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simplified

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Martin Diehl 2020-04-22 08:58:43 +02:00
parent a8c6fdd9ba
commit 53b8c1c893
1 changed files with 45 additions and 96 deletions
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python/tests/test_mechanics.py
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@ -1,4 +1,6 @@
import pytest
import numpy as np import numpy as np
from damask import mechanics from damask import mechanics
class TestMechanics: class TestMechanics:
@ -7,127 +9,78 @@ class TestMechanics:
c = np.random.randint(n) c = np.random.randint(n)
def test_vectorize_Cauchy(self): @pytest.mark.parametrize('function',[mechanics.deviatoric_part,
P = np.random.random((self.n,3,3)) mechanics.eigenvalues,
F = np.random.random((self.n,3,3)) mechanics.eigenvectors,
assert np.allclose(mechanics.Cauchy(P,F)[self.c], mechanics.deviatoric_part,
mechanics.Cauchy(P[self.c],F[self.c])) 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]))
def test_vectorize_deviatoric_part(self): @pytest.mark.parametrize('function',[mechanics.Cauchy,
x = np.random.random((self.n,3,3)) mechanics.PK2,
assert np.allclose(mechanics.deviatoric_part(x)[self.c], ])
mechanics.deviatoric_part(x[self.c])) def test_vectorize_2_arg(self,function):
P = np.random.rand(self.n,3,3)
def test_vectorize_eigenvalues(self): F = np.random.rand(self.n,3,3)
x = np.random.random((self.n,3,3)) assert np.allclose(function(P,F)[self.c],function(P[self.c],F[self.c]))
assert np.allclose(mechanics.eigenvalues(x)[self.c],
mechanics.eigenvalues(x[self.c]))
def test_vectorize_eigenvectors(self):
x = np.random.random((self.n,3,3))
assert np.allclose(mechanics.eigenvectors(x)[self.c],
mechanics.eigenvectors(x[self.c]))
def test_vectorize_left_stretch(self):
x = np.random.random((self.n,3,3))
assert np.allclose(mechanics.left_stretch(x)[self.c],
mechanics.left_stretch(x[self.c]))
def test_vectorize_maximum_shear(self):
x = np.random.random((self.n,3,3))
assert np.allclose(mechanics.maximum_shear(x)[self.c],
mechanics.maximum_shear(x[self.c]))
def test_vectorize_Mises_strain(self):
epsilon = np.random.random((self.n,3,3))
assert np.allclose(mechanics.Mises_strain(epsilon)[self.c],
mechanics.Mises_strain(epsilon[self.c]))
def test_vectorize_Mises_stress(self):
sigma = np.random.random((self.n,3,3))
assert np.allclose(mechanics.Mises_stress(sigma)[self.c],
mechanics.Mises_stress(sigma[self.c]))
def test_vectorize_PK2(self):
F = np.random.random((self.n,3,3))
P = np.random.random((self.n,3,3))
assert np.allclose(mechanics.PK2(P,F)[self.c],
mechanics.PK2(P[self.c],F[self.c]))
def test_vectorize_right_stretch(self):
x = np.random.random((self.n,3,3))
assert np.allclose(mechanics.right_stretch(x)[self.c],
mechanics.right_stretch(x[self.c]))
def test_vectorize_rotational_part(self):
x = np.random.random((self.n,3,3))
assert np.allclose(mechanics.rotational_part(x)[self.c],
mechanics.rotational_part(x[self.c]))
def test_vectorize_spherical_part(self):
x = np.random.random((self.n,3,3))
assert np.allclose(mechanics.spherical_part(x,True)[self.c],
mechanics.spherical_part(x[self.c],True))
def test_vectorize_strain_tensor(self): def test_vectorize_strain_tensor(self):
F = np.random.random((self.n,3,3)) F = np.random.rand(self.n,3,3)
t = ['V','U'][np.random.randint(0,2)] t = ['V','U'][np.random.randint(0,2)]
m = np.random.random()*10. -5.0 m = np.random.random()*10. -5.0
assert np.allclose(mechanics.strain_tensor(F,t,m)[self.c], assert np.allclose(mechanics.strain_tensor(F,t,m)[self.c],
mechanics.strain_tensor(F[self.c],t,m)) mechanics.strain_tensor(F[self.c],t,m))
def test_vectorize_symmetric(self):
x = np.random.random((self.n,3,3))
assert np.allclose(mechanics.symmetric(x)[self.c],
mechanics.symmetric(x[self.c]))
def test_vectorize_transpose(self):
x = np.random.random((self.n,3,3))
assert np.allclose(mechanics.transpose(x)[self.c],
mechanics.transpose(x[self.c]))
def test_Cauchy(self): def test_Cauchy(self):
"""Ensure Cauchy stress is symmetrized 1. Piola-Kirchhoff stress for no deformation.""" """Ensure Cauchy stress is symmetrized 1. Piola-Kirchhoff stress for no deformation."""
