Detailed Description

template<int DisplacementDim>
class MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >

A class for computing the BGRa creep model, which reads.

\[ \dot {\mathbf{\epsilon}}^{cr}=\sqrt{\frac{3}{2}}A \mathrm{e}^{-\frac{Q}{RT}} \left(\frac{\sigma_{eff}}{\sigma_0}\right)^n\frac{\mathbf{s}}{||\mathbf{s}||} \]

where \(\sigma_{eff}=\sqrt{\frac{3}{2}}||\mathbf{s}||\), \(A, \sigma_0, n, Q\) are parameter, and \(R\) is the gas constant.

Definition at line 39 of file CreepBGRa.h.

#include <CreepBGRa.h>

Inheritance diagram for MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >:

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Collaboration diagram for MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >:

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Public Types
using	ResidualVectorType = Eigen::Matrix< double, KelvinVectorSize, 1 >

using	JacobianMatrix = Eigen::Matrix< double, KelvinVectorSize, KelvinVectorSize, Eigen::RowMajor >

using	KelvinVector = MathLib::KelvinVector::KelvinVectorType< DisplacementDim >

using	KelvinMatrix = MathLib::KelvinVector::KelvinMatrixType< DisplacementDim >

using	Parameter = ParameterLib::Parameter< double >

Public Types inherited from MaterialLib::Solids::LinearElasticIsotropic< DisplacementDim >
using	KelvinVector = MathLib::KelvinVector::KelvinVectorType< DisplacementDim >

using	KelvinMatrix = MathLib::KelvinVector::KelvinMatrixType< DisplacementDim >

Public Types inherited from MaterialLib::Solids::MechanicsBase< DisplacementDim >
using	KelvinVector = MathLib::KelvinVector::KelvinVectorType< DisplacementDim >

using	KelvinMatrix = MathLib::KelvinVector::KelvinMatrixType< DisplacementDim >

Public Member Functions
std::unique_ptr< typename MechanicsBase< DisplacementDim >::MaterialStateVariables >	createMaterialStateVariables () const override

	CreepBGRa (typename LinearElasticIsotropic< DisplacementDim >::MaterialProperties mp, NumLib::NewtonRaphsonSolverParameters nonlinear_solver_parameters, Parameter const &A, Parameter const &n, Parameter const &sigma_f, Parameter const &Q)

std::optional< std::tuple< KelvinVector, std::unique_ptr< typename MechanicsBase< DisplacementDim >::MaterialStateVariables >, KelvinMatrix > >	integrateStress (MaterialPropertyLib::VariableArray const &variable_array_prev, MaterialPropertyLib::VariableArray const &variable_array, double const t, ParameterLib::SpatialPosition const &x, double const dt, typename MechanicsBase< DisplacementDim >::MaterialStateVariables const &material_state_variables) const override

ConstitutiveModel	getConstitutiveModel () const override
	Gets the type of constitutive model. More...

double	getTemperatureRelatedCoefficient (double const t, double const dt, ParameterLib::SpatialPosition const &x, double const T, double const deviatoric_stress_norm) const override

Public Member Functions inherited from MaterialLib::Solids::LinearElasticIsotropic< DisplacementDim >
	LinearElasticIsotropic (MaterialProperties material_properties)

double	computeFreeEnergyDensity (double const, ParameterLib::SpatialPosition const &, double const, KelvinVector const &eps, KelvinVector const &sigma, typename MechanicsBase< DisplacementDim >::MaterialStateVariables const &) const override

std::optional< std::tuple< typename MechanicsBase< DisplacementDim >::KelvinVector, std::unique_ptr< typename MechanicsBase< DisplacementDim >::MaterialStateVariables >, typename MechanicsBase< DisplacementDim >::KelvinMatrix > >	integrateStress (MaterialPropertyLib::VariableArray const &variable_array_prev, MaterialPropertyLib::VariableArray const &variable_array, double const t, ParameterLib::SpatialPosition const &x, double const, typename MechanicsBase< DisplacementDim >::MaterialStateVariables const &material_state_variables) const override

KelvinMatrix	getElasticTensor (double const t, ParameterLib::SpatialPosition const &x, double const T) const

MaterialProperties	getMaterialProperties () const

double	getBulkModulus (double const t, ParameterLib::SpatialPosition const &x, KelvinMatrix const *const) const override

Public Member Functions inherited from MaterialLib::Solids::MechanicsBase< DisplacementDim >
virtual std::optional< std::tuple< KelvinVector, std::unique_ptr< MaterialStateVariables >, KelvinMatrix > >	integrateStress (MaterialPropertyLib::VariableArray const &variable_array_prev, MaterialPropertyLib::VariableArray const &variable_array, double const t, ParameterLib::SpatialPosition const &x, double const dt, MaterialStateVariables const &material_state_variables) const =0

virtual std::vector< InternalVariable >	getInternalVariables () const

virtual double	computeFreeEnergyDensity (double const t, ParameterLib::SpatialPosition const &x, double const dt, KelvinVector const &eps, KelvinVector const &sigma, MaterialStateVariables const &material_state_variables) const =0

virtual	~MechanicsBase ()=default

Private Attributes
NumLib::NewtonRaphsonSolverParameters const	_nonlinear_solver_parameters

Parameter const &	_a

Parameter const &	_n
	A parameter determined by experiment. More...

