DAMASK_EICMD/python/tests/test_mechanics.py

180 lines
7.7 KiB
Python

import pytest
import numpy as np
from damask import mechanics
class TestMechanics:
n = 1000
c = np.random.randint(n)
@pytest.mark.parametrize('function',[mechanics.deviatoric_part,
mechanics.eigenvalues,
mechanics.eigenvectors,
mechanics.deviatoric_part,
mechanics.left_stretch,
mechanics.maximum_shear,
mechanics.Mises_strain,
mechanics.Mises_stress,
mechanics.right_stretch,
mechanics.rotational_part,
mechanics.spherical_part,
mechanics.symmetric,
mechanics.transpose,
])
def test_vectorize_1_arg(self,function):
epsilon = np.random.rand(self.n,3,3)
assert np.allclose(function(epsilon)[self.c],function(epsilon[self.c]))
@pytest.mark.parametrize('function',[mechanics.Cauchy,
mechanics.PK2,
])
def test_vectorize_2_arg(self,function):
P = np.random.rand(self.n,3,3)
F = np.random.rand(self.n,3,3)
assert np.allclose(function(P,F)[self.c],function(P[self.c],F[self.c]))
def test_vectorize_strain_tensor(self):
F = np.random.rand(self.n,3,3)
t = ['V','U'][np.random.randint(0,2)]
m = np.random.random()*10. -5.0
assert np.allclose(mechanics.strain_tensor(F,t,m)[self.c],
mechanics.strain_tensor(F[self.c],t,m))
def test_Cauchy(self):
"""Ensure Cauchy stress is symmetrized 1. Piola-Kirchhoff stress for no deformation."""
P = np.random.rand(self.n,3,3)
assert np.allclose(mechanics.Cauchy(P,np.broadcast_to(np.eye(3),(self.n,3,3))),
mechanics.symmetric(P))
def test_deviatoric_part(self):
I_n = np.broadcast_to(np.eye(3),(self.n,3,3))
r = np.logical_not(I_n)*np.random.rand(self.n,3,3)
assert np.allclose(mechanics.deviatoric_part(I_n+r),r)
def test_polar_decomposition(self):
"""F = RU = VR."""
F = np.broadcast_to(np.eye(3),[self.n,3,3])*np.random.rand(self.n,3,3)
R = mechanics.rotational_part(F)
V = mechanics.left_stretch(F)
U = mechanics.right_stretch(F)
assert np.allclose(np.matmul(R,U),
np.matmul(V,R))
def test_PK2(self):
"""Ensure 2. Piola-Kirchhoff stress is symmetrized 1. Piola-Kirchhoff stress for no deformation."""
P = np.random.rand(self.n,3,3)
assert np.allclose(mechanics.PK2(P,np.broadcast_to(np.eye(3),(self.n,3,3))),
mechanics.symmetric(P))
def test_strain_tensor_no_rotation(self):
"""Ensure that left and right stretch give same results for no rotation."""
F = np.broadcast_to(np.eye(3),[self.n,3,3])*np.random.rand(self.n,3,3)
m = np.random.random()*20.0-10.0
assert np.allclose(mechanics.strain_tensor(F,'U',m),
mechanics.strain_tensor(F,'V',m))
def test_strain_tensor_rotation_equivalence(self):
"""Ensure that left and right strain differ only by a rotation."""
F = np.broadcast_to(np.eye(3),[self.n,3,3]) + (np.random.rand(self.n,3,3)*0.5 - 0.25)
m = np.random.random()*5.0-2.5
assert np.allclose(np.linalg.det(mechanics.strain_tensor(F,'U',m)),
np.linalg.det(mechanics.strain_tensor(F,'V',m)))
def test_strain_tensor_rotation(self):
"""Ensure that pure rotation results in no strain."""
