import numpy as np
from damask import mechanics
class TestMechanics:
n = 1000
c = np.random.randint(n)
def test_vectorize_Cauchy(self):
P = np.random.random((self.n,3,3))
F = np.random.random((self.n,3,3))
assert np.allclose(mechanics.Cauchy(F,P)[self.c],
mechanics.Cauchy(F[self.c],P[self.c]))
def test_vectorize_strain_tensor(self):
F = np.random.random((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_vectorize_deviatoric_part(self):
x = np.random.random((self.n,3,3))
assert np.allclose(mechanics.deviatoric_part(x)[self.c],
mechanics.deviatoric_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_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_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_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_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_principal_components(self):
x = np.random.random((self.n,3,3))
assert np.allclose(mechanics.principal_components(x)[self.c],
mechanics.principal_components(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_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_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_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_Cauchy(self):
"""Ensure Cauchy stress is symmetrized 1. Piola-Kirchhoff stress for no deformation."""
P = np.random.random((self.n,3,3))
assert np.allclose(mechanics.Cauchy(np.broadcast_to(np.eye(3),(self.n,3,3)),P),
mechanics.symmetric(P))
def test_polar_decomposition(self):
"""F = RU = VR."""
F = np.broadcast_to(np.eye(3),[self.n,3,3])*np.random.random((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_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.random((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.random((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.random((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.random((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.random((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.random((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.random((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.random((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.random((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.random((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.random((self.n,3,3))
assert np.allclose(mechanics.Mises_stress(x)/mechanics.Mises_strain(x),
1.5)