Enforce equilibrium with a total Lagrangian formulation. More...

#include <TotalLagrangianStressDivergenceBase.h>

Inheritance diagram for TotalLagrangianStressDivergenceBase< G >:

Public Types
typedef std::vector< int >	JvarMap

Public Member Functions
	TotalLagrangianStressDivergenceBase (const InputParameters &parameters)

virtual void	initialSetup () override

template<>
InputParameters	validParams ()

template<>
void	initialSetup ()

template<>
InputParameters	validParams ()

template<>
void	initialSetup ()

template<>
InputParameters	validParams ()

template<>
void	initialSetup ()

virtual void	computeOffDiagJacobian (unsigned int jvar) override

unsigned int	mapJvarToCvar (unsigned int jvar)

int	mapJvarToCvar (unsigned int jvar, const JvarMap &jvar_map)

bool	mapJvarToCvar (unsigned int jvar, unsigned int &cvar)

const JvarMap &	getJvarMap ()

const JvarMap &	getParameterJvarMap (std::string parameter_name)

Static Public Member Functions
static InputParameters	baseParams ()

static InputParameters	validParams ()

Protected Member Functions
virtual RankTwoTensor	gradTest (unsigned int component) override

virtual RankTwoTensor	gradTrial (unsigned int component) override

virtual void	precalculateJacobianDisplacement (unsigned int component) override
	Prepare the average shape function gradients for stabilization. More...

virtual Real	computeQpResidual () override

virtual Real	computeQpJacobianDisplacement (unsigned int alpha, unsigned int beta) override

virtual Real	computeQpJacobianTemperature (unsigned int cvar) override

virtual Real	computeQpJacobianOutOfPlaneStrain () override

virtual void	precalculateJacobian () override

virtual void	precalculateOffDiagJacobian (unsigned int jvar) override

virtual Real	computeQpJacobian () override

virtual Real	computeQpOffDiagJacobian (unsigned int jvar) override

Protected Attributes
const MaterialProperty< RankTwoTensor > &	_pk1
	The 1st Piola-Kirchhoff stress. More...

const MaterialProperty< RankFourTensor > &	_dpk1
	The derivative of the PK1 stress with respect to the deformation gradient. More...

const bool	_large_kinematics
	If true use large deformation kinematics. More...

const bool	_stabilize_strain
	If true calculate the deformation gradient derivatives for F_bar. More...

const std::string	_base_name
	Prepend to the material properties. More...

const unsigned int	_alpha
	Which component of the vector residual this kernel is responsible for. More...

const unsigned int	_ndisp
	Total number of displacements/size of residual vector. More...

std::vector< unsigned int >	_disp_nums
	The displacement numbers. More...

std::vector< std::vector< RankTwoTensor > >	_avg_grad_trial

const MaterialProperty< RankTwoTensor > &	_F_ust
	The unmodified deformation gradient. More...

const MaterialProperty< RankTwoTensor > &	_F_avg
	The element-average deformation gradient. More...

const MaterialProperty< RankTwoTensor > &	_f_inv
	The inverse increment deformation gradient. More...

const MaterialProperty< RankTwoTensor > &	_F_inv
	The inverse deformation gradient. More...

const MaterialProperty< RankTwoTensor > &	_F
	The actual (stabilized) deformation gradient. More...

const MooseVariable *	_temperature
	Temperature, if provided. This is used only to get the trial functions. More...

const MooseVariable *	_out_of_plane_strain
	Out-of-plane strain, if provided. More...

std::vector< std::vector< const MaterialProperty< RankTwoTensor > * > >	_deigenstrain_dargs
	Eigenstrain derivatives wrt generate coupleds. More...

const unsigned int	_n_args

Private Member Functions
virtual RankTwoTensor	gradTrialUnstabilized (unsigned int component)
	The unstabilized trial function gradient. More...

virtual RankTwoTensor	gradTrialStabilized (unsigned int component)
	The stabilized trial function gradient. More...

Detailed Description

template<class G>
class TotalLagrangianStressDivergenceBase< G >

Enforce equilibrium with a total Lagrangian formulation.

This class enforces equilibrium when used in conjunction with the corresponding strain calculator (CalculateStrainLagrangianKernel) and with either a stress calculator that provides the 1st PK stress ("pk1_stress") and the derivative of the 1st PK stress with respect to the deformation gradient ("pk1_jacobian")

This kernel should be used with the new "ComputeLagrangianStressBase" stress update system and the "ComputeLagrangianStrain" system for strains.

