This class uses the stress update material in an anisotropic return mapping. More...

#include <HillPlasticityStressUpdate.h>

Inheritance diagram for HillPlasticityStressUpdateTempl< is_ad >:

Public Member Functions
	HillPlasticityStressUpdateTempl (const InputParameters &parameters)

Static Public Member Functions
static InputParameters	validParams ()

Protected Member Functions
virtual void	computeStressInitialize (const GenericDenseVector< is_ad > &stress_dev, const GenericDenseVector< is_ad > &stress, const GenericRankFourTensor< is_ad > &elasticity_tensor) override

virtual GenericReal< is_ad >	computeResidual (const GenericDenseVector< is_ad > &effective_trial_stress, const GenericDenseVector< is_ad > &stress_new, const GenericReal< is_ad > &scalar) override

virtual GenericReal< is_ad >	computeDerivative (const GenericDenseVector< is_ad > &effective_trial_stress, const GenericDenseVector< is_ad > &stress_new, const GenericReal< is_ad > &scalar) override

virtual Real	computeReferenceResidual (const GenericDenseVector< is_ad > &effective_trial_stress, const GenericDenseVector< is_ad > &stress_new, const GenericReal< is_ad > &residual, const GenericReal< is_ad > &scalar_effective_inelastic_strain) override

virtual void	propagateQpStatefulProperties () override

bool	requiresIsotropicTensor () override
	Does the model require the elasticity tensor to be isotropic? Yes, this class only does anisotropic plasticity More...

Real	computeHardeningDerivative ()

GenericReal< is_ad >	computeHardeningValue (const GenericReal< is_ad > &scalar, const GenericReal< is_ad > &omega)

void	computeHillTensorEigenDecomposition (const DenseMatrix< Real > &hill_tensor)
	Compute eigendecomposition of Hill's tensor for anisotropic plasticity. More...

virtual void	computeStrainFinalize (GenericRankTwoTensor< is_ad > &, const GenericRankTwoTensor< is_ad > &, const GenericDenseVector< is_ad > &, const GenericReal< is_ad > &) override
	Perform any necessary steps to finalize strain increment after return mapping iterations. More...

virtual void	computeStressFinalize (const GenericRankTwoTensor< is_ad > &inelasticStrainIncrement, const GenericReal< is_ad > &delta_gamma, GenericRankTwoTensor< is_ad > &stress, const GenericDenseVector< is_ad > &, const GenericRankTwoTensor< is_ad > &, const GenericRankFourTensor< is_ad > &) override
	Perform any necessary steps to finalize state after return mapping iterations. More...

GenericReal< is_ad >	computeOmega (const GenericReal< is_ad > &delta_gamma, const GenericDenseVector< is_ad > &stress_trial)

void	computeDeltaDerivatives (const GenericReal< is_ad > &delta_gamma, const GenericDenseVector< is_ad > &stress_trial, const GenericReal< is_ad > &sy_alpha, GenericReal< is_ad > &omega, GenericReal< is_ad > &omega_gamma, GenericReal< is_ad > &sy_gamma)

virtual void	initQpStatefulProperties () override

virtual GenericReal< is_ad >	computeStressDerivative (const Real, const Real) override
	Calculate the derivative of the strain increment with respect to the updated stress. More...

Protected Attributes
GenericReal< is_ad >	_qsigma
	Square of the q function for orthotropy. More...

GenericDenseVector< is_ad >	_eigenvalues_hill

GenericDenseMatrix< is_ad >	_eigenvectors_hill

const Real	_hardening_constant

const Real	_hardening_exponent

GenericMaterialProperty< Real, is_ad > &	_hardening_variable

const MaterialProperty< Real > &	_hardening_variable_old

GenericReal< is_ad >	_hardening_derivative

GenericReal< is_ad >	_yield_condition

GenericReal< is_ad >	_yield_stress

const MaterialProperty< DenseMatrix< Real > > &	_hill_tensor
	Hill tensor, when global axes do not (somehow) align with those of the material Example: Large rotation due to rigid body and/or large deformation kinematics. More...

GenericDenseVector< is_ad >	_stress_np1

GenericReal< is_ad >	_two_shear_modulus
	2 * shear modulus More...

unsigned int	_qp

GenericMaterialProperty< RankTwoTensor, is_ad > &	_plasticity_strain
	Plasticity strain tensor material property. More...

const MaterialProperty< RankTwoTensor > &	_plasticity_strain_old

Detailed Description

template<bool is_ad>
class HillPlasticityStressUpdateTempl< is_ad >

This class uses the stress update material in an anisotropic return mapping.

