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py_comparison_test_material_linear_elastic1.py
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py_comparison_test_material_linear_elastic1.py
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#!/usr/bin/env python3
# -*- coding:utf-8 -*-
"""
@file py_comparison_test_material_linear_elastic_1.py
@author Till Junge <till.junge@epfl.ch>
@date 05 Dec 2018
@brief compares MaterialLinearElastic1 to de Geus's python implementation
Copyright © 2018 Till Junge
µSpectre is free software; you can redistribute it and/or
modify it under the terms of the GNU General Lesser Public License as
published by the Free Software Foundation, either version 3, or (at
your option) any later version.
µSpectre 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
General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with µSpectre; see the file COPYING. If not, write to the
Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA.
Additional permission under GNU GPL version 3 section 7
If you modify this Program, or any covered work, by linking or combining it
with proprietary FFT implementations or numerical libraries, containing parts
covered by the terms of those libraries' licenses, the licensors of this
Program grant you additional permission to convey the resulting work.
"""
from material_linear_elastic1 import *
import itertools
import numpy as np
np.set_printoptions(linewidth=180)
import unittest
#####################
dyad22 = lambda A2,B2: np.einsum('ij ,kl ->ijkl',A2,B2)
dyad11 = lambda A1,B1: np.einsum('i ,j ->ij ',A1,B1)
dot22 = lambda A2,B2: np.einsum('ij ,jk ->ik ',A2,B2)
dot24 = lambda A2,B4: np.einsum('ij ,jkmn->ikmn',A2,B4)
dot42 = lambda A4,B2: np.einsum('ijkl,lm ->ijkm',A4,B2)
inv2 = np.linalg.inv
trans2 = np.transpose
ddot22 = lambda A2,B2: np.einsum('ij ,ji -> ',A2,B2)
ddot42 = lambda A4,B2: np.einsum('ijkl,lk ->ij ',A4,B2)
ddot44 = lambda A4,B4: np.einsum('ijkl,lkmn->ijmn',A4,B4)
class MatTest(unittest.TestCase):
def constitutive(self, F, dim):
I = np.eye(dim)
II = dyad22(I,I)
I4 = np.einsum('il,jk',I,I)
I4rt = np.einsum('ik,jl',I,I)
I4s = (I4+I4rt)/2.
C4 = self.K*II+2.*self.mu*(I4s-1./3.*II)
S = ddot42(C4,.5*(dot22(trans2(F),F)-I))
P = dot22(F,S)
K4 = dot24(S,I4)+ddot44(ddot44(I4rt,dot42(dot24(F,C4),trans2(F))),I4rt)
return P, S, K4, C4
def setUp(self):
pass
def prep(self, dimension):
self.dim=dimension
self.Young = 200e9+100*np.random.rand()
self.Poisson = .3 + .1*(np.random.rand()-.5)
self.K = self.Young/(3*(1-2*self.Poisson))
self.mu = self.Young/(2*(1+self.Poisson))
self.F = np.eye(self.dim) + (np.random.random((self.dim, self.dim))-.5)/10
self.tol = 1e-13
self.verbose=True
def test_equivalence_S_C(self):
for dim in (2, 3):
self.runner_equivalence_S_C(dim)
def runner_equivalence_S_C(self, dimension):
self.prep(dimension)
fun = PK2_fun_2d if self.dim == 2 else PK2_fun_3d
S_µ, C_µ_s = fun(self.Young, self.Poisson, self.F)
shape = (self.dim, self.dim, self.dim, self.dim)
C_µ = C_µ_s.reshape(shape).transpose((0,1,3,2))
response_p = self.constitutive(self.F, self.dim)
S_p, C_p = response_p[1], response_p[3]
S_error = np.linalg.norm(S_µ- S_p)/np.linalg.norm(S_µ)
if not S_error < self.tol:
print("Error(S) = {}".format(S_error))
print("S_µ:\n{}".format(S_µ))
print("S_p:\n{}".format(S_p))
self.assertLess(S_error,
self.tol)
C_error = np.linalg.norm(C_µ- C_p)/np.linalg.norm(C_µ)
if not C_error < self.tol:
print("Error(C) = {}".format(C_error))
flat_shape = (self.dim**2, self.dim**2)
print("C_µ:\n{}".format(C_µ.reshape(flat_shape)))
print("C_p:\n{}".format(C_p.reshape(flat_shape)))
self.assertLess(C_error,
self.tol)
def test_equivalence_P_K(self):
for dim in (2, 3):
self.runner_equivalence_P_K(dim)
def runner_equivalence_P_K(self, dimension):
self.prep(dimension)
fun = PK1_fun_2d if self.dim == 2 else PK1_fun_3d
P_µ, K_µ_s = fun(self.Young, self.Poisson, self.F)
shape = (self.dim, self.dim, self.dim, self.dim)
K_µ = K_µ_s.reshape(shape).transpose((0,1,3,2))
response_p = self.constitutive(self.F, self.dim)
P_p, K_p = response_p[0], response_p[2]
P_error = np.linalg.norm(P_µ- P_p)/np.linalg.norm(P_µ)
if not P_error < self.tol:
print("Error(P) = {}".format(P_error))
print("P_µ:\n{}".format(P_µ))
print("P_p:\n{}".format(P_p))
K_error = np.linalg.norm(K_µ- K_p)/np.linalg.norm(K_µ)
if not K_error < self.tol:
print("Error(K) = {}".format(K_error))
flat_shape = (self.dim**2, self.dim**2)
print("K_µ:\n{}".format(K_µ.reshape(flat_shape)))
print("K_p:\n{}".format(K_p.reshape(flat_shape)))
print("diff:\n{}".format(K_p.reshape(flat_shape)-
K_µ.reshape(flat_shape)))
self.assertLess(P_error,
self.tol)
self.assertLess(K_error,
self.tol)
if __name__ == "__main__":
unittest.main()

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