Definition at line 27 of file TotalLagrangianStressDivergenceBase.h.

Constructor & Destructor Documentation

◆ TotalLagrangianStressDivergenceBase()

template<class G >

TotalLagrangianStressDivergenceBase< G >::TotalLagrangianStressDivergenceBase ( const InputParameters & parameters )

Definition at line 23 of file TotalLagrangianStressDivergenceBase.C.

   : LagrangianStressDivergenceBase(parameters),
     _pk1(getMaterialPropertyByName<RankTwoTensor>(_base_name + "pk1_stress")),
     _dpk1(getMaterialPropertyByName<RankFourTensor>(_base_name + "pk1_jacobian"))
 {
 }

Member Function Documentation

◆ baseParams()

template<class G >

InputParameters TotalLagrangianStressDivergenceBase< G >::baseParams ( )

static

Definition at line 14 of file TotalLagrangianStressDivergenceBase.C.

Referenced by TotalLagrangianStressDivergenceBase< G >::validParams().

 {
   InputParameters params = LagrangianStressDivergenceBase::validParams();
   // This kernel requires use_displaced_mesh to be off
   params.suppressParameter<bool>("use_displaced_mesh");
   return params;
 }

◆ computeQpJacobian()

Real LagrangianStressDivergenceBase::computeQpJacobian ( )

overrideprotectedvirtualinherited

Reimplemented in TotalLagrangianWeakPlaneStress.

Definition at line 115 of file LagrangianStressDivergenceBase.C.

 {
   return computeQpJacobianDisplacement(_alpha, _alpha);
 }

◆ computeQpJacobianDisplacement()

template<class G >

Real TotalLagrangianStressDivergenceBase< G >::computeQpJacobianDisplacement	(	unsigned int	alpha,
		unsigned int	beta
	)

overrideprotectedvirtual

Implements LagrangianStressDivergenceBase.

Definition at line 101 of file TotalLagrangianStressDivergenceBase.C.

 {
   // J_{alpha beta} = phi^alpha_{i, J} T_{iJkL} G^beta_{kL}
   return gradTest(alpha).doubleContraction(_dpk1[_qp] * gradTrial(beta));
 }

◆ computeQpJacobianOutOfPlaneStrain()

template<class G >

Real TotalLagrangianStressDivergenceBase< G >::computeQpJacobianOutOfPlaneStrain ( )

overrideprotectedvirtual

Implements LagrangianStressDivergenceBase.

Definition at line 128 of file TotalLagrangianStressDivergenceBase.C.

 {
   return _dpk1[_qp].contractionKl(2, 2, gradTest(_alpha)) * _out_of_plane_strain->phi()[_j][_qp];
 }

◆ computeQpJacobianTemperature()

template<class G >

Real TotalLagrangianStressDivergenceBase< G >::computeQpJacobianTemperature ( unsigned int cvar )

overrideprotectedvirtual

Implements LagrangianStressDivergenceBase.

Definition at line 110 of file TotalLagrangianStressDivergenceBase.C.

 {
   usingTensorIndices(i_, j_, k_, l_);
   // Multiple eigenstrains may depend on the same coupled var
   RankTwoTensor total_deigen;
   for (const auto deigen_darg : _deigenstrain_dargs[cvar])
     total_deigen += (*deigen_darg)[_qp];
 
   const auto A = _f_inv[_qp].inverse();
   const auto B = _F_inv[_qp].inverse();
   const auto U = 0.5 * (A.template times<i_, k_, l_, j_>(B) + A.template times<i_, l_, k_, j_>(B));
 
   return -(_dpk1[_qp] * U * total_deigen).doubleContraction(gradTest(_alpha)) *
          _temperature->phi()[_j][_qp];
 }

◆ computeQpOffDiagJacobian()

Real LagrangianStressDivergenceBase::computeQpOffDiagJacobian ( unsigned int jvar )

overrideprotectedvirtualinherited

Reimplemented in TotalLagrangianWeakPlaneStress.

Definition at line 121 of file LagrangianStressDivergenceBase.C.