This class is one of the generalized radial return constitutive models based on Hill's criterion; it assumes and isotropic elasticity tensor and an anisotropic plastic yield surface. Constitutive models that combine creep and plasticity can be used.

Definition at line 22 of file HillPlasticityStressUpdate.h.

Constructor & Destructor Documentation

◆ HillPlasticityStressUpdateTempl()

template<bool is_ad>

HillPlasticityStressUpdateTempl< is_ad >::HillPlasticityStressUpdateTempl ( const InputParameters & parameters )

Definition at line 37 of file HillPlasticityStressUpdate.C.

   : AnisotropicReturnPlasticityStressUpdateBaseTempl<is_ad>(parameters),
     _qsigma(0.0),
     _eigenvalues_hill(6),
     _eigenvectors_hill(6, 6),
     _hardening_constant(this->template getParam<Real>("hardening_constant")),
     _hardening_exponent(this->template getParam<Real>("hardening_exponent")),
     _hardening_variable(this->template declareGenericProperty<Real, is_ad>(this->_base_name +
                                                                            "hardening_variable")),
     _hardening_variable_old(
         this->template getMaterialPropertyOld<Real>(this->_base_name + "hardening_variable")),
     _hardening_derivative(0.0),
     _yield_condition(1.0),
     _yield_stress(this->template getParam<Real>("yield_stress")),
     _hill_tensor(this->template getMaterialPropertyByName<DenseMatrix<Real>>(this->_base_name +
                                                                              "hill_tensor")),
     _stress_np1(6)
 {
 }

Member Function Documentation

◆ computeDeltaDerivatives()

template<bool is_ad>

void HillPlasticityStressUpdateTempl< is_ad >::computeDeltaDerivatives	(	const GenericReal< is_ad > &	delta_gamma,
		const GenericDenseVector< is_ad > &	stress_trial,
		const GenericReal< is_ad > &	sy_alpha,
		GenericReal< is_ad > &	omega,
		GenericReal< is_ad > &	omega_gamma,
		GenericReal< is_ad > &	sy_gamma
	)

protected

Definition at line 112 of file HillPlasticityStressUpdate.C.

 {
   omega_gamma = 0.0;
   sy_gamma = 0.0;
 
   GenericDenseVector<is_ad> K_deltaGamma(6);
   omega = computeOmega(delta_gamma, stress_trial);
 
   GenericDenseVector<is_ad> K(6);
   for (unsigned int i = 0; i < 6; i++)
     K(i) = _eigenvalues_hill(i) /
            (Utility::pow<2>(1 + _two_shear_modulus * delta_gamma * _eigenvalues_hill(i)));
 
   for (unsigned int i = 0; i < 6; i++)
     K_deltaGamma(i) = -2.0 * _two_shear_modulus * _eigenvalues_hill(i) * K(i) /
                       (1 + _two_shear_modulus * delta_gamma * _eigenvalues_hill(i));
 
   for (unsigned int i = 0; i < 6; i++)
     omega_gamma += K_deltaGamma(i) * stress_trial(i) * stress_trial(i);
 
   omega_gamma /= 4.0 * omega;
   sy_gamma = 2.0 * sy_alpha * (omega + delta_gamma * omega_gamma);
 }

◆ computeDerivative()

template<bool is_ad>

GenericReal< is_ad > HillPlasticityStressUpdateTempl< is_ad >::computeDerivative	(	const GenericDenseVector< is_ad > &	effective_trial_stress,
		const GenericDenseVector< is_ad > &	stress_new,
		const GenericReal< is_ad > &	scalar
	)

overrideprotectedvirtual

Definition at line 187 of file HillPlasticityStressUpdate.C.