F = mechanics.rotational_part(np.random.rand(self.n,3,3))
t = ['V','U'][np.random.randint(0,2)]
m = np.random.random()*2.0 - 1.0
assert np.allclose(mechanics.strain_tensor(F,t,m),
0.0)
def test_rotation_determinant(self):
"""
Ensure that the determinant of the rotational part is +- 1.
Should be +1, but random F might contain a reflection.
"""
x = np.random.rand(self.n,3,3)
assert np.allclose(np.abs(np.linalg.det(mechanics.rotational_part(x))),
1.0)
def test_spherical_deviatoric_part(self):
"""Ensure that full tensor is sum of spherical and deviatoric part."""
x = np.random.rand(self.n,3,3)
sph = mechanics.spherical_part(x,True)
assert np.allclose(sph + mechanics.deviatoric_part(x),
x)
def test_deviatoric_Mises(self):
"""Ensure that Mises equivalent stress depends only on deviatoric part."""
x = np.random.rand(self.n,3,3)
full = mechanics.Mises_stress(x)
dev = mechanics.Mises_stress(mechanics.deviatoric_part(x))
assert np.allclose(full,
dev)
def test_spherical_mapping(self):
"""Ensure that mapping to tensor is correct."""
x = np.random.rand(self.n,3,3)
tensor = mechanics.spherical_part(x,True)
scalar = mechanics.spherical_part(x)
assert np.allclose(np.linalg.det(tensor),
scalar**3.0)
def test_spherical_Mises(self):
"""Ensure that Mises equivalent strrain of spherical strain is 0."""
x = np.random.rand(self.n,3,3)
sph = mechanics.spherical_part(x,True)
assert np.allclose(mechanics.Mises_strain(sph),
0.0)
def test_symmetric(self):
"""Ensure that a symmetric tensor is half of the sum of a tensor and its transpose."""
x = np.random.rand(self.n,3,3)
assert np.allclose(mechanics.symmetric(x)*2.0,
mechanics.transpose(x)+x)
def test_transpose(self):
"""Ensure that a symmetric tensor equals its transpose."""
x = mechanics.symmetric(np.random.rand(self.n,3,3))
assert np.allclose(mechanics.transpose(x),
x)
def test_Mises(self):
"""Ensure that equivalent stress is 3/2 of equivalent strain."""
x = np.random.rand(self.n,3,3)
assert np.allclose(mechanics.Mises_stress(x)/mechanics.Mises_strain(x),
1.5)
def test_eigenvalues(self):
"""Ensure that the characteristic polynomial can be solved."""
A = mechanics.symmetric(np.random.rand(self.n,3,3))
lambd = mechanics.eigenvalues(A)
s = np.random.randint(self.n)
for i in range(3):
assert np.allclose(np.linalg.det(A[s]-lambd[s,i]*np.eye(3)),.0)
def test_eigenvalues_and_vectors(self):
"""Ensure that eigenvalues and -vectors are the solution to the characteristic polynomial."""
A = mechanics.symmetric(np.random.rand(self.n,3,3))
lambd = mechanics.eigenvalues(A)
x = mechanics.eigenvectors(A)
s = np.random.randint(self.n)
for i in range(3):
assert np.allclose(np.dot(A[s]-lambd[s,i]*np.eye(3),x[s,:,i]),.0)
def test_eigenvectors_RHS(self):
"""Ensure that RHS coordinate system does only change sign of determinant."""
A = mechanics.symmetric(np.random.rand(self.n,3,3))
LRHS = np.linalg.det(mechanics.eigenvectors(A,RHS=False))
RHS = np.linalg.det(mechanics.eigenvectors(A,RHS=True))
assert np.allclose(np.abs(LRHS),RHS)
def test_spherical_no_shear(self):
"""Ensure that sherical stress has max shear of 0.0."""
A = mechanics.spherical_part(mechanics.symmetric(np.random.rand(self.n,3,3)),True)
assert np.allclose(mechanics.maximum_shear(A),0.0)