P = np.random.random((self.n,3,3)) P = np.random.rand(self.n,3,3)
assert np.allclose(mechanics.Cauchy(P,np.broadcast_to(np.eye(3),(self.n,3,3))), assert np.allclose(mechanics.Cauchy(P,np.broadcast_to(np.eye(3),(self.n,3,3))),
mechanics.symmetric(P)) mechanics.symmetric(P))
def test_polar_decomposition(self): def test_polar_decomposition(self):
"""F = RU = VR.""" """F = RU = VR."""
F = np.broadcast_to(np.eye(3),[self.n,3,3])*np.random.random((self.n,3,3)) F = np.broadcast_to(np.eye(3),[self.n,3,3])*np.random.rand(self.n,3,3)
R = mechanics.rotational_part(F) R = mechanics.rotational_part(F)
V = mechanics.left_stretch(F) V = mechanics.left_stretch(F)
U = mechanics.right_stretch(F) U = mechanics.right_stretch(F)
assert np.allclose(np.matmul(R,U), assert np.allclose(np.matmul(R,U),
np.matmul(V,R)) np.matmul(V,R))
def test_PK2(self): def test_PK2(self):
"""Ensure 2. Piola-Kirchhoff stress is symmetrized 1. Piola-Kirchhoff stress for no deformation.""" """Ensure 2. Piola-Kirchhoff stress is symmetrized 1. Piola-Kirchhoff stress for no deformation."""
P = np.random.random((self.n,3,3)) P = np.random.rand(self.n,3,3)
assert np.allclose(mechanics.PK2(P,np.broadcast_to(np.eye(3),(self.n,3,3))), assert np.allclose(mechanics.PK2(P,np.broadcast_to(np.eye(3),(self.n,3,3))),
mechanics.symmetric(P)) mechanics.symmetric(P))
def test_strain_tensor_no_rotation(self): def test_strain_tensor_no_rotation(self):
"""Ensure that left and right stretch give same results for no rotation.""" """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.random((self.n,3,3)) 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 m = np.random.random()*20.0-10.0
assert np.allclose(mechanics.strain_tensor(F,'U',m), assert np.allclose(mechanics.strain_tensor(F,'U',m),
mechanics.strain_tensor(F,'V',m)) mechanics.strain_tensor(F,'V',m))
def test_strain_tensor_rotation_equivalence(self): def test_strain_tensor_rotation_equivalence(self):
"""Ensure that left and right strain differ only by a rotation.""" """Ensure that left and right strain differ only by a rotation."""
F = np.broadcast_to(np.eye(3),[self.n,3,3]) + (np.random.random((self.n,3,3))*0.5 - 0.25) 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 m = np.random.random()*5.0-2.5
assert np.allclose(np.linalg.det(mechanics.strain_tensor(F,'U',m)), assert np.allclose(np.linalg.det(mechanics.strain_tensor(F,'U',m)),
np.linalg.det(mechanics.strain_tensor(F,'V',m))) np.linalg.det(mechanics.strain_tensor(F,'V',m)))
def test_strain_tensor_rotation(self): def test_strain_tensor_rotation(self):
"""Ensure that pure rotation results in no strain.""" """Ensure that pure rotation results in no strain."""
F = mechanics.rotational_part(np.random.random((self.n,3,3))) F = mechanics.rotational_part(np.random.rand(self.n,3,3))
t = ['V','U'][np.random.randint(0,2)] t = ['V','U'][np.random.randint(0,2)]
m = np.random.random()*2.0 - 1.0 m = np.random.random()*2.0 - 1.0
assert np.allclose(mechanics.strain_tensor(F,t,m), assert np.allclose(mechanics.strain_tensor(F,t,m),
@ -139,21 +92,20 @@ class TestMechanics:
Should be +1, but random F might contain a reflection. Should be +1, but random F might contain a reflection.
""" """
x = np.random.random((self.n,3,3)) x = np.random.rand(self.n,3,3)
assert np.allclose(np.abs(np.linalg.det(mechanics.rotational_part(x))), assert np.allclose(np.abs(np.linalg.det(mechanics.rotational_part(x))),
1.0) 1.0)
def test_spherical_deviatoric_part(self): def test_spherical_deviatoric_part(self):
"""Ensure that full tensor is sum of spherical and deviatoric part.""" """Ensure that full tensor is sum of spherical and deviatoric part."""
x = np.random.random((self.n,3,3)) x = np.random.rand(self.n,3,3)
sph = mechanics.spherical_part(x,True) sph = mechanics.spherical_part(x,True)
assert np.allclose(sph + mechanics.deviatoric_part(x), assert np.allclose(sph + mechanics.deviatoric_part(x),
x) x)
def test_deviatoric_Mises(self): def test_deviatoric_Mises(self):
"""Ensure that Mises equivalent stress depends only on deviatoric part.""" """Ensure that Mises equivalent stress depends only on deviatoric part."""
x = np.random.random((self.n,3,3)) x = np.random.rand(self.n,3,3)
full = mechanics.Mises_stress(x) full = mechanics.Mises_stress(x)
dev = mechanics.Mises_stress(mechanics.deviatoric_part(x)) dev = mechanics.Mises_stress(mechanics.deviatoric_part(x))
assert np.allclose(full, assert np.allclose(full,
@ -161,7 +113,7 @@ class TestMechanics:
def test_spherical_mapping(self): def test_spherical_mapping(self):
"""Ensure that mapping to tensor is correct.""" """Ensure that mapping to tensor is correct."""