 {
   // If in elastic regime, return unit derivative
   if (_yield_condition <= 0.0)
     return 1.0;
 
   GenericReal<is_ad> omega = computeOmega(delta_gamma, _stress_np1);
   _hardening_derivative = computeHardeningDerivative();
 
   GenericReal<is_ad> sy =
       _hardening_derivative * computeHardeningValue(delta_gamma, omega) + _yield_stress;
   GenericReal<is_ad> sy_alpha = _hardening_derivative;
 
   GenericReal<is_ad> omega_gamma;
   GenericReal<is_ad> sy_gamma;
 
   computeDeltaDerivatives(delta_gamma, _stress_np1, sy_alpha, omega, omega_gamma, sy_gamma);
   GenericReal<is_ad> residual_derivative = 1 / omega * (sy_gamma - 1 / omega * omega_gamma * sy);
 
   return residual_derivative;
 }

◆ computeHardeningDerivative()

template<bool is_ad>

Real HillPlasticityStressUpdateTempl< is_ad >::computeHardeningDerivative ( )

protected

Definition at line 276 of file HillPlasticityStressUpdate.C.

 {
   return _hardening_constant * _hardening_exponent *
          MetaPhysicL::raw_value(
              std::pow(_hardening_variable[_qp] + 1.0e-30, _hardening_exponent - 1));
 }

◆ computeHardeningValue()

template<bool is_ad>

GenericReal< is_ad > HillPlasticityStressUpdateTempl< is_ad >::computeHardeningValue	(	const GenericReal< is_ad > &	scalar,
		const GenericReal< is_ad > &	omega
	)

protected

Definition at line 268 of file HillPlasticityStressUpdate.C.

 {
   return _hardening_variable_old[_qp] + 2.0 * delta_gamma * omega;
 }

◆ computeHillTensorEigenDecomposition()

template<bool is_ad>

void HillPlasticityStressUpdateTempl< is_ad >::computeHillTensorEigenDecomposition ( const DenseMatrix< Real > & hill_tensor )

protected

Compute eigendecomposition of Hill's tensor for anisotropic plasticity.

Parameters

hill_tensor 6x6 matrix representing fourth order Hill's tensor describing anisotropy

Definition at line 214 of file HillPlasticityStressUpdate.C.

 {
   const unsigned int dimension = hill_tensor.n();
 
   AnisotropyMatrixReal A;
   for (unsigned int index_i = 0; index_i < dimension; index_i++)
     for (unsigned int index_j = 0; index_j < dimension; index_j++)
       A(index_i, index_j) = MetaPhysicL::raw_value(hill_tensor(index_i, index_j));
 
   if (isBlockDiagonal(A))
   {
     Eigen::SelfAdjointEigenSolver<AnisotropyMatrixRealBlock> es(A.block<3, 3>(0, 0));
 
     auto lambda = es.eigenvalues();
     auto v = es.eigenvectors();
 
     _eigenvalues_hill(0) = lambda(0);
     _eigenvalues_hill(1) = lambda(1);
     _eigenvalues_hill(2) = lambda(2);
     _eigenvalues_hill(3) = A(3, 3);
     _eigenvalues_hill(4) = A(4, 4);
     _eigenvalues_hill(5) = A(5, 5);
 
     _eigenvectors_hill(0, 0) = v(0, 0);
     _eigenvectors_hill(0, 1) = v(0, 1);
     _eigenvectors_hill(0, 2) = v(0, 2);
     _eigenvectors_hill(1, 0) = v(1, 0);
     _eigenvectors_hill(1, 1) = v(1, 1);
     _eigenvectors_hill(1, 2) = v(1, 2);
     _eigenvectors_hill(2, 0) = v(2, 0);
     _eigenvectors_hill(2, 1) = v(2, 1);
     _eigenvectors_hill(2, 2) = v(2, 2);
     _eigenvectors_hill(3, 3) = 1.0;
     _eigenvectors_hill(4, 4) = 1.0;
     _eigenvectors_hill(5, 5) = 1.0;
   }
   else
   {
     Eigen::SelfAdjointEigenSolver<AnisotropyMatrixReal> es_b(A);
 
     auto lambda_b = es_b.eigenvalues();
     auto v_b = es_b.eigenvectors();
     for (unsigned int index_i = 0; index_i < dimension; index_i++)
       _eigenvalues_hill(index_i) = lambda_b(index_i);
 
     for (unsigned int index_i = 0; index_i < dimension; index_i++)
       for (unsigned int index_j = 0; index_j < dimension; index_j++)
         _eigenvectors_hill(index_i, index_j) = v_b(index_i, index_j);
   }
 }

◆ computeOmega()

template<bool is_ad>

GenericReal< is_ad > HillPlasticityStressUpdateTempl< is_ad >::computeOmega	(	const GenericReal< is_ad > &	delta_gamma,
		const GenericDenseVector< is_ad > &	stress_trial
	)

protected

Definition at line 90 of file HillPlasticityStressUpdate.C.