Parameter const &	_sigma_f
	Creep rate exponent n. More...

Parameter const &	_q
	A stress scaling factor. More...

Additional Inherited Members
Static Public Attributes inherited from MaterialLib::Solids::LinearElasticIsotropic< DisplacementDim >
static int const	KelvinVectorSize

Protected Attributes inherited from MaterialLib::Solids::LinearElasticIsotropic< DisplacementDim >
MaterialProperties	_mp

Member Typedef Documentation

◆ JacobianMatrix

template<int DisplacementDim>

using MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::JacobianMatrix = Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize, Eigen::RowMajor>

Definition at line 44 of file CreepBGRa.h.

◆ KelvinMatrix

template<int DisplacementDim>

using MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::KelvinMatrix = MathLib::KelvinVector::KelvinMatrixType<DisplacementDim>

Definition at line 49 of file CreepBGRa.h.

◆ KelvinVector

template<int DisplacementDim>

using MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::KelvinVector = MathLib::KelvinVector::KelvinVectorType<DisplacementDim>

Definition at line 47 of file CreepBGRa.h.

◆ Parameter

template<int DisplacementDim>

using MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::Parameter = ParameterLib::Parameter<double>

Definition at line 52 of file CreepBGRa.h.

◆ ResidualVectorType

template<int DisplacementDim>

using MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::ResidualVectorType = Eigen::Matrix<double, KelvinVectorSize, 1>

Definition at line 43 of file CreepBGRa.h.

Constructor & Destructor Documentation

◆ CreepBGRa()

template<int DisplacementDim>

MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::CreepBGRa	(	typename LinearElasticIsotropic< DisplacementDim >::MaterialProperties	mp,
		NumLib::NewtonRaphsonSolverParameters	nonlinear_solver_parameters,
		Parameter const &	A,
		Parameter const &	n,
		Parameter const &	sigma_f,
		Parameter const &	Q
	)

inline

Definition at line 64 of file CreepBGRa.h.

         : LinearElasticIsotropic<DisplacementDim>(std::move(mp)),
           _nonlinear_solver_parameters(std::move(nonlinear_solver_parameters)),
           _a(A),
           _n(n),
           _sigma_f(sigma_f),
           _q(Q)
     {
     }

Member Function Documentation

◆ createMaterialStateVariables()

template<int DisplacementDim>

std::unique_ptr< typename MechanicsBase<DisplacementDim>::MaterialStateVariables> MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::createMaterialStateVariables ( ) const

inlineoverridevirtual

Polymorphic creator for MaterialStateVariables objects specific for a material model.

Reimplemented from MaterialLib::Solids::MechanicsBase< DisplacementDim >.

Definition at line 58 of file CreepBGRa.h.

     {
         return LinearElasticIsotropic<
             DisplacementDim>::createMaterialStateVariables();
     }

◆ getConstitutiveModel()

template<int DisplacementDim>

ConstitutiveModel MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::getConstitutiveModel ( ) const

inlineoverridevirtual

Gets the type of constitutive model.

Reimplemented from MaterialLib::Solids::MechanicsBase< DisplacementDim >.

Definition at line 89 of file CreepBGRa.h.

     {
         return ConstitutiveModel::CreepBGRa;
     }

References MaterialLib::Solids::CreepBGRa.

◆ getTemperatureRelatedCoefficient()

template<int DisplacementDim>

double MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::getTemperatureRelatedCoefficient	(	double const	,
		double const	,
		ParameterLib::SpatialPosition const &	,
		double const	,
		double const
	)		const

overridevirtual

Get temperature related coefficient for the global assembly if there is one.

Reimplemented from MaterialLib::Solids::MechanicsBase< DisplacementDim >.

Definition at line 143 of file CreepBGRa.cpp.

 {
     const double A = _a(t, x)[0];
     const double n = _n(t, x)[0];
     const double sigma0 = _sigma_f(t, x)[0];
     const double Q = _q(t, x)[0];
  
     const double constant_coefficient =
         getCreepConstantCoefficient(A, n, sigma0);
  
     return 2.0 * constant_coefficient *
            std::exp(-Q /
                     (MaterialLib::PhysicalConstant::IdealGasConstant * T)) *
            this->_mp.mu(t, x) * std::pow(deviatoric_stress_norm, n - 1) * dt *
            Q / (MaterialLib::PhysicalConstant::IdealGasConstant * T * T);
 }

References MaterialLib::Solids::Creep::getCreepConstantCoefficient(), and MaterialLib::PhysicalConstant::IdealGasConstant.

