def test_Shear_Plus_Strech_KirchhoffSaintVenant_3D(self):
nnodes = 4
dim = 3
# Define a model and geometry
model_part = KratosMultiphysics.ModelPart("test")
geom = self._create_geometry(model_part, dim, nnodes)
# Material properties
young_modulus = 200e9
poisson_ratio = 0.3
properties = self._create_properties(model_part, young_modulus, poisson_ratio)
N = KratosMultiphysics.Vector(nnodes)
DN_DX = KratosMultiphysics.Matrix(nnodes, dim)
# Construct a constitutive law
cl = StructuralMechanicsApplication.KirchhoffSaintVenant3DLaw()
self._cl_check(cl, properties, geom, model_part, dim)
# Set the parameters to be employed
dict_options = {'USE_ELEMENT_PROVIDED_STRAIN': False,
'COMPUTE_STRESS': True,
'COMPUTE_CONSTITUTIVE_TENSOR': True,
'FINITE_STRAINS': True,
'ISOTROPIC': True,
}
cl_options = self._set_cl_options(dict_options)
# Define deformation gradient
F = self._create_F()
detF = 1.0
stress_vector = KratosMultiphysics.Vector(cl.GetStrainSize())
strain_vector = KratosMultiphysics.Vector(cl.GetStrainSize())
constitutive_matrix = KratosMultiphysics.Matrix(cl.GetStrainSize(),cl.GetStrainSize())
# Setting the parameters - note that a constitutive law may not need them all!
cl_params = self._set_cl_parameters(cl_options, F, detF, strain_vector, stress_vector, constitutive_matrix, N, DN_DX, model_part, properties, geom)
# Check the results
lame_lambda = (young_modulus * poisson_ratio) / ((1.0 + poisson_ratio) * (1.0 - 2.0 * poisson_ratio))
lame_mu = young_modulus / (2.0 * (1.0 + poisson_ratio))
reference_stress = KratosMultiphysics.Vector(cl.GetStrainSize())
for i in range(cl.GetStrainSize()):
reference_stress[i] = 0.0
x1beta = 1.0
x2beta = 1.0
x3beta = math.pi/200
for i in range(100):
F[0,0] = math.cos(x3beta * i)
F[0,1] = -math.sin(x3beta * i)
F[1,0] = math.sin(x3beta * i)
F[1,1] = math.cos(x3beta * i)
F[0,2] = - x1beta * math.sin(x3beta * i) - x2beta * math.cos(x3beta * i)
F[1,2] = x1beta * math.cos(x3beta * i) - x2beta * math.sin(x3beta * i)
cl_params.SetDeformationGradientF(F)
# Cauchy
cl.CalculateMaterialResponseCauchy(cl_params)
cl.FinalizeMaterialResponseCauchy(cl_params)
cl.FinalizeSolutionStep(properties, geom, N, model_part.ProcessInfo)
reference_stress[0]= math.cos(x3beta * i)*(x2beta*lame_mu*(x2beta*math.cos(x3beta * i) + x1beta*math.sin(x3beta * i)) + (lame_lambda*math.cos(x3beta * i)*(x1beta**2 + x2beta**2))/2) + (x2beta*math.cos(x3beta * i) + x1beta*math.sin(x3beta * i))*((lame_lambda/2 + lame_mu)*(x1beta**2 + x2beta**2)*(x2beta*math.cos(x3beta * i) + x1beta*math.sin(x3beta * i)) + x2beta*lame_mu*math.cos(x3beta * i) + x1beta*lame_mu*math.sin(x3beta * i)) + math.sin(x3beta * i)*((lame_lambda*math.sin(x3beta * i)*(x1beta**2 + x2beta**2))/2 + x1beta*lame_mu*(x2beta*math.cos(x3beta * i) + x1beta*math.sin(x3beta * i)))
reference_stress[1]= math.cos(x3beta * i)*(x1beta*lame_mu*(x1beta*math.cos(x3beta * i) - x2beta*math.sin(x3beta * i)) + (lame_lambda*math.cos(x3beta * i)*(x1beta**2 + x2beta**2))/2) + (x1beta*math.cos(x3beta * i) - x2beta*math.sin(x3beta * i))*((lame_lambda/2 + lame_mu)*(x1beta**2 + x2beta**2)*(x1beta*math.cos(x3beta * i) - x2beta*math.sin(x3beta * i)) + x1beta*lame_mu*math.cos(x3beta * i) - x2beta*lame_mu*math.sin(x3beta * i)) + math.sin(x3beta * i)*((lame_lambda*math.sin(x3beta * i)*(x1beta**2 + x2beta**2))/2 - x2beta*lame_mu*(x1beta*math.cos(x3beta * i) - x2beta*math.sin(x3beta * i)))
reference_stress[2]=(lame_lambda/2 + lame_mu)*(x1beta**2 + x2beta**2)
reference_stress[3]= math.sin(x3beta * i)*(x2beta*lame_mu*(x2beta*math.cos(x3beta * i) + x1beta*math.sin(x3beta * i)) + (lame_lambda*math.cos(x3beta * i)*(x1beta**2 + x2beta**2))/2) - math.cos(x3beta * i)*((lame_lambda*math.sin(x3beta * i)*(x1beta**2 + x2beta**2))/2 + x1beta*lame_mu*(x2beta*math.cos(x3beta * i) + x1beta*math.sin(x3beta * i))) - (x1beta*math.cos(x3beta * i) - x2beta*math.sin(x3beta * i))*((lame_lambda/2 + lame_mu)*(x1beta**2 + x2beta**2)*(x2beta*math.cos(x3beta * i) + x1beta*math.sin(x3beta * i)) + x2beta*lame_mu*math.cos(x3beta * i) + x1beta*lame_mu*math.sin(x3beta * i))
reference_stress[4]=(lame_lambda/2 + lame_mu)*(x1beta**2 + x2beta**2)*(x1beta*math.cos(x3beta * i) - x2beta*math.sin(x3beta * i)) + x1beta*lame_mu*math.cos(x3beta * i) - x2beta*lame_mu*math.sin(x3beta * i)
reference_stress[5]=- (lame_lambda/2 + lame_mu)*(x1beta**2 + x2beta**2)*(x2beta*math.cos(x3beta * i) + x1beta*math.sin(x3beta * i)) - x2beta*lame_mu*math.cos(x3beta * i) - x1beta*lame_mu*math.sin(x3beta * i)
stress = cl_params.GetStressVector()
for j in range(cl.GetStrainSize()):
self.assertAlmostEqual(reference_stress[j], stress[j], 2)
def create_constitutive_Law():
return StructuralMechanicsApplication.KirchhoffSaintVenant3DLaw()