 {
   GenericDenseVector<is_ad> K(6);
   GenericReal<is_ad> omega = 0.0;
 
   for (unsigned int i = 0; i < 6; i++)
   {
     K(i) = _eigenvalues_hill(i) /
            (Utility::pow<2>(1 + _two_shear_modulus * delta_gamma * _eigenvalues_hill(i)));
     omega += K(i) * stress_trial(i) * stress_trial(i);
   }
   omega *= 0.5;
 
   if (omega == 0.0)
     omega = 1.0e-36;
 
   return std::sqrt(omega);
 }

◆ computeReferenceResidual()

template<bool is_ad>

Real HillPlasticityStressUpdateTempl< is_ad >::computeReferenceResidual	(	const GenericDenseVector< is_ad > &	effective_trial_stress,
		const GenericDenseVector< is_ad > &	stress_new,
		const GenericReal< is_ad > &	residual,
		const GenericReal< is_ad > &	scalar_effective_inelastic_strain
	)

overrideprotectedvirtual

Definition at line 144 of file HillPlasticityStressUpdate.C.

 {
   // Equation is already normalized.
   return 1.0;
 }

◆ computeResidual()

template<bool is_ad>

GenericReal< is_ad > HillPlasticityStressUpdateTempl< is_ad >::computeResidual	(	const GenericDenseVector< is_ad > &	effective_trial_stress,
		const GenericDenseVector< is_ad > &	stress_new,
		const GenericReal< is_ad > &	scalar
	)

overrideprotectedvirtual

Definition at line 156 of file HillPlasticityStressUpdate.C.

 {
 
   // If in elastic regime, just return
   if (_yield_condition <= 0.0)
     return 0.0;
 
   GenericDenseMatrix<is_ad> eigenvectors_hill_transpose(6, 6);
 
   _eigenvectors_hill.get_transpose(eigenvectors_hill_transpose);
   eigenvectors_hill_transpose.vector_mult(_stress_np1, stress_dev);
 
   GenericReal<is_ad> omega = computeOmega(delta_gamma, _stress_np1);
 
   // Hardening variable is \alpha isotropic hardening for now.
   _hardening_variable[_qp] = computeHardeningValue(delta_gamma, omega);
   GenericReal<is_ad> s_y =
       _hardening_constant * std::pow(_hardening_variable[_qp] + 1.0e-30, _hardening_exponent) +
       _yield_stress;
 
   GenericReal<is_ad> residual = 0.0;
   residual = s_y / omega - 1.0;
 
   return residual;
 }

◆ computeStrainFinalize()

template<bool is_ad>

void HillPlasticityStressUpdateTempl< is_ad >::computeStrainFinalize	(	GenericRankTwoTensor< is_ad > &	inelasticStrainIncrement,
		const GenericRankTwoTensor< is_ad > &	stress,
		const GenericDenseVector< is_ad > &	stress_dev,
		const GenericReal< is_ad > &	delta_gamma
	)

overrideprotectedvirtual

Perform any necessary steps to finalize strain increment after return mapping iterations.

Parameters

inelasticStrainIncrement Inelastic strain increment

Reimplemented from AnisotropicReturnPlasticityStressUpdateBaseTempl< is_ad >.

Definition at line 285 of file HillPlasticityStressUpdate.C.

 {
   // e^P = delta_gamma * hill_tensor * stress
   GenericDenseVector<is_ad> inelasticStrainIncrement_vector(6);
   GenericDenseVector<is_ad> hill_stress(6);
   _hill_tensor[_qp].vector_mult(hill_stress, stress_dev);
   hill_stress.scale(delta_gamma);
   inelasticStrainIncrement_vector = hill_stress;
 
   inelasticStrainIncrement(0, 0) = inelasticStrainIncrement_vector(0);
   inelasticStrainIncrement(1, 1) = inelasticStrainIncrement_vector(1);
   inelasticStrainIncrement(2, 2) = inelasticStrainIncrement_vector(2);
   inelasticStrainIncrement(0, 1) = inelasticStrainIncrement(1, 0) =
       inelasticStrainIncrement_vector(3) / 2.0;
   inelasticStrainIncrement(1, 2) = inelasticStrainIncrement(2, 1) =
       inelasticStrainIncrement_vector(4) / 2.0;
   inelasticStrainIncrement(0, 2) = inelasticStrainIncrement(2, 0) =
       inelasticStrainIncrement_vector(5) / 2.0;
 
