218 lines
8.0 KiB
Python
218 lines
8.0 KiB
Python
import pytest
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import numpy as np
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from damask import tensor
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from damask import mechanics
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from damask import Rotation
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def stress_Cauchy(P,F):
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sigma = 1.0/np.linalg.det(F) * np.dot(P,F.T)
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return symmetric(sigma)
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def eigenvalues(T_sym):
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return np.linalg.eigvalsh(symmetric(T_sym))
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def maximum_shear(T_sym):
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w = eigenvalues(T_sym)
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return (w[0] - w[2])*0.5
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def equivalent_strain_Mises(epsilon):
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return equivalent_Mises(epsilon,2.0/3.0)
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def equivalent_stress_Mises(sigma):
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return equivalent_Mises(sigma,3.0/2.0)
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def stress_second_Piola_Kirchhoff(P,F):
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S = np.dot(np.linalg.inv(F),P)
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return symmetric(S)
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def rotational(T):
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return polar_decomposition(T,'R')[0]
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def strain(F,t,m):
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if t == 'V':
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B = np.matmul(F,F.T)
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w,n = np.linalg.eigh(B)
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elif t == 'U':
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C = np.matmul(F.T,F)
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w,n = np.linalg.eigh(C)
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if m > 0.0:
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eps = 1.0/(2.0*abs(m)) * (+ np.matmul(n,np.einsum('j,kj->jk',w**m,n))
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- np.eye(3))
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elif m < 0.0:
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eps = 1.0/(2.0*abs(m)) * (- np.matmul(n,np.einsum('j,kj->jk',w**m,n))
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+ np.eye(3))
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else:
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eps = np.matmul(n,np.einsum('j,kj->jk',0.5*np.log(w),n))
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return eps
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def stretch_left(T):
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return polar_decomposition(T,'V')[0]
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def stretch_right(T):
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return polar_decomposition(T,'U')[0]
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def symmetric(T):
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return (T+T.T)*0.5
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def polar_decomposition(T,requested):
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u, s, vh = np.linalg.svd(T)
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R = np.dot(u,vh)
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output = []
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if 'R' in requested:
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output.append(R)
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if 'V' in requested:
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output.append(np.dot(T,R.T))
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if 'U' in requested:
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output.append(np.dot(R.T,T))
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return tuple(output)
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def equivalent_Mises(T_sym,s):
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return np.sqrt(s*(np.sum(deviatoric(T_sym)**2.0)))
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def deviatoric(T):
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return T - np.eye(3)*np.trace(T)/3.0
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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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@pytest.mark.parametrize('vectorized,single',[(mechanics.maximum_shear, maximum_shear),
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(mechanics.equivalent_stress_Mises, equivalent_stress_Mises),
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(mechanics.equivalent_strain_Mises, equivalent_strain_Mises),
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(mechanics.stretch_left, stretch_left),
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(mechanics.stretch_right, stretch_right),
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])
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def test_vectorize_1_arg(self,vectorized,single):
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epsilon = np.random.rand(self.n,3,3)
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epsilon_vec = np.reshape(epsilon,(self.n//10,10,3,3))
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for i,v in enumerate(np.reshape(vectorized(epsilon_vec),vectorized(epsilon).shape)):
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assert np.allclose(single(epsilon[i]),v)
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def test_vectorize_rotation(self):
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epsilon = Rotation.from_random(self.n).as_matrix()
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epsilon_vec = np.reshape(epsilon,(self.n//10,10,3,3))
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for i,v in enumerate(np.reshape(mechanics.rotational(epsilon_vec).as_matrix(),
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mechanics.rotational(epsilon).as_matrix().shape)):
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assert np.allclose(rotational(epsilon[i]),v)
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@pytest.mark.parametrize('vectorized,single',[(mechanics.stress_Cauchy, stress_Cauchy),
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(mechanics.stress_second_Piola_Kirchhoff, stress_second_Piola_Kirchhoff)
