RichardsMechanicsFEM-impl.h

Go to the documentation of this file.

 
#pragma once
 
#include <Eigen/LU>
#include <cassert>
 
#include "ComputeMicroPorosity.h"
#include "ConstitutiveRelations/ConstitutiveModels.h"
#include "IntegrationPointData.h"
#include "MaterialLib/MPL/Medium.h"
#include "MaterialLib/MPL/Utils/FormEigenTensor.h"
#include "MaterialLib/SolidModels/SelectSolidConstitutiveRelation.h"
#include "MathLib/EigenBlockMatrixView.h"
#include "MathLib/KelvinVector.h"
#include "NumLib/Fem/Interpolation.h"
#include "ProcessLib/Utils/SetOrGetIntegrationPointData.h"
#include "ProcessLib/Utils/TransposeInPlace.h"
#include "RichardsMechanicsFEM.h"
 
namespace ProcessLib
{
namespace RichardsMechanics
{
template <int DisplacementDim>
void updateSwellingStressAndVolumetricStrain(
    MaterialPropertyLib::Medium const& medium,
    MaterialPropertyLib::Phase const& solid_phase,
    MathLib::KelvinVector::KelvinMatrixType<DisplacementDim> const& C_el,
    double const rho_LR, double const mu,
    std::optional<MicroPorosityParameters> micro_porosity_parameters,
    double const alpha, double const phi, double const p_cap_ip,
    MPL::VariableArray& variables, MPL::VariableArray& variables_prev,
    ParameterLib::SpatialPosition const& x_position, double const t,
    double const dt,
    ProcessLib::ThermoRichardsMechanics::ConstitutiveStress_StrainTemperature::
        SwellingDataStateful<DisplacementDim>& sigma_sw,
    PrevState<ProcessLib::ThermoRichardsMechanics::
                  ConstitutiveStress_StrainTemperature::SwellingDataStateful<
                      DisplacementDim>> const& sigma_sw_prev,
    PrevState<ProcessLib::ThermoRichardsMechanics::TransportPorosityData> const
        phi_M_prev,
    PrevState<ProcessLib::ThermoRichardsMechanics::PorosityData> const phi_prev,
    ProcessLib::ThermoRichardsMechanics::TransportPorosityData& phi_M,
    PrevState<MicroPressure> const p_L_m_prev,
    PrevState<MicroSaturation> const S_L_m_prev, MicroPressure& p_L_m,
    MicroSaturation& S_L_m)
{
    auto const& identity2 = MathLib::KelvinVector::Invariants<
        MathLib::KelvinVector::kelvin_vector_dimensions(
            DisplacementDim)>::identity2;
 
    if (!medium.hasProperty(MPL::PropertyType::saturation_micro))
    {
        // If there is swelling, compute it. Update volumetric strain rate,
        // s.t. it corresponds to the mechanical part only.
        sigma_sw = *sigma_sw_prev;
        if (solid_phase.hasProperty(MPL::PropertyType::swelling_stress_rate))
        {
            auto const sigma_sw_dot =
                MathLib::KelvinVector::tensorToKelvin<DisplacementDim>(
                    MPL::formEigenTensor<3>(
                        solid_phase[MPL::PropertyType::swelling_stress_rate]
                            .value(variables, variables_prev, x_position, t,
                                   dt)));
            sigma_sw.sigma_sw += sigma_sw_dot * dt;
 
            variables.volumetric_mechanical_strain =
                variables.volumetric_strain +
                identity2.transpose() * C_el.inverse() * sigma_sw.sigma_sw;
            variables_prev.volumetric_mechanical_strain =
                variables_prev.volumetric_strain + identity2.transpose() *
                                                       C_el.inverse() *
                                                       sigma_sw_prev->sigma_sw;
        }
        else
        {
            variables.volumetric_mechanical_strain =
                variables.volumetric_strain;
            variables_prev.volumetric_mechanical_strain =
                variables_prev.volumetric_strain;
        }
    }
 
