Detailed Description

template<int DisplacementDim>
class MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >

Permeability model as proposed by Olivella&Alonso.

This property must be a medium property, it computes the permeability in dependence of the strain

The model was proposed in [2] and it was further investigated in [31] .

The model takes the form of

\[ \mathbf{k} = k_\text{m} \mathbf{I} + \frac{b}{a} \left( \frac{b^2}{12} - k_\text{m} \right) \left( \mathbf{I} - \mathbf{M} \right) \]

with

\[ \mathbf{M} = \vec{n} \otimes \vec{n} \]

and

\[ b = b_0 + \Delta b \\ \Delta b = a \langle \varepsilon_\text{n}- \varepsilon_0 \rangle \]

where

\( k_\text{m} \)	permeability of undisturbed material
\( b \)	fracture aperture
\( b_0 \)	initial aperture
\( a \)	mean fracture distance
\( \vec{n} \)	fracture normal vector
\( \varepsilon_n \)	strain in fracture normal direction
\( \varepsilon_0 \)	threshold strain

Definition at line 50 of file EmbeddedFracturePermeability.h.

#include <EmbeddedFracturePermeability.h>

Inheritance diagram for MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >:

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Collaboration diagram for MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >:

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

Public Member Functions
	EmbeddedFracturePermeability (std::string name, Eigen::Matrix< double, 3, 1 > const fracture_normal, bool const fracture_normal_is_constant, double const intrinsic_permeability, double const initial_aperture, double const mean_fracture_distance, double const threshold_strain, ParameterLib::Parameter< double > const &fracture_rotation_xy, ParameterLib::Parameter< double > const &fracture_rotation_yz, double const jacobian_factor)

void	checkScale () const override

PropertyDataType	value (VariableArray const &variable_array, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const override

PropertyDataType	dValue (VariableArray const &variable_array, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const override

Public Member Functions inherited from MaterialPropertyLib::Property
virtual	~Property ()

virtual PropertyDataType	initialValue (ParameterLib::SpatialPosition const &pos, double const t) const

virtual PropertyDataType	value () const

virtual PropertyDataType	value (VariableArray const &variable_array, VariableArray const &variable_array_prev, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

virtual PropertyDataType	dValue (VariableArray const &variable_array, VariableArray const &variable_array_prev, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

virtual PropertyDataType	d2Value (VariableArray const &variable_array, Variable const variable1, Variable const variable2, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const
	Default implementation: 2nd derivative of any constant property is zero.

virtual void	setProperties (std::vector< std::unique_ptr< Phase > > const &phases)
	Default implementation:

void	setScale (std::variant< Medium , Phase , Component * > scale)

template<typename T >
T	initialValue (ParameterLib::SpatialPosition const &pos, double const t) const

template<typename T >
T	value () const

template<typename T >
T	value (VariableArray const &variable_array, VariableArray const &variable_array_prev, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	value (VariableArray const &variable_array, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	dValue (VariableArray const &variable_array, VariableArray const &variable_array_prev, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	dValue (VariableArray const &variable_array, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	d2Value (VariableArray const &variable_array, Variable const &variable1, Variable const &variable2, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

Static Public Attributes
static int const	KelvinVectorSize

Private Attributes
Medium *	_medium = nullptr

Eigen::Matrix< double, 3, 1 > const	_n

bool const	_n_const

double const	_k

double const	_b0

double const	_a

double const	_e0

ParameterLib::Parameter< double > const &	_phi_xy

ParameterLib::Parameter< double > const &	_phi_yz

double const	_jf

Additional Inherited Members
Protected Attributes inherited from MaterialPropertyLib::Property
std::string	name_

PropertyDataType	value_
	The single value of a property.

PropertyDataType	dvalue_

std::variant< Medium , Phase , Component * >	scale_

Member Typedef Documentation

◆ SymmetricTensor

template<int DisplacementDim>

using MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >::SymmetricTensor = Eigen::Matrix<double, KelvinVectorSize, 1>

Definition at line 79 of file EmbeddedFracturePermeability.h.

Constructor & Destructor Documentation

◆ EmbeddedFracturePermeability()

template<int DisplacementDim>

MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >::EmbeddedFracturePermeability	(	std::string	name,
		Eigen::Matrix< double, 3, 1 > const	fracture_normal,
		bool const	fracture_normal_is_constant,
		double const	intrinsic_permeability,
		double const	initial_aperture,
		double const	mean_fracture_distance,
		double const	threshold_strain,
		ParameterLib::Parameter< double > const &	fracture_rotation_xy,
		ParameterLib::Parameter< double > const &	fracture_rotation_yz,
		double const	jacobian_factor )

Definition at line 22 of file EmbeddedFracturePermeability.cpp.

    : _n(fracture_normal),
      _n_const(fracture_normal_is_constant),
      _k(intrinsic_permeability),
      _b0(initial_aperture),
      _a(mean_fracture_distance),
      _e0(threshold_strain),
      _phi_xy(fracture_rotation_xy),
      _phi_yz(fracture_rotation_yz),
      _jf(jacobian_factor)
{
    name_ = std::move(name);
}

References MaterialPropertyLib::name, and MaterialPropertyLib::Property::name_.

Member Function Documentation

◆ checkScale()

template<int DisplacementDim>

void MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >::checkScale ( ) const

overridevirtual

Reimplemented from MaterialPropertyLib::Property.

