diff --git a/python/tests/test_mechanics.py b/python/tests/test_mechanics.py index d0ec7219d..91e3d2d9e 100644 --- a/python/tests/test_mechanics.py +++ b/python/tests/test_mechanics.py @@ -8,219 +8,219 @@ class TestMechanics: 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])) + 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_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])) + 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_eigenvalues(self): - x = np.random.random((self.n,3,3)) - assert np.allclose(mechanics.eigenvalues(x)[self.c], - mechanics.eigenvalues(x[self.c])) + x = np.random.random((self.n,3,3)) + 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])) + 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])) + 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])) + 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])) + 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])) + 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(F,P)[self.c], - mechanics.PK2(F[self.c],P[self.c])) + F = np.random.random((self.n,3,3)) + P = np.random.random((self.n,3,3)) + assert np.allclose(mechanics.PK2(F,P)[self.c], + mechanics.PK2(F[self.c],P[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])) + 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])) + 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)) + 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): - 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)) + 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_symmetric(self): - x = np.random.random((self.n,3,3)) - assert np.allclose(mechanics.symmetric(x)[self.c], - mechanics.symmetric(x[self.c])) + 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])) + 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): - """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)) + """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)) + """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_PK2(self): - """Ensure 2. Piola-Kirchhoff stress is symmetrized 1. Piola-Kirchhoff stress for no deformation.""" - P = np.random.random((self.n,3,3)) - assert np.allclose(mechanics.PK2(np.broadcast_to(np.eye(3),(self.n,3,3)),P), - mechanics.symmetric(P)) + """Ensure 2. Piola-Kirchhoff stress is symmetrized 1. Piola-Kirchhoff stress for no deformation.""" + P = np.random.random((self.n,3,3)) + assert np.allclose(mechanics.PK2(np.broadcast_to(np.eye(3),(self.n,3,3)),P), + 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.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)) + """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))) + """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) + """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. + """ + 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) + 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) + """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) + """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) + """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) + """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) + """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) + """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) + """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) def test_eigenvalues(self): - """Ensure that the characteristic polynomial can be solved.""" - A = mechanics.symmetric(np.random.random((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) + """Ensure that the characteristic polynomial can be solved.""" + A = mechanics.symmetric(np.random.random((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.random((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) + """Ensure that eigenvalues and -vectors are the solution to the characteristic polynomial.""" + A = mechanics.symmetric(np.random.random((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.random((self.n,3,3))) - LRHS = np.linalg.det(mechanics.eigenvectors(A,RHS=False)) - RHS = np.linalg.det(mechanics.eigenvectors(A,RHS=True)) - s = np.random.randint(self.n) - assert np.allclose(np.abs(LRHS),RHS) + """Ensure that RHS coordinate system does only change sign of determinant.""" + A = mechanics.symmetric(np.random.random((self.n,3,3))) + LRHS = np.linalg.det(mechanics.eigenvectors(A,RHS=False)) + RHS = np.linalg.det(mechanics.eigenvectors(A,RHS=True)) + s = np.random.randint(self.n) + 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.random((self.n,3,3))),True) - assert np.allclose(mechanics.maximum_shear(A),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) + assert np.allclose(mechanics.maximum_shear(A),0.0)