    // TODO (naumov) saturation_micro must be always defined together with
    // the micro_porosity_parameters.
    if (medium.hasProperty(MPL::PropertyType::saturation_micro))
    {
        double const phi_m_prev = phi_prev->phi - phi_M_prev->phi;
 
        auto const [delta_phi_m, delta_e_sw, delta_p_L_m, delta_sigma_sw] =
            computeMicroPorosity<DisplacementDim>(
                identity2.transpose() * C_el.inverse(), rho_LR, mu,
                *micro_porosity_parameters, alpha, phi, -p_cap_ip, **p_L_m_prev,
                variables_prev, **S_L_m_prev, phi_m_prev, x_position, t, dt,
                medium.property(MPL::PropertyType::saturation_micro),
                solid_phase.property(MPL::PropertyType::swelling_stress_rate));
 
        phi_M.phi = phi - (phi_m_prev + delta_phi_m);
        variables_prev.transport_porosity = phi_M_prev->phi;
        variables.transport_porosity = phi_M.phi;
 
        *p_L_m = **p_L_m_prev + delta_p_L_m;
        {  // Update micro saturation.
            MPL::VariableArray variables_prev;
            variables_prev.capillary_pressure = -**p_L_m_prev;
            MPL::VariableArray variables;
            variables.capillary_pressure = -*p_L_m;
 
            *S_L_m = medium.property(MPL::PropertyType::saturation_micro)
                         .template value<double>(variables, x_position, t, dt);
        }
        sigma_sw.sigma_sw = sigma_sw_prev->sigma_sw + delta_sigma_sw;
    }
}
void updateSwellingStressAndVolumetricStrain( {…}
 
template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
          int DisplacementDim>
RichardsMechanicsLocalAssembler<ShapeFunctionDisplacement,
                                ShapeFunctionPressure, DisplacementDim>::
    RichardsMechanicsLocalAssembler(
        MeshLib::Element const& e,
        std::size_t const /*local_matrix_size*/,
        NumLib::GenericIntegrationMethod const& integration_method,
        bool const is_axially_symmetric,
        RichardsMechanicsProcessData<DisplacementDim>& process_data)
    : LocalAssemblerInterface<DisplacementDim>{
          e, integration_method, is_axially_symmetric, process_data}
{
    unsigned const n_integration_points =
        this->integration_method_.getNumberOfPoints();
 
    _ip_data.resize(n_integration_points);
    _secondary_data.N_u.resize(n_integration_points);
 
    auto const shape_matrices_u =
        NumLib::initShapeMatrices<ShapeFunctionDisplacement,
                                  ShapeMatricesTypeDisplacement,
                                  DisplacementDim>(e, is_axially_symmetric,
                                                   this->integration_method_);
 
    auto const shape_matrices_p =
        NumLib::initShapeMatrices<ShapeFunctionPressure,
                                  ShapeMatricesTypePressure, DisplacementDim>(
            e, is_axially_symmetric, this->integration_method_);
 
    auto const& medium =
        this->process_data_.media_map.getMedium(this->element_.getID());
 
    ParameterLib::SpatialPosition x_position;
    x_position.setElementID(this->element_.getID());
    for (unsigned ip = 0; ip < n_integration_points; ip++)
    {
        auto& ip_data = _ip_data[ip];
        auto const& sm_u = shape_matrices_u[ip];
        _ip_data[ip].integration_weight =
            this->integration_method_.getWeightedPoint(ip).getWeight() *
            sm_u.integralMeasure * sm_u.detJ;
 
        ip_data.N_u = sm_u.N;
        ip_data.dNdx_u = sm_u.dNdx;
 
        ip_data.N_p = shape_matrices_p[ip].N;
        ip_data.dNdx_p = shape_matrices_p[ip].dNdx;
 
