta+'))')
# fbound = ('(Norm(2*mu*Deviator('+Etheta+')-(2*mu+c2)*'+Eptheta
# +'-max(c1, (Norm('+Btheta+')-c3)/(theta*xi+1e-25)'
# +'-(2*mu+c2)*c3)*Normalized('+Eptheta
# +'))-sqrt(2/3)*sigma_y)')
# fbound = ('(Norm(2*mu*Deviator('+Etheta+')-(2*mu+c2)*'+Eptheta
# +'-pos_part(pos_part(Norm('+Btheta
# +')/(theta*xi+1e-10)-c1)/c3-(1/(theta*xi+1e-10)+2*mu+c2))*'
# +Eptheta+') - sqrt(2/3)*sigma_y)')
fbound = ('(Norm(2*mu*Deviator('+Etheta+')-(2*mu+c2)*'+Eptheta
+'-pos_part( Norm('+Btheta
+')/(c3*(theta*xi+1e-10)) - (1/(theta*xi+1e-10)+2*mu+c2))*'
+Eptheta+') - sqrt(2/3)*sigma_y)')
# fbound = ('(Norm(2*mu*Deviator('+Etheta+')-(2*mu+c2)*'+Eptheta
# +') - sqrt(2/3)*sigma_y)')
expr = (sigma_np1+':Grad_Test_u + (1/r)*(xi - pos_part(xi+r*'+fbound
+'))*Test_xi')
# expr = (sigma_np1+':Grad_Test_u + ('+fbound+' + pos_part(-xi/r-'
# +fbound+'))*Test_xi')
md.add_nonlinear_term(mim, expr)
VM=np.zeros(mf_vm.nbdof())
sigma_fig = np.zeros(len(t))
Epsilon_u_fig = np.zeros(len(t))
for step in range(0, len(t)):
print('step %d / %d, coeff = %g' % (step, len(t)-1, t[step]))
source = mf_data.eval('[f[0]*t[step], f[1]*t[step]]', globals(), locals())
md.set_variable('VolumicData', source)
if (test_tangent_matrix):
md.test_tangent_matrix(1E-8, 10, 0.000001)
# Solve the system
md.solve('noisy', 'lsearch', 'simplest', 'alpha min', 0.4, 'max_iter', 50,
'max_res', 1e-6, 'lsolver', 'mumps')
# md.solve('noisy', 'max_iter', 80)
U = md.variable('u')
# Compute new plastic internal variables
if (option == 1):
if (use_small_strain_pl_brick):
md.small_strain_elastoplasticity_next_iter(mim, 'Prandtl Reuss',
'displacement only',
'u', 'xi', 'Epn', 'lambda',
'mu', 'sigma_y', 'theta',
'timestep');
else:
md.elastoplasticity_next_iter(mim, 'u', 'Previous_u', 'VM', 'lambda',
'mu', 'sigma_y', 'sigma')
plast = md.compute_plastic_part(mim, mf_vm, 'u', 'Previous_u', 'VM',
'lambda', 'mu', 'sigma_y',
'sigma')
# Compute Von Mises or Tresca stress
VM = md.compute_elastoplasticity_Von_Mises_or_Tresca('sigma', mf_vm,
'Von Mises')
if (option == 2):
if (use_small_strain_pl_brick):
md.small_strain_elastoplasticity_next_iter(mim, 'Prandtl Reuss',
'displacement and plastic multiplier',
'u', 'xi', 'Epn', 'lambda',
'mu', 'sigma_y', 'theta',
'timestep');
else:
NewEpn = md.interpolation(Epnp1, mim_data)
md.set_variable('Epn', NewEpn)
md.set_variable('Previous_u', U)
if (trapezoidal):
md.set_variable('Previous_xi', md.variable('xi'))
if (option == 3):
if (use_small_strain_pl_brick):
md.small_strain_elastoplasticity_next_iter
(mim,'Prandtl Reuss linear hardening',
'displacement and plastic multiplier', 'u', 'xi', 'Epn', 'alphan',
'lambda', 'mu', 'sigma_y', 'Hk', 'Hi', 'theta', 'timestep');
else:
NewEpn = md.interpolation(Epnp1, mim_data)
Newalphan = md.interpolation(alpha_np1, mim_data_scal)
md.set_variable('Epn', NewEpn)
md.set_variable('alphan', Newalphan)
md.set_variable('Previous_u', U)
if (option == 4):
if (use_small_strain_pl_brick):
md.small_strain_elastoplasticity_next_iter
(mim,'Prandtl Reuss linear hardening',
'displacement only', 'u', 'xi', 'Epn','alphan',
'lambda', 'mu', 'sigma_y', 'Hk', 'Hi', 'theta', 'timestep');
else:
NewEpn = md.interpolation(Epnp1, mim_data)
Newalphan = md.interpolation(alpha_np1, mim_data_scal)
md.set_variable('Epn', NewEpn)
md.set_variable('alphan', Newalphan)
md.set_variable('Previous_u', U)
if (option == 5):
NewEpn = md.interpolation(Epnp1, mim_data)
md.set_variable('Epn', NewEpn)
md.set_variable('Previous_u', U)
# Compute Von Mises and plastic part for graphical post-treatment
if (do_export >= 2):
if (option == 1 and not(use_small_strain_pl_brick)):
sigma1 = 'sigma';
else:
Ep ='Norm(Epn)'
sigma1 = '(lambda*Trace(Sym(Grad_u))*Id(meshdim)+2*mu*(Sym(Grad_u)-Epn))'
von_mises = 'sqrt(3/2)*Norm(Deviator('+sigma1+'))'
VM = md.local_projection(mim, von_mises, mf_vm);
plast = md.local_projection(mim, Ep, mf_vm);
sigma = md.interpolation(sigma1, mim_data);
Epsilon_u = md.interpolation('Sym(Grad_u)', mim_data);
ind_gauss_pt = 22500
if (sigma.shape[0] <= N*N*(ind_gauss_pt + 1)):
ind_gauss_pt = int(3.*sigma.shape[0] / (4*N*N))
sigma_fig[step]=sigma[N*N*ind_gauss_pt]
Epsilon_u_fig[step]=Epsilon_u[N*N*ind_gauss_pt]
if (do_export >= 1):
filename = resultspath+('/mf_%d.mf' % (step))
mf_u.save(filename, 'with_mesh')
filename = resultspath+('/U_%d.dat' % (step))
np.savetxt(filename, U)
if (do_export >= 2):
# Export Von Mises and plastic part
filename = resultspath+('/von_mises_%d.vtk' % (step))
mf_vm.export_to_vtk(filename, mf_vm, VM.reshape((len(VM))),
'Von Mises Stresses', mf_u, U, 'Displacements')
filename = resultspath+('/plast_%d.vtk' % (step))
mf_vm.export_to_vtk(filename, mf_vm, plast.reshape((len(plast))),
'Norm of plastic strain tensor', mf_u, U,
'Displacements')
# Draw the stress/strain evolution on a selected Gauss point
if (step == 0):
fig, ax = plt.subplots()
plt.show(block=False)
ax.clear()
ax.plot(Epsilon_u_fig[0:(step+1)], sigma_fig[0:(step+1)], linewidth=2)
ax.set_xlabel('Strain')
ax.set_ylabel('Stress')
ax.set_title('stress/strain evolution')
ax.axis([-0.2, 0.35, -15000, 25000])
plt.draw()
# time.sleep(1)
# plt.show()
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