◆ integrateStress()

template<int DisplacementDim>

std::optional< std::tuple< typename CreepBGRa< DisplacementDim >::KelvinVector, std::unique_ptr< typename MechanicsBase< DisplacementDim >::MaterialStateVariables >, typename CreepBGRa< DisplacementDim >::KelvinMatrix > > MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::integrateStress	(	MaterialPropertyLib::VariableArray const &	variable_array_prev,
		MaterialPropertyLib::VariableArray const &	variable_array,
		double const	t,
		ParameterLib::SpatialPosition const &	x,
		double const	dt,
		typename MechanicsBase< DisplacementDim >::MaterialStateVariables const &	material_state_variables
	)		const

override

Definition at line 38 of file CreepBGRa.cpp.

 {
     auto const& eps_m = std::get<MPL::SymmetricTensor<DisplacementDim>>(
         variable_array[static_cast<int>(MPL::Variable::mechanical_strain)]);
     auto const& eps_m_prev = std::get<MPL::SymmetricTensor<DisplacementDim>>(
         variable_array_prev[static_cast<int>(
             MPL::Variable::mechanical_strain)]);
     auto const& sigma_prev = std::get<MPL::SymmetricTensor<DisplacementDim>>(
         variable_array_prev[static_cast<int>(MPL::Variable::stress)]);
     auto const T = std::get<double>(
         variable_array_prev[static_cast<int>(MPL::Variable::temperature)]);
  
     using Invariants = MathLib::KelvinVector::Invariants<KelvinVectorSize>;
  
     Eigen::FullPivLU<Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize,
                                    Eigen::RowMajor>>
         linear_solver;
  
     const auto C = this->getElasticTensor(t, x, T);
     KelvinVector sigma_try = sigma_prev + C * (eps_m - eps_m_prev);
  
     auto const& deviatoric_matrix = Invariants::deviatoric_projection;
  
     double const norm_s_try =
         Invariants::FrobeniusNorm(deviatoric_matrix * sigma_try);
     // In case |s_{try}| is zero and _n < 3 (rare case).
     if (norm_s_try < std::numeric_limits<double>::epsilon() * C(0, 0))
     {
         return {std::make_tuple(sigma_try, createMaterialStateVariables(), C)};
     }
  
     ResidualVectorType solution = sigma_try;
  
     const double A = _a(t, x)[0];
     const double n = _n(t, x)[0];
     const double sigma0 = _sigma_f(t, x)[0];
     const double Q = _q(t, x)[0];
  
     const double constant_coefficient =
         getCreepConstantCoefficient(A, n, sigma0);
  
     const double b =
         dt * constant_coefficient *
         std::exp(-Q / (MaterialLib::PhysicalConstant::IdealGasConstant * T));
  
     double const G2b = 2.0 * b * this->_mp.mu(t, x);
  
     auto const update_jacobian = [&solution, &G2b, &n](JacobianMatrix& jacobian)
     {
         auto const& D = Invariants::deviatoric_projection;
         KelvinVector const s_n1 = D * solution;
         double const norm_s_n1 = Invariants::FrobeniusNorm(s_n1);
         double const pow_norm_s_n1_n_minus_one_2b_G =
             G2b * std::pow(norm_s_n1, n - 1);
         jacobian = KelvinMatrix::Identity() +
                    (pow_norm_s_n1_n_minus_one_2b_G * D +
                     (n - 1) * G2b * std::pow(norm_s_n1, n - 3) * s_n1 *
                         s_n1.transpose());
     };
  
     auto const update_residual =
         [&solution, &G2b, &n, &sigma_try](ResidualVectorType& r)
     {
         KelvinVector const s_n1 = Invariants::deviatoric_projection * solution;
         double const norm_s_n1 = Invariants::FrobeniusNorm(s_n1);
         double const pow_norm_s_n1_n_minus_one_2b_G =
             G2b * std::pow(norm_s_n1, n - 1);
         r = solution - sigma_try + pow_norm_s_n1_n_minus_one_2b_G * s_n1;
     };
  
     auto const update_solution = [&](ResidualVectorType const& increment)
     { solution += increment; };
  
     auto newton_solver =
         NumLib::NewtonRaphson<decltype(linear_solver), JacobianMatrix,
                               decltype(update_jacobian), ResidualVectorType,
                               decltype(update_residual),
                               decltype(update_solution)>(
             linear_solver, update_jacobian, update_residual, update_solution,
             _nonlinear_solver_parameters);
  
     JacobianMatrix jacobian;
     auto const success_iterations = newton_solver.solve(jacobian);
  
     if (!success_iterations)
     {
         return {};
     }
  
     // If *success_iterations>0, tangentStiffness = J_(sigma)^{-1}C
     // where J_(sigma) is the Jacobian of the last local Newton-Raphson
     // iteration, which is already LU decomposed.
     KelvinMatrix tangentStiffness =
         (*success_iterations == 0) ? C : linear_solver.solve(C);
  
     return {std::make_tuple(solution, createMaterialStateVariables(),
                             tangentStiffness)};
 }