        // Initial porosity. Could be read from integration point data or mesh.
        auto& porosity =
            std::get<ProcessLib::ThermoRichardsMechanics::PorosityData>(
                this->current_states_[ip])
                .phi;
        porosity = medium->property(MPL::porosity)
                       .template initialValue<double>(
                           x_position,
                           std::numeric_limits<
                               double>::quiet_NaN() /* t independent */);
 
        auto& transport_porosity =
            std::get<
                ProcessLib::ThermoRichardsMechanics::TransportPorosityData>(
                this->current_states_[ip])
                .phi;
        transport_porosity = porosity;
        if (medium->hasProperty(MPL::PropertyType::transport_porosity))
        {
            transport_porosity =
                medium->property(MPL::transport_porosity)
                    .template initialValue<double>(
                        x_position,
                        std::numeric_limits<
                            double>::quiet_NaN() /* t independent */);
        }
 
        _secondary_data.N_u[ip] = shape_matrices_u[ip].N;
    }
}
                                ShapeFunctionPressure, DisplacementDim>:: {…}
 
template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
          int DisplacementDim>
void RichardsMechanicsLocalAssembler<ShapeFunctionDisplacement,
                                     ShapeFunctionPressure, DisplacementDim>::
    setInitialConditionsConcrete(Eigen::VectorXd const local_x,
                                 double const t,
                                 int const /*process_id*/)
{
    assert(local_x.size() == pressure_size + displacement_size);
 
    auto const [p_L, u] = localDOF(local_x);
 
    constexpr double dt = std::numeric_limits<double>::quiet_NaN();
    auto const& medium =
        this->process_data_.media_map.getMedium(this->element_.getID());
    MPL::VariableArray variables;
 
    ParameterLib::SpatialPosition x_position;
    x_position.setElementID(this->element_.getID());
 
    auto const& solid_phase = medium->phase("Solid");
 
    auto const& identity2 = MathLib::KelvinVector::Invariants<
        MathLib::KelvinVector::kelvin_vector_dimensions(
            DisplacementDim)>::identity2;
 
    unsigned const n_integration_points =
        this->integration_method_.getNumberOfPoints();
    for (unsigned ip = 0; ip < n_integration_points; ip++)
    {
        auto const& N_p = _ip_data[ip].N_p;
 
        double p_cap_ip;
        NumLib::shapeFunctionInterpolate(-p_L, N_p, p_cap_ip);
 
        variables.capillary_pressure = p_cap_ip;
        variables.liquid_phase_pressure = -p_cap_ip;
        // setting pG to 1 atm
        // TODO : rewrite equations s.t. p_L = pG-p_cap
        variables.gas_phase_pressure = 1.0e5;
 
        {
            auto& p_L_m = std::get<MicroPressure>(this->current_states_[ip]);
            auto& p_L_m_prev =
                std::get<PrevState<MicroPressure>>(this->prev_states_[ip]);
            **p_L_m_prev = -p_cap_ip;
            *p_L_m = -p_cap_ip;
        }
 
        auto const temperature =
            medium->property(MPL::PropertyType::reference_temperature)
                .template value<double>(variables, x_position, t, dt);
        variables.temperature = temperature;
 
        auto& S_L_prev =
            std::get<
                PrevState<ProcessLib::ThermoRichardsMechanics::SaturationData>>(
                this->prev_states_[ip])
                ->S_L;
        S_L_prev = medium->property(MPL::PropertyType::saturation)
                       .template value<double>(variables, x_position, t, dt);
 
        if (this->process_data_.initial_stress.isTotalStress())
        {
            auto const alpha_b =
                medium->property(MPL::PropertyType::biot_coefficient)
                    .template value<double>(variables, x_position, t, dt);
 
            variables.liquid_saturation = S_L_prev;
            double const chi_S_L =
                medium->property(MPL::PropertyType::bishops_effective_stress)
                    .template value<double>(variables, x_position, t, dt);
 
