def setUp(self):
mu, kappa, rho = sp.rand(3)
A10 = mu / 2
A01 = 0
F = sp.rand(3, 3)
self.E = 1 / 2 * (F.T @ F - sp.eye(3))
self.mooney = MooneyRivlin(A10, A01, kappa, rho)
self.neo = NeoHookean(mu, kappa, rho)
def setUp(self):
F = sp.zeros((3, 3))
F[:2, :2] = sp.rand(2, 2)
F[2, 2] = 1
self.E = 1 / 2 * (F.T @ F - sp.eye(3))
A10, A01, kappa, rho = sp.rand(4)
mu = A10 * 2
self.mooney = MooneyRivlin(A10, A01, kappa, rho, plane_stress=False)
self.neo = NeoHookean(mu, kappa, rho, plane_stress=False)
def create_material(material_type='Kirchhoff', **kwargs):
if kwargs is None:
print(
'No material-parameters were given. I am setting them to default.')
else:
if material_type is 'Kirchhoff':
if 'E' in kwargs:
E = kwargs['E']
else:
E = 210E9
if 'nu' in kwargs:
nu = kwargs['nu']
else:
nu = 0.3
if 'rho' in kwargs:
rho = kwargs['rho']
else:
rho = 7.85E3
if 'plane_stress' in kwargs:
plane_stress = kwargs['plane_stress']
else:
plane_stress = True
if 'thickness' in kwargs:
thickness = kwargs['thickness']
else:
thickness = 1.0
return KirchhoffMaterial(E, nu, rho, plane_stress, thickness)
elif material_type is 'MooneyRivlin':
if 'A10' in kwargs:
A10 = kwargs['A10']
else:
A10 = 0.4E3
if 'A01' in kwargs:
A01 = kwargs['A01']
else:
A01 = 0.1E3
if 'kappa' in kwargs:
kappa = kwargs['kappa']
else:
kappa = 1E5
if 'rho' in kwargs:
rho = kwargs['rho']
else:
rho = 0.94E3
if 'plane_stress' in kwargs:
plane_stress = kwargs['plane_stress']
else:
plane_stress = True
if 'thickness' in kwargs:
thickness = kwargs['thickness']
else:
thickness = 1.0
return MooneyRivlin(A10, A01, kappa, rho, plane_stress, thickness)
else:
raise ValueError(
'Unknown material-type given. Please use one of these supported types: \n ',
'Kirchhoff\n', 'MooneyRivlin\n')
class MaterialTest2dPlaneStress(unittest.TestCase):
def setUp(self):
F = sp.zeros((3, 3))
F[:2, :2] = sp.rand(2, 2)
F[2, 2] = 1
self.E = 1 / 2 * (F.T @ F - sp.eye(3))
A10, A01, kappa, rho = sp.rand(4)
mu = A10 * 2
self.mooney = MooneyRivlin(A10, A01, kappa, rho, plane_stress=False)
self.neo = NeoHookean(mu, kappa, rho, plane_stress=False)
def test_mooney_2d(self):
E = self.E
S, S_v, C = self.mooney.S_Sv_and_C(E)
S2d, S_v2d, C2d = self.mooney.S_Sv_and_C_2d(E[:2, :2])
np.testing.assert_allclose(S[:2, :2], S2d)
np.testing.assert_allclose(C[np.ix_([0, 1, -1], [0, 1, -1])], C2d)
def test_neo_2d(self):
E = self.E
S, S_v, C = self.neo.S_Sv_and_C(E)
S2d, S_v2d, C2d = self.neo.S_Sv_and_C_2d(E[:2, :2])
np.testing.assert_allclose(S[:2, :2], S2d)
np.testing.assert_allclose(C[np.ix_([0, 1, -1], [0, 1, -1])], C2d)
class MaterialTest(unittest.TestCase):
def setUp(self):
mu, kappa, rho = sp.rand(3)
A10 = mu / 2
A01 = 0
F = sp.rand(3, 3)
self.E = 1 / 2 * (F.T @ F - sp.eye(3))
self.mooney = MooneyRivlin(A10, A01, kappa, rho)
self.neo = NeoHookean(mu, kappa, rho)
def test_Neo_vs_Mooney_S(self):
S_mooney, Sv_mooney, C_mooney = self.mooney.S_Sv_and_C(self.E)
S_neo, Sv_neo, C_neo = self.neo.S_Sv_and_C(self.E)
np.testing.assert_allclose(S_mooney, S_neo)
def test_Neo_vs_Mooney_Sv(self):
S_mooney, Sv_mooney, C_mooney = self.mooney.S_Sv_and_C(self.E)
S_neo, Sv_neo, C_neo = self.neo.S_Sv_and_C(self.E)
np.testing.assert_allclose(Sv_mooney, Sv_neo)
def test_Neo_vs_Mooney_C(self):
S_mooney, Sv_mooney, C_mooney = self.mooney.S_Sv_and_C(self.E)
S_neo, Sv_neo, C_neo = self.neo.S_Sv_and_C(self.E)
np.testing.assert_allclose(C_mooney, C_neo)
def test_Mooney(self):
A10, A01, kappa, rho = sp.rand(4) * 1E3 + 100
my_material = MooneyRivlin(A10, A01, kappa, rho)
self.my_element.material = my_material
self.jacobi_test_element(rtol=5E-4)
def test_Mooney(self):
A10, A01, kappa, rho = sp.rand(4) * 1E3 + 100
print('Material parameters A10, A01 and kappa:', A10, A01, kappa)
my_material = MooneyRivlin(A10, A01, kappa, rho)
self.my_element.material = my_material
self.jacobi_test_element(rtol=1E-3)