Definition at line 47 of file EmbeddedFracturePermeability.cpp.

{
    if (!std::holds_alternative<Medium*>(scale_))
    {
        OGS_FATAL(
            "The property 'EmbeddedFracturePermeability' is "
            "implemented on the 'medium' scale only.");
    }
}

References OGS_FATAL.

◆ dValue()

template<int DisplacementDim>

PropertyDataType MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >::dValue	(	VariableArray const &	variable_array,
		Variable const	variable,
		ParameterLib::SpatialPosition const &	pos,
		double const	t,
		double const	dt ) const

overridevirtual

This virtual method will compute the property derivative value based on the variables that are passed as arguments with the default implementation using empty variables array for the previous time step.

The default implementation of this method only returns the property value derivative without altering it.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 97 of file EmbeddedFracturePermeability.cpp.

{
    if (variable != Variable::mechanical_strain)
    {
        OGS_FATAL(
            "EmbeddedFracturePermeability::dValue is implemented for "
            "derivatives with respect to strain only.");
    }
 
    Eigen::Matrix<double, 3, 1> const n = [&]
    {
        if (_n_const)
        {
            return _n;
        }
        auto const sigma = formEigenTensor<3>(
            std::get<SymmetricTensor>(variable_array.total_stress));
        Eigen::SelfAdjointEigenSolver<Eigen::Matrix<double, 3, 3>> e_s(sigma);
        return (Eigen::Matrix<double, 3, 1>)e_s.eigenvectors().col(2);
    }();
 
    auto const rotMat_xy =
        Eigen::AngleAxisd(_phi_xy(t, pos)[0], Eigen::Vector3d::UnitZ());
    auto const rotMat_yz =
        Eigen::AngleAxisd(_phi_yz(t, pos)[0], Eigen::Vector3d::UnitX());
 
    Eigen::Matrix<double, 3, 1> const n_r = rotMat_yz * (rotMat_xy * n);
 
    auto const eps = MathLib::KelvinVector::kelvinVectorToTensor(
        std::get<MathLib::KelvinVector::KelvinVectorType<DisplacementDim>>(
            variable_array.mechanical_strain));
    double const e_n = (eps * n_r).dot(n_r.transpose());
    double const H_de = (e_n > _e0) ? 1.0 : 0.0;
    double const b_f = _b0 + H_de * _a * (e_n - _e0);
 
    Eigen::Matrix3d const M = n_r * n_r.transpose();
    return Eigen::MatrixXd(
        _jf * H_de * (b_f * b_f / 4 - _k) *
        MathLib::KelvinVector::tensorToKelvin<DisplacementDim>(
            Eigen::Matrix3d::Identity() - M) *
        MathLib::KelvinVector::tensorToKelvin<DisplacementDim>(M).transpose());
}

References MaterialPropertyLib::formEigenTensor< 3 >(), MathLib::KelvinVector::kelvinVectorToTensor(), MaterialPropertyLib::mechanical_strain, MaterialPropertyLib::VariableArray::mechanical_strain, OGS_FATAL, MathLib::KelvinVector::tensorToKelvin(), and MaterialPropertyLib::VariableArray::total_stress.

◆ value()

template<int DisplacementDim>

PropertyDataType MaterialPropertyLib::EmbeddedFracturePermeability< DisplacementDim >::value	(	VariableArray const &	variable_array,
		ParameterLib::SpatialPosition const &	pos,
		double const	t,
		double const	dt ) const

overridevirtual

This virtual method will compute the property value based on the variables that are passed as arguments with the default implementation using empty variables array for the previous time step.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 58 of file EmbeddedFracturePermeability.cpp.

{
    Eigen::Matrix<double, 3, 1> const n = [&]
    {
        if (_n_const)
        {
            return _n;
        }
        auto const sigma = formEigenTensor<3>(
            std::get<SymmetricTensor>(variable_array.total_stress));
        Eigen::SelfAdjointEigenSolver<Eigen::Matrix<double, 3, 3>> e_s(sigma);
        return (Eigen::Matrix<double, 3, 1>)e_s.eigenvectors().col(2);
    }();
 
    auto const rotMat_xy =
        Eigen::AngleAxisd(_phi_xy(t, pos)[0], Eigen::Vector3d::UnitZ());
    auto const rotMat_yz =
        Eigen::AngleAxisd(_phi_yz(t, pos)[0], Eigen::Vector3d::UnitX());
 
    Eigen::Matrix<double, 3, 1> const n_r = rotMat_yz * (rotMat_xy * n);
 
    auto const eps = MathLib::KelvinVector::kelvinVectorToTensor(
        std::get<MathLib::KelvinVector::KelvinVectorType<DisplacementDim>>(
            variable_array.mechanical_strain));
    double const e_n = (eps * n_r).dot(n_r.transpose());
    double const H_de = (e_n > _e0) ? 1.0 : 0.0;
    double const b_f = _b0 + H_de * _a * (e_n - _e0);
    double const coeff = H_de * (b_f / _a) * ((b_f * b_f / 12.0) - _k);
 
    Eigen::Matrix3d I = Eigen::Matrix3d::Identity();
    return (coeff * (I - n_r * n_r.transpose()) + _k * I)
        .template topLeftCorner<DisplacementDim, DisplacementDim>()
        .eval();
}