            // Initial stresses are total stress, which were assigned to
            // sigma_eff in
            // RichardsMechanicsLocalAssembler::initializeConcrete().
            auto& sigma_eff =
                std::get<ProcessLib::ConstitutiveRelations::EffectiveStressData<
                    DisplacementDim>>(this->current_states_[ip]);
 
            auto& sigma_eff_prev =
                std::get<PrevState<ProcessLib::ConstitutiveRelations::
                                       EffectiveStressData<DisplacementDim>>>(
                    this->prev_states_[ip]);
 
            // Reset sigma_eff to effective stress
            sigma_eff.sigma_eff.noalias() +=
                chi_S_L * alpha_b * (-p_cap_ip) * identity2;
            sigma_eff_prev->sigma_eff = sigma_eff.sigma_eff;
        }
 
        if (medium->hasProperty(MPL::PropertyType::saturation_micro))
        {
            MPL::VariableArray vars;
            vars.capillary_pressure = p_cap_ip;
 
            auto& S_L_m = std::get<MicroSaturation>(this->current_states_[ip]);
            auto& S_L_m_prev =
                std::get<PrevState<MicroSaturation>>(this->prev_states_[ip]);
 
            *S_L_m = medium->property(MPL::PropertyType::saturation_micro)
                         .template value<double>(vars, x_position, t, dt);
            *S_L_m_prev = S_L_m;
        }
 
        // Set eps_m_prev from potentially non-zero eps and sigma_sw from
        // restart.
        auto const C_el = _ip_data[ip].computeElasticTangentStiffness(
            t, x_position, dt, temperature, this->solid_material_,
            *this->material_states_[ip].material_state_variables);
 
        auto const& N_u = _ip_data[ip].N_u;
        auto const& dNdx_u = _ip_data[ip].dNdx_u;
        auto const x_coord =
            NumLib::interpolateXCoordinate<ShapeFunctionDisplacement,
                                           ShapeMatricesTypeDisplacement>(
                this->element_, N_u);
        auto const B =
            LinearBMatrix::computeBMatrix<DisplacementDim,
                                          ShapeFunctionDisplacement::NPOINTS,
                                          typename BMatricesType::BMatrixType>(
                dNdx_u, N_u, x_coord, this->is_axially_symmetric_);
        auto& eps =
            std::get<StrainData<DisplacementDim>>(this->current_states_[ip])
                .eps;
        eps.noalias() = B * u;
 
        auto const& sigma_sw =
            std::get<ProcessLib::ThermoRichardsMechanics::
                         ConstitutiveStress_StrainTemperature::
                             SwellingDataStateful<DisplacementDim>>(
                this->current_states_[ip])
                .sigma_sw;
        auto& eps_m_prev =
            std::get<PrevState<ProcessLib::ConstitutiveRelations::
                                   MechanicalStrainData<DisplacementDim>>>(
                this->prev_states_[ip])
                ->eps_m;
 
        eps_m_prev.noalias() =
            solid_phase.hasProperty(MPL::PropertyType::swelling_stress_rate)
                ? eps + C_el.inverse() * sigma_sw
                : eps;
    }
}
                                     ShapeFunctionPressure, DisplacementDim>:: {…}
 
template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
          int DisplacementDim>
void RichardsMechanicsLocalAssembler<
    ShapeFunctionDisplacement, ShapeFunctionPressure,
    DisplacementDim>::assemble(double const t, double const dt,
                               std::vector<double> const& local_x,
                               std::vector<double> const& local_x_prev,
                               std::vector<double>& local_M_data,
                               std::vector<double>& local_K_data,
                               std::vector<double>& local_rhs_data)
{
    assert(local_x.size() == pressure_size + displacement_size);
 
    auto const [p_L, u] = localDOF(local_x);
    auto const [p_L_prev, u_prev] = localDOF(local_x_prev);
 
    auto K = MathLib::createZeroedMatrix<
        typename ShapeMatricesTypeDisplacement::template MatrixType<
            displacement_size + pressure_size,
            displacement_size + pressure_size>>(
        local_K_data, displacement_size + pressure_size,
        displacement_size + pressure_size);
 