x = np.random.random((self.n,3,3)) x = np.random.rand(self.n,3,3)
tensor = mechanics.spherical_part(x,True) tensor = mechanics.spherical_part(x,True)
scalar = mechanics.spherical_part(x) scalar = mechanics.spherical_part(x)
assert np.allclose(np.linalg.det(tensor), assert np.allclose(np.linalg.det(tensor),
@ -169,35 +121,32 @@ class TestMechanics:
def test_spherical_Mises(self): def test_spherical_Mises(self):
"""Ensure that Mises equivalent strrain of spherical strain is 0.""" """Ensure that Mises equivalent strrain of spherical strain is 0."""
x = np.random.random((self.n,3,3)) x = np.random.rand(self.n,3,3)
sph = mechanics.spherical_part(x,True) sph = mechanics.spherical_part(x,True)
assert np.allclose(mechanics.Mises_strain(sph), assert np.allclose(mechanics.Mises_strain(sph),
0.0) 0.0)
def test_symmetric(self): def test_symmetric(self):
"""Ensure that a symmetric tensor is half of the sum of a tensor and its transpose.""" """Ensure that a symmetric tensor is half of the sum of a tensor and its transpose."""
x = np.random.random((self.n,3,3)) x = np.random.rand(self.n,3,3)
assert np.allclose(mechanics.symmetric(x)*2.0, assert np.allclose(mechanics.symmetric(x)*2.0,
mechanics.transpose(x)+x) mechanics.transpose(x)+x)
def test_transpose(self): def test_transpose(self):
"""Ensure that a symmetric tensor equals its transpose.""" """Ensure that a symmetric tensor equals its transpose."""
x = mechanics.symmetric(np.random.random((self.n,3,3))) x = mechanics.symmetric(np.random.rand(self.n,3,3))
assert np.allclose(mechanics.transpose(x), assert np.allclose(mechanics.transpose(x),
x) x)
def test_Mises(self): def test_Mises(self):
"""Ensure that equivalent stress is 3/2 of equivalent strain.""" """Ensure that equivalent stress is 3/2 of equivalent strain."""
x = np.random.random((self.n,3,3)) x = np.random.rand(self.n,3,3)
assert np.allclose(mechanics.Mises_stress(x)/mechanics.Mises_strain(x), assert np.allclose(mechanics.Mises_stress(x)/mechanics.Mises_strain(x),
1.5) 1.5)
def test_eigenvalues(self): def test_eigenvalues(self):
"""Ensure that the characteristic polynomial can be solved.""" """Ensure that the characteristic polynomial can be solved."""
A = mechanics.symmetric(np.random.random((self.n,3,3))) A = mechanics.symmetric(np.random.rand(self.n,3,3))
lambd = mechanics.eigenvalues(A) lambd = mechanics.eigenvalues(A)
s = np.random.randint(self.n) s = np.random.randint(self.n)
for i in range(3): for i in range(3):
@ -205,7 +154,7 @@ class TestMechanics:
def test_eigenvalues_and_vectors(self): def test_eigenvalues_and_vectors(self):
"""Ensure that eigenvalues and -vectors are the solution to the characteristic polynomial.""" """Ensure that eigenvalues and -vectors are the solution to the characteristic polynomial."""
A = mechanics.symmetric(np.random.random((self.n,3,3))) A = mechanics.symmetric(np.random.rand(self.n,3,3))
lambd = mechanics.eigenvalues(A) lambd = mechanics.eigenvalues(A)
x = mechanics.eigenvectors(A) x = mechanics.eigenvectors(A)
s = np.random.randint(self.n) s = np.random.randint(self.n)
@ -214,12 +163,12 @@ class TestMechanics:
def test_eigenvectors_RHS(self): def test_eigenvectors_RHS(self):
"""Ensure that RHS coordinate system does only change sign of determinant.""" """Ensure that RHS coordinate system does only change sign of determinant."""
A = mechanics.symmetric(np.random.random((self.n,3,3))) A = mechanics.symmetric(np.random.rand(self.n,3,3))
LRHS = np.linalg.det(mechanics.eigenvectors(A,RHS=False)) LRHS = np.linalg.det(mechanics.eigenvectors(A,RHS=False))
RHS = np.linalg.det(mechanics.eigenvectors(A,RHS=True)) RHS = np.linalg.det(mechanics.eigenvectors(A,RHS=True))
assert np.allclose(np.abs(LRHS),RHS) assert np.allclose(np.abs(LRHS),RHS)
def test_spherical_no_shear(self): def test_spherical_no_shear(self):
"""Ensure that sherical stress has max shear of 0.0.""" """Ensure that sherical stress has max shear of 0.0."""
A = mechanics.spherical_part(mechanics.symmetric(np.random.random((self.n,3,3))),True) A = mechanics.spherical_part(mechanics.symmetric(np.random.rand(self.n,3,3)),True)
assert np.allclose(mechanics.maximum_shear(A),0.0) assert np.allclose(mechanics.maximum_shear(A),0.0)