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])
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def test_vectorize_2_arg(self,vectorized,single):
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P = np.random.rand(self.n,3,3)
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F = np.random.rand(self.n,3,3)
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P_vec = np.reshape(P,(self.n//10,10,3,3))
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F_vec = np.reshape(F,(self.n//10,10,3,3))
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for i,v in enumerate(np.reshape(vectorized(P_vec,F_vec),vectorized(P,F).shape)):
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assert np.allclose(single(P[i],F[i]),v)
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@pytest.mark.parametrize('vectorized,single',[(mechanics.strain,strain)])
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def test_vectorize_strain(self,vectorized,single):
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F = np.random.rand(self.n,3,3)
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F_vec = np.reshape(F,(self.n//10,10,3,3))
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t = ['V','U'][np.random.randint(0,2)]
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m = np.random.random()*10.0 -5.0
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for i,v in enumerate(np.reshape(vectorized(F_vec,t,m),vectorized(F,t,m).shape)):
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assert np.allclose(single(F[i],t,m),v)
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@pytest.mark.parametrize('function',[mechanics.stress_Cauchy,
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mechanics.stress_second_Piola_Kirchhoff,
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])
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def test_stress_measures(self,function):
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"""Ensure that all stress measures are equivalent for no deformation."""
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P = np.random.rand(self.n,3,3)
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assert np.allclose(function(P,np.broadcast_to(np.eye(3),(self.n,3,3))),tensor.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.rand(self.n,3,3)
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R = mechanics.rotational(F).as_matrix()
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V = mechanics.stretch_left(F)
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U = mechanics.stretch_right(F)
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assert np.allclose(np.matmul(R,U),
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np.matmul(V,R))
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@pytest.mark.parametrize('m',[0.0,np.random.random()*10.,np.random.random()*-10.])
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def test_strain_no_rotation(self,m):
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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.rand(self.n,3,3)
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assert np.allclose(mechanics.strain(F,'U',m),
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mechanics.strain(F,'V',m))
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@pytest.mark.parametrize('m',[0.0,np.random.random()*2.5,np.random.random()*-2.5])
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def test_strain_rotation_equivalence(self,m):
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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.rand(self.n,3,3)*0.5 - 0.25)
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assert np.allclose(np.linalg.det(mechanics.strain(F,'U',m)),
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np.linalg.det(mechanics.strain(F,'V',m)))
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@pytest.mark.parametrize('m',[0.0,np.random.random(),np.random.random()*-1.])
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@pytest.mark.parametrize('t',['V','U'])
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def test_strain_rotation(self,m,t):
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"""Ensure that pure rotation results in no strain."""
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F = Rotation.from_random(self.n).as_matrix()
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assert np.allclose(mechanics.strain(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.rand(self.n,3,3)
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assert np.allclose(np.abs(np.linalg.det(mechanics._polar_decomposition(x,'R')[0])),
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1.0)
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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.rand(self.n,3,3)
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full = mechanics.equivalent_stress_Mises(x)
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dev = mechanics.equivalent_stress_Mises(tensor.deviatoric(x))
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assert np.allclose(full,
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dev)
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@pytest.mark.parametrize('Mises_equivalent',[mechanics.equivalent_strain_Mises,
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mechanics.equivalent_stress_Mises])
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def test_spherical_Mises(self,Mises_equivalent):
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"""Ensure that Mises equivalent strain/stress of spherical strain is 0."""
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x = np.random.rand(self.n,3,3)
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assert np.allclose(Mises_equivalent(tensor.spherical(x,True)),
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0.0)
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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.rand(self.n,3,3)
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assert np.allclose(mechanics.equivalent_stress_Mises(x)/mechanics.equivalent_strain_Mises(x),
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1.5)
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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 = tensor.spherical(tensor.symmetric(np.random.rand(self.n,3,3)),True)
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assert np.allclose(mechanics.maximum_shear(A),0.0)
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def test_invalid_decomposition(self):
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with pytest.raises(ValueError):
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mechanics._polar_decomposition(np.random.rand(10,3,3),'A')
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