    auto M = MathLib::createZeroedMatrix<
        typename ShapeMatricesTypeDisplacement::template MatrixType<
            displacement_size + pressure_size,
            displacement_size + pressure_size>>(
        local_M_data, displacement_size + pressure_size,
        displacement_size + pressure_size);
 
    auto rhs = MathLib::createZeroedVector<
        typename ShapeMatricesTypeDisplacement::template VectorType<
            displacement_size + pressure_size>>(
        local_rhs_data, displacement_size + pressure_size);
 
    auto const& identity2 = MathLib::KelvinVector::Invariants<
        MathLib::KelvinVector::kelvin_vector_dimensions(
            DisplacementDim)>::identity2;
 
    auto const& medium =
        this->process_data_.media_map.getMedium(this->element_.getID());
    auto const& liquid_phase = medium->phase("AqueousLiquid");
    auto const& solid_phase = medium->phase("Solid");
    MPL::VariableArray variables;
    MPL::VariableArray variables_prev;
 
    ParameterLib::SpatialPosition x_position;
    x_position.setElementID(this->element_.getID());
 
    unsigned const n_integration_points =
        this->integration_method_.getNumberOfPoints();
    for (unsigned ip = 0; ip < n_integration_points; ip++)
    {
        auto const& w = _ip_data[ip].integration_weight;
 
        auto const& N_u = _ip_data[ip].N_u;
        auto const& dNdx_u = _ip_data[ip].dNdx_u;
 
        auto const& N_p = _ip_data[ip].N_p;
        auto const& dNdx_p = _ip_data[ip].dNdx_p;
 
        auto const x_coord =
            NumLib::interpolateXCoordinate<ShapeFunctionDisplacement,
                                           ShapeMatricesTypeDisplacement>(
                this->element_, N_u);
        auto const B =
            LinearBMatrix::computeBMatrix<DisplacementDim,
                                          ShapeFunctionDisplacement::NPOINTS,
                                          typename BMatricesType::BMatrixType>(
                dNdx_u, N_u, x_coord, this->is_axially_symmetric_);
 
        auto& eps =
            std::get<StrainData<DisplacementDim>>(this->current_states_[ip]);
        eps.eps.noalias() = B * u;
 
        auto& S_L =
            std::get<ProcessLib::ThermoRichardsMechanics::SaturationData>(
                this->current_states_[ip])
                .S_L;
        auto const S_L_prev =
            std::get<
                PrevState<ProcessLib::ThermoRichardsMechanics::SaturationData>>(
                this->prev_states_[ip])
                ->S_L;
 
        double p_cap_ip;
        NumLib::shapeFunctionInterpolate(-p_L, N_p, p_cap_ip);
 
        double p_cap_prev_ip;
        NumLib::shapeFunctionInterpolate(-p_L_prev, N_p, p_cap_prev_ip);
 
        variables.capillary_pressure = p_cap_ip;
        variables.liquid_phase_pressure = -p_cap_ip;
        // setting pG to 1 atm
        // TODO : rewrite equations s.t. p_L = pG-p_cap
        variables.gas_phase_pressure = 1.0e5;
 
        auto const temperature =
            medium->property(MPL::PropertyType::reference_temperature)
                .template value<double>(variables, x_position, t, dt);
        variables.temperature = temperature;
 
        auto const alpha =
            medium->property(MPL::PropertyType::biot_coefficient)
                .template value<double>(variables, x_position, t, dt);
        auto const C_el = _ip_data[ip].computeElasticTangentStiffness(
            t, x_position, dt, temperature, this->solid_material_,
            *this->material_states_[ip].material_state_variables);
 
        auto const beta_SR = (1 - alpha) / this->solid_material_.getBulkModulus(
                                               t, x_position, &C_el);
        variables.grain_compressibility = beta_SR;
 
        auto const rho_LR =
            liquid_phase.property(MPL::PropertyType::density)
                .template value<double>(variables, x_position, t, dt);
        variables.density = rho_LR;
 
        auto const& b = this->process_data_.specific_body_force;
 
