226 lines
9.2 KiB
Python
226 lines
9.2 KiB
Python
import numpy as np
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from damask import mechanics
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class TestMechanics:
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n = 1000
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c = np.random.randint(n)
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def test_vectorize_Cauchy(self):
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P = np.random.random((self.n,3,3))
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F = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.Cauchy(F,P)[self.c],
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mechanics.Cauchy(F[self.c],P[self.c]))
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def test_vectorize_deviatoric_part(self):
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.deviatoric_part(x)[self.c],
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mechanics.deviatoric_part(x[self.c]))
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def test_vectorize_eigenvalues(self):
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.eigenvalues(x)[self.c],
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mechanics.eigenvalues(x[self.c]))
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def test_vectorize_eigenvectors(self):
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.eigenvectors(x)[self.c],
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mechanics.eigenvectors(x[self.c]))
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def test_vectorize_left_stretch(self):
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.left_stretch(x)[self.c],
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mechanics.left_stretch(x[self.c]))
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def test_vectorize_maximum_shear(self):
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.maximum_shear(x)[self.c],
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mechanics.maximum_shear(x[self.c]))
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def test_vectorize_Mises_strain(self):
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epsilon = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.Mises_strain(epsilon)[self.c],
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mechanics.Mises_strain(epsilon[self.c]))
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def test_vectorize_Mises_stress(self):
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sigma = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.Mises_stress(sigma)[self.c],
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mechanics.Mises_stress(sigma[self.c]))
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def test_vectorize_PK2(self):
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F = np.random.random((self.n,3,3))
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P = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.PK2(F,P)[self.c],
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mechanics.PK2(F[self.c],P[self.c]))
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def test_vectorize_right_stretch(self):
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.right_stretch(x)[self.c],
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mechanics.right_stretch(x[self.c]))
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def test_vectorize_rotational_part(self):
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.rotational_part(x)[self.c],
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mechanics.rotational_part(x[self.c]))
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def test_vectorize_spherical_part(self):
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.spherical_part(x,True)[self.c],
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mechanics.spherical_part(x[self.c],True))
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def test_vectorize_strain_tensor(self):
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F = np.random.random((self.n,3,3))
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t = ['V','U'][np.random.randint(0,2)]
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m = np.random.random()*10. -5.0
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assert np.allclose(mechanics.strain_tensor(F,t,m)[self.c],
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mechanics.strain_tensor(F[self.c],t,m))
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def test_vectorize_symmetric(self):
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.symmetric(x)[self.c],
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mechanics.symmetric(x[self.c]))
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def test_vectorize_transpose(self):
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.transpose(x)[self.c],
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mechanics.transpose(x[self.c]))
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def test_Cauchy(self):
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"""Ensure Cauchy stress is symmetrized 1. Piola-Kirchhoff stress for no deformation."""
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P = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.Cauchy(np.broadcast_to(np.eye(3),(self.n,3,3)),P),
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mechanics.symmetric(P))
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def test_polar_decomposition(self):
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"""F = RU = VR."""
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F = np.broadcast_to(np.eye(3),[self.n,3,3])*np.random.random((self.n,3,3))
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R = mechanics.rotational_part(F)
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V = mechanics.left_stretch(F)
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U = mechanics.right_stretch(F)
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assert np.allclose(np.matmul(R,U),
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np.matmul(V,R))
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def test_PK2(self):
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"""Ensure 2. Piola-Kirchhoff stress is symmetrized 1. Piola-Kirchhoff stress for no deformation."""
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P = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.PK2(np.broadcast_to(np.eye(3),(self.n,3,3)),P),
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mechanics.symmetric(P))
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def test_strain_tensor_no_rotation(self):
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"""Ensure that left and right stretch give same results for no rotation."""
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F = np.broadcast_to(np.eye(3),[self.n,3,3])*np.random.random((self.n,3,3))
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m = np.random.random()*20.0-10.0
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assert np.allclose(mechanics.strain_tensor(F,'U',m),
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mechanics.strain_tensor(F,'V',m))
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def test_strain_tensor_rotation_equivalence(self):
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"""Ensure that left and right strain differ only by a rotation."""
