def __GetLocalStiffness__(self,
function_space,
material,
LagrangeElemCoords,
EulerELemCoords,
fem_solver,
elem=0):
"""Get stiffness matrix of the system"""
# GET LOCAL KINEMATICS
SpatialGradient, F, detJ, dV = _KinematicMeasures_(
function_space.Jm, function_space.AllGauss[:,
0], LagrangeElemCoords,
EulerELemCoords, fem_solver.requires_geometry_update)
# PARAMETERS FOR INCOMPRESSIBILITY (MEAN DILATATION METHOD HU-WASHIZU)
if material.is_nearly_incompressible:
stiffness_k = self.VolumetricStiffnessIntegrand(
material, SpatialGradient, detJ, dV)
# COMPUTE WORK-CONJUGATES AND HESSIAN AT THIS GAUSS POINT
CauchyStressTensor, H_Voigt = material.KineticMeasures(F, elem=elem)
# COMPUTE LOCAL CONSTITUTIVE STIFFNESS AND TRACTION
stiffness, tractionforce = __ConstitutiveStiffnessIntegrandDF__(
SpatialGradient, CauchyStressTensor, H_Voigt, detJ, self.nvar,
fem_solver.requires_geometry_update)
# COMPUTE GEOMETRIC STIFFNESS
if material.nature != "linear":
stiffness += self.__GeometricStiffnessIntegrand__(
SpatialGradient, CauchyStressTensor, detJ)
if material.is_nearly_incompressible:
stiffness += stiffness_k
return stiffness, tractionforce
def __GetLocalStiffness__(self,
function_space,
material,
LagrangeElemCoords,
EulerELemCoords,
ElectricPotentialElem,
fem_solver,
elem=0):
"""Get stiffness matrix of the system"""
# GET LOCAL KINEMATICS
SpatialGradient, F, detJ = _KinematicMeasures_(
function_space.Jm, function_space.AllGauss[:,
0], LagrangeElemCoords,
EulerELemCoords, fem_solver.requires_geometry_update)
# GET ELECTRIC FIELD
ElectricFieldx = -np.einsum('ijk,j', SpatialGradient,
ElectricPotentialElem)
# COMPUTE WORK-CONJUGATES AND HESSIAN AT THIS GAUSS POINT
ElectricDisplacementx, _, H_Voigt = material.KineticMeasures(
F, ElectricFieldx, elem=elem)
# COMPUTE LOCAL CONSTITUTIVE STIFFNESS AND TRACTION
stiffness, tractionforce = __ConstitutiveStiffnessIntegrandLaplacian__(
SpatialGradient, ElectricDisplacementx, H_Voigt, detJ, self.nvar,
fem_solver.requires_geometry_update)
return stiffness, tractionforce
def __GetLocalTraction__(self,
function_space,
material,
LagrangeElemCoords,
EulerELemCoords,
ElectricPotentialElem,
fem_solver,
elem=0):
"""Get traction vector of the system"""
# GET LOCAL KINEMATICS
SpatialGradient, F, detJ = _KinematicMeasures_(
function_space.Jm, function_space.AllGauss[:,
0], LagrangeElemCoords,
EulerELemCoords, fem_solver.requires_geometry_update)
# GET ELECTRIC FIELD
ElectricFieldx = -np.einsum('ijk,j', SpatialGradient,
ElectricPotentialElem)
# COMPUTE WORK-CONJUGATES AND HESSIAN AT THIS GAUSS POINT
ElectricDisplacementx, CauchyStressTensor, _ = material.KineticMeasures(
F, ElectricFieldx, elem=elem)
# COMPUTE LOCAL CONSTITUTIVE STIFFNESS AND TRACTION
tractionforce = __TractionIntegrandDPF__(
SpatialGradient, ElectricDisplacementx, CauchyStressTensor, detJ,
material.H_VoigtSize, self.nvar,
fem_solver.requires_geometry_update)
return tractionforce
def __GetLocalMass__(self, function_space, material, LagrangeElemCoords,