        S_L = medium->property(MPL::PropertyType::saturation)
                  .template value<double>(variables, x_position, t, dt);
        variables.liquid_saturation = S_L;
        variables_prev.liquid_saturation = S_L_prev;
 
        // tangent derivative for Jacobian
        double const dS_L_dp_cap =
            medium->property(MPL::PropertyType::saturation)
                .template dValue<double>(variables,
                                         MPL::Variable::capillary_pressure,
                                         x_position, t, dt);
        // secant derivative from time discretization for storage
        // use tangent, if secant is not available
        double const DeltaS_L_Deltap_cap =
            (p_cap_ip == p_cap_prev_ip)
                ? dS_L_dp_cap
                : (S_L - S_L_prev) / (p_cap_ip - p_cap_prev_ip);
 
        auto const chi = [medium, x_position, t, dt](double const S_L)
        {
            MPL::VariableArray vs;
            vs.liquid_saturation = S_L;
            return medium->property(MPL::PropertyType::bishops_effective_stress)
                .template value<double>(vs, x_position, t, dt);
        };
        double const chi_S_L = chi(S_L);
        double const chi_S_L_prev = chi(S_L_prev);
 
        double const p_FR = -chi_S_L * p_cap_ip;
        variables.effective_pore_pressure = p_FR;
        variables_prev.effective_pore_pressure = -chi_S_L_prev * p_cap_prev_ip;
 
        // Set volumetric strain rate for the general case without swelling.
        variables.volumetric_strain = Invariants::trace(eps.eps);
        variables_prev.volumetric_strain = Invariants::trace(B * u_prev);
 
        auto& phi = std::get<ProcessLib::ThermoRichardsMechanics::PorosityData>(
                        this->current_states_[ip])
                        .phi;
        {  // Porosity update
            auto const phi_prev = std::get<PrevState<
                ProcessLib::ThermoRichardsMechanics::PorosityData>>(
                                      this->prev_states_[ip])
                                      ->phi;
            variables_prev.porosity = phi_prev;
            phi = medium->property(MPL::PropertyType::porosity)
                      .template value<double>(variables, variables_prev,
                                              x_position, t, dt);
            variables.porosity = phi;
        }
 
        if (alpha < phi)
        {
            OGS_FATAL(
                "RichardsMechanics: Biot-coefficient {} is smaller than "
                "porosity {} in element/integration point {}/{}.",
                alpha, phi, this->element_.getID(), ip);
        }
 
        // Swelling and possibly volumetric strain rate update.
        {
            auto& sigma_sw =
                std::get<ProcessLib::ThermoRichardsMechanics::
                             ConstitutiveStress_StrainTemperature::
                                 SwellingDataStateful<DisplacementDim>>(
                    this->current_states_[ip])
                    .sigma_sw;
            auto const& sigma_sw_prev = std::get<PrevState<
                ProcessLib::ThermoRichardsMechanics::
                    ConstitutiveStress_StrainTemperature::SwellingDataStateful<
                        DisplacementDim>>>(this->prev_states_[ip])
                                            ->sigma_sw;
 
            // If there is swelling, compute it. Update volumetric strain rate,
            // s.t. it corresponds to the mechanical part only.
            sigma_sw = sigma_sw_prev;
            if (solid_phase.hasProperty(
                    MPL::PropertyType::swelling_stress_rate))
            {
                auto const sigma_sw_dot =
                    MathLib::KelvinVector::tensorToKelvin<DisplacementDim>(
                        MPL::formEigenTensor<3>(
                            solid_phase[MPL::PropertyType::swelling_stress_rate]
                                .value(variables, variables_prev, x_position, t,
                                       dt)));
                sigma_sw += sigma_sw_dot * dt;
 