   // Calculate equivalent plastic strain
   GenericDenseVector<is_ad> Mepsilon(6);
   _hill_tensor[_qp].vector_mult(Mepsilon, inelasticStrainIncrement_vector);
   GenericReal<is_ad> eq_plastic_strain_inc = Mepsilon.dot(inelasticStrainIncrement_vector);
 
   if (eq_plastic_strain_inc > 0.0)
     eq_plastic_strain_inc = std::sqrt(eq_plastic_strain_inc);
 
   _effective_inelastic_strain[_qp] = _effective_inelastic_strain_old[_qp] + eq_plastic_strain_inc;
 
   AnisotropicReturnPlasticityStressUpdateBaseTempl<is_ad>::computeStrainFinalize(
       inelasticStrainIncrement, stress, stress_dev, delta_gamma);
 }

◆ computeStressDerivative()

template<bool is_ad>

virtual GenericReal<is_ad> AnisotropicReturnPlasticityStressUpdateBaseTempl< is_ad >::computeStressDerivative	(	const Real	,
		const Real
	)

inlineoverrideprotectedvirtualinherited

Calculate the derivative of the strain increment with respect to the updated stress.

Parameters

effective_trial_stress	Effective trial stress
scalar	Inelastic strain increment magnitude being solved for

Definition at line 47 of file AnisotropicReturnPlasticityStressUpdateBase.h.

   {
     return 0.0;
   }

◆ computeStressFinalize()

template<bool is_ad>

void HillPlasticityStressUpdateTempl< is_ad >::computeStressFinalize	(	const GenericRankTwoTensor< is_ad > &	inelasticStrainIncrement,
		const GenericReal< is_ad > &	delta_gamma,
		GenericRankTwoTensor< is_ad > &	stress,
		const GenericDenseVector< is_ad > &	stress_dev,
		const GenericRankTwoTensor< is_ad > &	,
		const GenericRankFourTensor< is_ad > &
	)

overrideprotectedvirtual

Perform any necessary steps to finalize state after return mapping iterations.

Parameters

inelasticStrainIncrement Inelastic strain increment

Definition at line 324 of file HillPlasticityStressUpdate.C.

 {
   // Need to compute this iteration's stress tensor based on the scalar variable for deviatoric
   // s(n+1) = {Q [I + 2*nu*delta_gamma*Delta]^(-1) Q^T}  s(trial)
 
   if (_yield_condition <= 0.0)
     return;
 
   GenericDenseMatrix<is_ad> inv_matrix(6, 6);
   for (unsigned int i = 0; i < 6; i++)
     inv_matrix(i, i) = 1 / (1 + _two_shear_modulus * delta_gamma * _eigenvalues_hill(i));
 
   GenericDenseMatrix<is_ad> eigenvectors_hill_transpose(6, 6);
 
   _eigenvectors_hill.get_transpose(eigenvectors_hill_transpose);
   GenericDenseMatrix<is_ad> eigenvectors_hill_copy(_eigenvectors_hill);
 
   // Right multiply by matrix of eigenvectors transpose
   inv_matrix.right_multiply(eigenvectors_hill_transpose);
   // Right multiply eigenvector matrix by [I + 2*nu*delta_gamma*Delta]^(-1) Q^T
   eigenvectors_hill_copy.right_multiply(inv_matrix);
 
   GenericDenseVector<is_ad> stress_np1(6);
   eigenvectors_hill_copy.vector_mult(stress_np1, stress_dev);
 
   GenericRankTwoTensor<is_ad> stress_new_volumetric = stress_new - stress_new.deviatoric();
 
   stress_new(0, 0) = stress_new_volumetric(0, 0) + stress_np1(0);
   stress_new(1, 1) = stress_new_volumetric(1, 1) + stress_np1(1);
   stress_new(2, 2) = stress_new_volumetric(2, 2) + stress_np1(2);
   stress_new(0, 1) = stress_new(1, 0) = stress_np1(3);
   stress_new(1, 2) = stress_new(2, 1) = stress_np1(4);
   stress_new(0, 2) = stress_new(2, 0) = stress_np1(5);
 
