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 31 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
using	KelvinVector
using	KelvinMatrix
using	Parameter = ParameterLib::Parameter<double>
Public Types inherited from MaterialLib::Solids::LinearElasticIsotropic< DisplacementDim >
using	KelvinVector
using	KelvinMatrix
Public Types inherited from MaterialLib::Solids::MechanicsBase< DisplacementDim >
using	KelvinVector
using	KelvinMatrix

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.
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 void	initializeInternalStateVariables (double const, ParameterLib::SpatialPosition const &, typename MechanicsBase< DisplacementDim >::MaterialStateVariables &) const
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.
Parameter const &	_sigma_f
	Creep rate exponent n.
Parameter const &	_q
	A stress scaling factor.

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

Initial value:

Eigen::Matrix<double, KelvinVectorSize,

KelvinVectorSize, Eigen::RowMajor>

MaterialLib::Solids::LinearElasticIsotropic::KelvinVectorSize

static int const KelvinVectorSize

Definition SolidModels/LinearElasticIsotropic.h:57

Definition at line 36 of file CreepBGRa.h.

◆ KelvinMatrix

template<int DisplacementDim>

using MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::KelvinMatrix

Initial value:

MathLib::KelvinVector::KelvinMatrixType<DisplacementDim>

MathLib::KelvinVector::KelvinMatrixType

Eigen::Matrix< double, kelvin_vector_dimensions(DisplacementDim), kelvin_vector_dimensions(DisplacementDim), Eigen::RowMajor > KelvinMatrixType

Definition KelvinVector.h:49

Definition at line 41 of file CreepBGRa.h.

◆ KelvinVector

template<int DisplacementDim>

using MaterialLib::Solids::Creep::CreepBGRa< DisplacementDim >::KelvinVector

Initial value:

MathLib::KelvinVector::KelvinVectorType<DisplacementDim>

MathLib::KelvinVector::KelvinVectorType

Eigen::Matrix< double, kelvin_vector_dimensions(DisplacementDim), 1, Eigen::ColMajor > KelvinVectorType

Definition KelvinVector.h:41

Definition at line 39 of file CreepBGRa.h.

◆ Parameter

template<int DisplacementDim>

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

Definition at line 44 of file CreepBGRa.h.

◆ ResidualVectorType

template<int DisplacementDim>

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

Definition at line 35 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 56 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)
    {
    }

References MaterialLib::Solids::LinearElasticIsotropic< DisplacementDim >::LinearElasticIsotropic(), _a, _n, _nonlinear_solver_parameters, _q, and _sigma_f.

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 50 of file CreepBGRa.h.

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

References MaterialLib::Solids::LinearElasticIsotropic< DisplacementDim >::LinearElasticIsotropic(), and createMaterialStateVariables().

Referenced by createMaterialStateVariables(), and integrateStress().

◆ 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 81 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 130 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 _a, MaterialLib::Solids::LinearElasticIsotropic< DisplacementDim >::_mp, _n, _q, _sigma_f, 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 31 of file CreepBGRa.cpp.

{
    auto const& eps_m = std::get<MPL::SymmetricTensor<DisplacementDim>>(
        variable_array.mechanical_strain);
    auto const& eps_m_prev = std::get<MPL::SymmetricTensor<DisplacementDim>>(
        variable_array_prev.mechanical_strain);
    auto const& sigma_prev = std::get<MPL::SymmetricTensor<DisplacementDim>>(
        variable_array_prev.stress);
    auto const T = variable_array_prev.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(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)};
}