                variables.volumetric_mechanical_strain =
                    variables.volumetric_strain +
                    identity2.transpose() * C_el.inverse() * sigma_sw;
                variables_prev.volumetric_mechanical_strain =
                    variables_prev.volumetric_strain +
                    identity2.transpose() * C_el.inverse() * sigma_sw_prev;
            }
            else
            {
                variables.volumetric_mechanical_strain =
                    variables.volumetric_strain;
                variables_prev.volumetric_mechanical_strain =
                    variables_prev.volumetric_strain;
            }
 
            if (medium->hasProperty(MPL::PropertyType::transport_porosity))
            {
                auto& transport_porosity =
                    std::get<ProcessLib::ThermoRichardsMechanics::
                                 TransportPorosityData>(
                        this->current_states_[ip])
                        .phi;
                auto const transport_porosity_prev =
                    std::get<PrevState<ProcessLib::ThermoRichardsMechanics::
                                           TransportPorosityData>>(
                        this->prev_states_[ip])
                        ->phi;
                variables_prev.transport_porosity = transport_porosity_prev;
 
                transport_porosity =
                    medium->property(MPL::PropertyType::transport_porosity)
                        .template value<double>(variables, variables_prev,
                                                x_position, t, dt);
                variables.transport_porosity = transport_porosity;
            }
            else
            {
                variables.transport_porosity = phi;
            }
        }
 
        double const k_rel =
            medium->property(MPL::PropertyType::relative_permeability)
                .template value<double>(variables, x_position, t, dt);
        auto const mu =
            liquid_phase.property(MPL::PropertyType::viscosity)
                .template value<double>(variables, x_position, t, dt);
 
        auto const& sigma_sw =
            std::get<ProcessLib::ThermoRichardsMechanics::
                         ConstitutiveStress_StrainTemperature::
                             SwellingDataStateful<DisplacementDim>>(
                this->current_states_[ip])
                .sigma_sw;
        auto const& sigma_eff =
            std::get<ProcessLib::ConstitutiveRelations::EffectiveStressData<
                DisplacementDim>>(this->current_states_[ip])
                .sigma_eff;
 
        // Set mechanical variables for the intrinsic permeability model
        // For stress dependent permeability.
        {
            auto const sigma_total =
                (sigma_eff - alpha * p_FR * identity2).eval();
 
            // For stress dependent permeability.
            variables.total_stress.emplace<SymmetricTensor>(
                MathLib::KelvinVector::kelvinVectorToSymmetricTensor(
                    sigma_total));
        }
 
        variables.equivalent_plastic_strain =
            this->material_states_[ip]
                .material_state_variables->getEquivalentPlasticStrain();
 
        auto const K_intrinsic = MPL::formEigenTensor<DisplacementDim>(
            medium->property(MPL::PropertyType::permeability)
                .value(variables, x_position, t, dt));
 
        GlobalDimMatrixType const rho_K_over_mu =
            K_intrinsic * rho_LR * k_rel / mu;
 
        //
        // displacement equation, displacement part
        //
        {
            auto& eps_m = std::get<ProcessLib::ConstitutiveRelations::
                                       MechanicalStrainData<DisplacementDim>>(
                              this->current_states_[ip])
                              .eps_m;
            eps_m.noalias() =
                solid_phase.hasProperty(MPL::PropertyType::swelling_stress_rate)
                    ? eps.eps + C_el.inverse() * sigma_sw
                    : eps.eps;
            variables.mechanical_strain.emplace<
                MathLib::KelvinVector::KelvinVectorType<DisplacementDim>>(
                eps_m);
        }
 
        {
            auto& SD = this->current_states_[ip];
            auto const& SD_prev = this->prev_states_[ip];
            auto& sigma_eff =
                std::get<ProcessLib::ConstitutiveRelations::EffectiveStressData<
                    DisplacementDim>>(SD);
            auto const& sigma_eff_prev =
                std::get<PrevState<ProcessLib::ConstitutiveRelations::
                                       EffectiveStressData<DisplacementDim>>>(
                    SD_prev);
            auto const& eps_m =
                std::get<ProcessLib::ConstitutiveRelations::
                             MechanicalStrainData<DisplacementDim>>(SD);
            auto& eps_m_prev =
                std::get<PrevState<ProcessLib::ConstitutiveRelations::
                                       MechanicalStrainData<DisplacementDim>>>(
                    SD_prev);
 