 {
   // Bail if jvar not coupled
   if (getJvarMap()[jvar] < 0)
     return 0.0;
 
   // Off diagonal terms for other displacements
   for (auto beta : make_range(_ndisp))
     if (jvar == _disp_nums[beta])
       return computeQpJacobianDisplacement(_alpha, beta);
 
   // Off diagonal temperature term due to eigenstrain
   if (_temperature && jvar == _temperature->number())
     return computeQpJacobianTemperature(mapJvarToCvar(jvar));
 
   // Off diagonal term due to weak plane stress
   if (_out_of_plane_strain && jvar == _out_of_plane_strain->number())
     return computeQpJacobianOutOfPlaneStrain();
 
   return 0;
 }

◆ computeQpResidual()

template<class G >

Real TotalLagrangianStressDivergenceBase< G >::computeQpResidual ( )

overrideprotectedvirtual

Reimplemented in TotalLagrangianWeakPlaneStress.

Definition at line 94 of file TotalLagrangianStressDivergenceBase.C.

 {
   return gradTest(_alpha).doubleContraction(_pk1[_qp]);
 }

◆ gradTest()

template<class G >

RankTwoTensor TotalLagrangianStressDivergenceBase< G >::gradTest ( unsigned int component )

overrideprotectedvirtual

Implements LagrangianStressDivergenceBase.

Definition at line 33 of file TotalLagrangianStressDivergenceBase.C.

Referenced by HomogenizedTotalLagrangianStressDivergence::computeOffDiagJacobianScalar().

 {
   // F-bar doesn't modify the test function
   return G::gradOp(component, _grad_test[_i][_qp], _test[_i][_qp], _q_point[_qp]);
 }

◆ gradTrial()

template<class G >

RankTwoTensor TotalLagrangianStressDivergenceBase< G >::gradTrial ( unsigned int component )

overrideprotectedvirtual

Implements LagrangianStressDivergenceBase.

Definition at line 41 of file TotalLagrangianStressDivergenceBase.C.

Referenced by HomogenizedTotalLagrangianStressDivergence::computeOffDiagJacobianScalar(), and TotalLagrangianWeakPlaneStress::computeQpOffDiagJacobian().

 {
   return _stabilize_strain ? gradTrialStabilized(component) : gradTrialUnstabilized(component);
 }

◆ gradTrialStabilized()

template<class G >

RankTwoTensor TotalLagrangianStressDivergenceBase< G >::gradTrialStabilized ( unsigned int component )

privatevirtual

The stabilized trial function gradient.

Definition at line 56 of file TotalLagrangianStressDivergenceBase.C.

 {
   // The base unstabilized trial function gradient
   const auto Gb = G::gradOp(component, _grad_phi[_j][_qp], _phi[_j][_qp], _q_point[_qp]);
   // The average trial function gradient
   const auto Ga = _avg_grad_trial[component][_j];
 
   // The F-bar stabilization depends on kinematics
   if (_large_kinematics)
   {
     // Horrible thing, see the documentation for how we get here
     const Real dratio = std::pow(_F_avg[_qp].det() / _F_ust[_qp].det(), 1.0 / 3.0);
     const Real fact = (_F_avg[_qp].inverse().transpose().doubleContraction(Ga) -
                        _F_ust[_qp].inverse().transpose().doubleContraction(Gb)) /
                       3.0;
     return dratio * (Gb + fact * _F_ust[_qp]);
   }
 
   // The small kinematics modification is linear
   return Gb + (Ga.trace() - Gb.trace()) / 3.0 * RankTwoTensor::Identity();
 }

◆ gradTrialUnstabilized()

template<class G >

RankTwoTensor TotalLagrangianStressDivergenceBase< G >::gradTrialUnstabilized ( unsigned int component )

privatevirtual

The unstabilized trial function gradient.

Definition at line 48 of file TotalLagrangianStressDivergenceBase.C.

 {
   // Without F-bar stabilization, simply return the gradient of the trial functions
   return G::gradOp(component, _grad_phi[_j][_qp], _phi[_j][_qp], _q_point[_qp]);
 }

◆ initialSetup() [1/4]

template<>

void TotalLagrangianStressDivergenceBase< GradientOperatorAxisymmetricCylindrical >::initialSetup ( )

Definition at line 26 of file TotalLagrangianStressDivergenceAxisymmetricCylindrical.h.

 {
   if (getBlockCoordSystem() != Moose::COORD_RZ)
     mooseError("This kernel should only act in axisymmetric cylindrical coordinates.");
 }

◆ initialSetup() [2/4]

template<>

void TotalLagrangianStressDivergenceBase< GradientOperatorCentrosymmetricSpherical >::initialSetup ( )

Definition at line 26 of file TotalLagrangianStressDivergenceCentrosymmetricSpherical.h.