   GenericReal<is_ad> omega = computeOmega(delta_gamma, _stress_np1);
   _hardening_variable[_qp] = computeHardeningValue(delta_gamma, omega);
 }

◆ computeStressInitialize()

template<bool is_ad>

void HillPlasticityStressUpdateTempl< is_ad >::computeStressInitialize	(	const GenericDenseVector< is_ad > &	stress_dev,
		const GenericDenseVector< is_ad > &	stress,
		const GenericRankFourTensor< is_ad > &	elasticity_tensor
	)

overrideprotectedvirtual

Definition at line 69 of file HillPlasticityStressUpdate.C.

 {
   _hardening_variable[_qp] = _hardening_variable_old[_qp];
   _plasticity_strain[_qp] = _plasticity_strain_old[_qp];
   _effective_inelastic_strain[_qp] = _effective_inelastic_strain_old[_qp];
 
   _two_shear_modulus = 2.0 * ElasticityTensorTools::getIsotropicShearModulus(elasticity_tensor);
 
   // Hill constants: We use directly the transformation tensor, which won't be updated if not
   // necessary in the Hill tensor material.
   computeHillTensorEigenDecomposition(_hill_tensor[_qp]);
 
   _yield_condition = 1.0; // Some positive value
   _yield_condition = -computeResidual(stress_dev, stress_dev, 0.0);
 }

◆ initQpStatefulProperties()

template<bool is_ad>

void AnisotropicReturnPlasticityStressUpdateBaseTempl< is_ad >::initQpStatefulProperties ( )

overrideprotectedvirtualinherited

Reimplemented in HillElastoPlasticityStressUpdateTempl< is_ad >.

Definition at line 37 of file AnisotropicReturnPlasticityStressUpdateBase.C.

Referenced by HillElastoPlasticityStressUpdateTempl< is_ad >::initQpStatefulProperties().

 {
   _plasticity_strain[this->_qp].zero();
 
   GeneralizedRadialReturnStressUpdateTempl<is_ad>::initQpStatefulProperties();
 }

◆ propagateQpStatefulProperties()

template<bool is_ad>

void HillPlasticityStressUpdateTempl< is_ad >::propagateQpStatefulProperties ( )

overrideprotectedvirtual

Reimplemented from AnisotropicReturnPlasticityStressUpdateBaseTempl< is_ad >.

Definition at line 60 of file HillPlasticityStressUpdate.C.

 {
   _hardening_variable[_qp] = _hardening_variable_old[_qp];
   _plasticity_strain[_qp] = _plasticity_strain_old[_qp];
   AnisotropicReturnPlasticityStressUpdateBaseTempl<is_ad>::propagateQpStatefulProperties();
 }

◆ requiresIsotropicTensor()

template<bool is_ad>

bool HillPlasticityStressUpdateTempl< is_ad >::requiresIsotropicTensor ( )

inlineoverrideprotected

Does the model require the elasticity tensor to be isotropic? Yes, this class only does anisotropic plasticity

Definition at line 62 of file HillPlasticityStressUpdate.h.

62 { return true; }

◆ validParams()

template<bool is_ad>

InputParameters HillPlasticityStressUpdateTempl< is_ad >::validParams ( )

static

Definition at line 18 of file HillPlasticityStressUpdate.C.

 {
   InputParameters params = AnisotropicReturnPlasticityStressUpdateBaseTempl<is_ad>::validParams();
   params.addClassDescription(
       "This class uses the generalized radial return for anisotropic plasticity model."
       "This class can be used in conjunction with other creep and plasticity materials for "
       "more complex simulations.");
 
   params.addRequiredParam<Real>("hardening_constant",
                                 "Hardening constant (H) for anisotropic plasticity");
   params.addParam<Real>(
       "hardening_exponent", 1.0, "Hardening exponent (n) for anisotropic plasticity");
   params.addRequiredParam<Real>("yield_stress",
                                 "Yield stress (constant value) for anisotropic plasticity");
 
   return params;
 }

Hill tensor, when global axes do not (somehow) align with those of the material Example: Large rotation due to rigid body and/or large deformation kinematics.

Definition at line 121 of file HillPlasticityStressUpdate.h.