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F = np.broadcast_to(np.eye(3),[self.n,3,3]) + (np.random.random((self.n,3,3))*0.5 - 0.25)
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m = np.random.random()*5.0-2.5
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assert np.allclose(np.linalg.det(mechanics.strain_tensor(F,'U',m)),
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np.linalg.det(mechanics.strain_tensor(F,'V',m)))
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def test_strain_tensor_rotation(self):
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"""Ensure that pure rotation results in no strain."""
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F = mechanics.rotational_part(np.random.random((self.n,3,3)))
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t = ['V','U'][np.random.randint(0,2)]
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m = np.random.random()*2.0 - 1.0
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assert np.allclose(mechanics.strain_tensor(F,t,m),
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0.0)
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def test_rotation_determinant(self):
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"""
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Ensure that the determinant of the rotational part is +- 1.
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Should be +1, but random F might contain a reflection.
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"""
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x = np.random.random((self.n,3,3))
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assert np.allclose(np.abs(np.linalg.det(mechanics.rotational_part(x))),
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1.0)
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def test_spherical_deviatoric_part(self):
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"""Ensure that full tensor is sum of spherical and deviatoric part."""
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x = np.random.random((self.n,3,3))
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sph = mechanics.spherical_part(x,True)
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assert np.allclose(sph + mechanics.deviatoric_part(x),
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x)
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def test_deviatoric_Mises(self):
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"""Ensure that Mises equivalent stress depends only on deviatoric part."""
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x = np.random.random((self.n,3,3))
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full = mechanics.Mises_stress(x)
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dev = mechanics.Mises_stress(mechanics.deviatoric_part(x))
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assert np.allclose(full,
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dev)
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def test_spherical_mapping(self):
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"""Ensure that mapping to tensor is correct."""
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x = np.random.random((self.n,3,3))
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tensor = mechanics.spherical_part(x,True)
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scalar = mechanics.spherical_part(x)
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assert np.allclose(np.linalg.det(tensor),
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scalar**3.0)
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def test_spherical_Mises(self):
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"""Ensure that Mises equivalent strrain of spherical strain is 0."""
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x = np.random.random((self.n,3,3))
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sph = mechanics.spherical_part(x,True)
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assert np.allclose(mechanics.Mises_strain(sph),
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0.0)
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def test_symmetric(self):
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"""Ensure that a symmetric tensor is half of the sum of a tensor and its transpose."""
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.symmetric(x)*2.0,
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mechanics.transpose(x)+x)
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def test_transpose(self):
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"""Ensure that a symmetric tensor equals its transpose."""
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x = mechanics.symmetric(np.random.random((self.n,3,3)))
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assert np.allclose(mechanics.transpose(x),
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x)
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def test_Mises(self):
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"""Ensure that equivalent stress is 3/2 of equivalent strain."""
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x = np.random.random((self.n,3,3))
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assert np.allclose(mechanics.Mises_stress(x)/mechanics.Mises_strain(x),
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1.5)
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def test_eigenvalues(self):
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"""Ensure that the characteristic polynomial can be solved."""
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A = mechanics.symmetric(np.random.random((self.n,3,3)))
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lambd = mechanics.eigenvalues(A)
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s = np.random.randint(self.n)
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for i in range(3):
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assert np.allclose(np.linalg.det(A[s]-lambd[s,i]*np.eye(3)),.0)
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def test_eigenvalues_and_vectors(self):
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"""Ensure that eigenvalues and -vectors are the solution to the characteristic polynomial."""
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A = mechanics.symmetric(np.random.random((self.n,3,3)))
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lambd = mechanics.eigenvalues(A)
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x = mechanics.eigenvectors(A)
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s = np.random.randint(self.n)
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for i in range(3):
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assert np.allclose(np.dot(A[s]-lambd[s,i]*np.eye(3),x[s,:,i]),.0)
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def test_eigenvectors_RHS(self):
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"""Ensure that RHS coordinate system does only change sign of determinant."""
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A = mechanics.symmetric(np.random.random((self.n,3,3)))
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LRHS = np.linalg.det(mechanics.eigenvectors(A,RHS=False))
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RHS = np.linalg.det(mechanics.eigenvectors(A,RHS=True))
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assert np.allclose(np.abs(LRHS),RHS)
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def test_spherical_no_shear(self):
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"""Ensure that sherical stress has max shear of 0.0."""
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A = mechanics.spherical_part(mechanics.symmetric(np.random.random((self.n,3,3))),True)
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assert np.allclose(mechanics.maximum_shear(A),0.0)
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