 {
   if (getBlockCoordSystem() != Moose::COORD_RSPHERICAL)
     mooseError("This kernel should only act in centrosymmetric spherical coordinates.");
 }

◆ initialSetup() [3/4]

template<>

void TotalLagrangianStressDivergenceBase< GradientOperatorCartesian >::initialSetup ( )

inline

Definition at line 26 of file TotalLagrangianStressDivergence.h.

 {
   if (getBlockCoordSystem() != Moose::COORD_XYZ)
     mooseError("This kernel should only act in Cartesian coordinates.");
 }

◆ initialSetup() [4/4]

template<class G >

virtual void TotalLagrangianStressDivergenceBase< G >::initialSetup ( )

overridevirtual

◆ precalculateJacobian()

void LagrangianStressDivergenceBase::precalculateJacobian ( )

overrideprotectedvirtualinherited

Reimplemented in TotalLagrangianWeakPlaneStress.

Definition at line 85 of file LagrangianStressDivergenceBase.C.

 {
   // Skip if we are not doing stabilization
   if (!_stabilize_strain)
     return;
 
   // We need the gradients of shape functions in the reference frame
   _fe_problem.prepareShapes(_var.number(), _tid);
   _avg_grad_trial[_alpha].resize(_phi.size());
   precalculateJacobianDisplacement(_alpha);
 }

◆ precalculateJacobianDisplacement()

template<class G >

void TotalLagrangianStressDivergenceBase< G >::precalculateJacobianDisplacement ( unsigned int component )

overrideprotectedvirtual

Prepare the average shape function gradients for stabilization.

Implements LagrangianStressDivergenceBase.

Definition at line 80 of file TotalLagrangianStressDivergenceBase.C.

 {
   // For total Lagrangian, the averaging is taken on the reference frame regardless of geometric
   // nonlinearity. Convenient!
   for (auto j : make_range(_phi.size()))
     _avg_grad_trial[component][j] = StabilizationUtils::elementAverage(
         [this, component, j](unsigned int qp)
         { return G::gradOp(component, _grad_phi[j][qp], _phi[j][qp], _q_point[qp]); },
         _JxW,
         _coord);
 }

◆ precalculateOffDiagJacobian()

void LagrangianStressDivergenceBase::precalculateOffDiagJacobian ( unsigned int jvar )

overrideprotectedvirtualinherited

Definition at line 98 of file LagrangianStressDivergenceBase.C.

 {
   // Skip if we are not doing stabilization
   if (!_stabilize_strain)
     return;
 
   for (auto beta : make_range(_ndisp))
     if (jvar == _disp_nums[beta])
     {
       // We need the gradients of shape functions in the reference frame
       _fe_problem.prepareShapes(jvar, _tid);
       _avg_grad_trial[beta].resize(_phi.size());
       precalculateJacobianDisplacement(beta);
     }
 }

◆ validParams() [1/4]

template<>

InputParameters TotalLagrangianStressDivergenceBase< GradientOperatorCartesian >::validParams ( )

inline

Definition at line 16 of file TotalLagrangianStressDivergence.h.

 {
   InputParameters params = TotalLagrangianStressDivergenceBase::baseParams();
   params.addClassDescription(
       "Enforce equilibrium with a total Lagrangian formulation in Cartesian coordinates.");
   return params;
 }

◆ validParams() [2/4]

template<>

InputParameters TotalLagrangianStressDivergenceBase< GradientOperatorCentrosymmetricSpherical >::validParams ( )

inline

Definition at line 16 of file TotalLagrangianStressDivergenceCentrosymmetricSpherical.h.

 {
   InputParameters params = TotalLagrangianStressDivergenceBase::baseParams();
   params.addClassDescription("Enforce equilibrium with a total Lagrangian formulation in "
                              "centrosymmetric spherical coordinates.");
   return params;
 }

◆ validParams() [3/4]

template<>

InputParameters TotalLagrangianStressDivergenceBase< GradientOperatorAxisymmetricCylindrical >::validParams ( )

inline

Definition at line 16 of file TotalLagrangianStressDivergenceAxisymmetricCylindrical.h.

 {
   InputParameters params = TotalLagrangianStressDivergenceBase::baseParams();
   params.addClassDescription("Enforce equilibrium with a total Lagrangian formulation in "
                              "axisymmetric cylindrical coordinates.");
   return params;
 }