EulerELemCoords, fem_solver, elem):
# GET LOCAL KINEMATICS
_, _, detJ = _KinematicMeasures_(function_space.Jm,
function_space.AllGauss[:, 0],
LagrangeElemCoords, EulerELemCoords,
False)
return __MassIntegrand__(material.rho, function_space.Bases, detJ,
material.ndim, material.nvar)
def __GetLocalMass_Efficient__(self, function_space, material,
LagrangeElemCoords, EulerELemCoords,
fem_solver, elem):
"""Computes elemental mass matrix in a very efficient way by computing rhoNN only once"""
# GET LOCAL KINEMATICS
_, _, detJ = _KinematicMeasures_(function_space.Jm,
function_space.AllGauss[:, 0],
LagrangeElemCoords, EulerELemCoords,
False)
return __ConstantMassIntegrand__(self.constant_mass_integrand, detJ)
def GetAverageJacobian(self,
function_space,
LagrangeElemCoords,
EulerELemCoords,
requires_geometry_update,
elem=0):
""" Find the average Jacobian of element [could be curved or straight]
"""
# GET LOCAL KINEMATICS
detJ = _KinematicMeasures_(function_space.Jm,
function_space.AllGauss[:, 0],
LagrangeElemCoords, EulerELemCoords,
requires_geometry_update)[2]
return detJ.mean()
def GetVolume(self, function_space, LagrangeElemCoords, EulerELemCoords, requires_geometry_update, elem=0):
""" Find the volume (area in 2D) of element [could be curved or straight]
"""
# GET LOCAL KINEMATICS
detJ = _KinematicMeasures_(function_space.Jm, function_space.AllGauss[:,0],
LagrangeElemCoords, EulerELemCoords, requires_geometry_update)[2]
# volume = 0.
# LOOP OVER GAUSS POINTS
# for counter in range(function_space.AllGauss.shape[0]):
# volume += detJ[counter]
# return volume
return detJ.sum()
def K_uu(self, material, fem_solver, Eulerx, Eulerp=None, elem=0):
"""Get stiffness matrix of the system"""
meshes = self.meshes
mesh = self.meshes[0]
function_spaces = self.function_spaces
function_space = self.function_spaces[0]
ndim = self.ndim
nvar = self.nvar
nodeperelem = meshes[0].elements.shape[1]
# print nodeperelem
# GET THE FIELDS AT THE ELEMENT LEVEL
LagrangeElemCoords = mesh.points[mesh.elements[elem,:],:]
EulerELemCoords = Eulerx[mesh.elements[elem,:],:]
Jm = function_spaces[0].Jm
AllGauss = function_space.AllGauss
# GET LOCAL KINEMATICS
SpatialGradient, F, detJ = _KinematicMeasures_(Jm, AllGauss[:,0],
LagrangeElemCoords, EulerELemCoords, fem_solver.requires_geometry_update)
# COMPUTE WORK-CONJUGATES AND HESSIAN AT THIS GAUSS POINT
CauchyStressTensor, H_Voigt, _ = material.KineticMeasures(F,elem=elem)
# COMPUTE LOCAL CONSTITUTIVE STIFFNESS AND TRACTION
stiffness, tractionforce = __ConstitutiveStiffnessIntegrandDF__(SpatialGradient,
CauchyStressTensor,H_Voigt,detJ,self.nvar,fem_solver.requires_geometry_update)
# # COMPUTE GEOMETRIC STIFFNESS
# if fem_solver.requires_geometry_update:
# stiffness += self.__GeometricStiffnessIntegrand__(SpatialGradient,CauchyStressTensor,detJ)
# SAVE AT THIS GAUSS POINT
self.SpatialGradient = SpatialGradient
self.detJ = detJ
return stiffness, tractionforce