            _ip_data[ip].updateConstitutiveRelation(
                variables, t, x_position, dt, temperature, sigma_eff,
                sigma_eff_prev, eps_m, eps_m_prev, this->solid_material_,
                this->material_states_[ip].material_state_variables);
        }
 
        // p_SR
        variables.solid_grain_pressure =
            p_FR - sigma_eff.dot(identity2) / (3 * (1 - phi));
        auto const rho_SR =
            solid_phase.property(MPL::PropertyType::density)
                .template value<double>(variables, x_position, t, dt);
 
        //
        // displacement equation, displacement part
        //
        double const rho = rho_SR * (1 - phi) + S_L * phi * rho_LR;
        rhs.template segment<displacement_size>(displacement_index).noalias() -=
            (B.transpose() * sigma_eff - N_u_op(N_u).transpose() * rho * b) * w;
 
        //
        // pressure equation, pressure part.
        //
        auto const beta_LR =
            1 / rho_LR *
            liquid_phase.property(MPL::PropertyType::density)
                .template dValue<double>(variables,
                                         MPL::Variable::liquid_phase_pressure,
                                         x_position, t, dt);
 
        double const a0 = S_L * (alpha - phi) * beta_SR;
        // Volumetric average specific storage of the solid and fluid phases.
        double const specific_storage =
            DeltaS_L_Deltap_cap * (p_cap_ip * a0 - phi) +
            S_L * (phi * beta_LR + a0);
        M.template block<pressure_size, pressure_size>(pressure_index,
                                                       pressure_index)
            .noalias() += N_p.transpose() * rho_LR * specific_storage * N_p * w;
 
        K.template block<pressure_size, pressure_size>(pressure_index,
                                                       pressure_index)
            .noalias() += dNdx_p.transpose() * rho_K_over_mu * dNdx_p * w;
 
        rhs.template segment<pressure_size>(pressure_index).noalias() +=
            dNdx_p.transpose() * rho_LR * rho_K_over_mu * b * w;
 
        //
        // displacement equation, pressure part
        //
        K.template block<displacement_size, pressure_size>(displacement_index,
                                                           pressure_index)
            .noalias() -= B.transpose() * alpha * chi_S_L * identity2 * N_p * w;
 
        //
        // pressure equation, displacement part.
        //
        M.template block<pressure_size, displacement_size>(pressure_index,
                                                           displacement_index)
            .noalias() += N_p.transpose() * S_L * rho_LR * alpha *
                          identity2.transpose() * B * w;
    }
 
    if (this->process_data_.apply_mass_lumping)
    {
        auto Mpp = M.template block<pressure_size, pressure_size>(
            pressure_index, pressure_index);
        Mpp = Mpp.colwise().sum().eval().asDiagonal();
    }
}
    DisplacementDim>::assemble(double const t, double const dt, {…}
 
template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
          int DisplacementDim>
void RichardsMechanicsLocalAssembler<ShapeFunctionDisplacement,
                                     ShapeFunctionPressure, DisplacementDim>::
    assembleWithJacobianEvalConstitutiveSetting(
        double const t, double const dt,
        ParameterLib::SpatialPosition const& x_position,
        RichardsMechanicsLocalAssembler<ShapeFunctionDisplacement,
                                        ShapeFunctionPressure,
                                        DisplacementDim>::IpData& ip_data,
        MPL::VariableArray& variables, MPL::VariableArray& variables_prev,
        MPL::Medium const* const medium, TemperatureData const T_data,
        CapillaryPressureData<DisplacementDim> const& p_cap_data,
        ConstitutiveData<DisplacementDim>& CD,
        StatefulData<DisplacementDim>& SD,
        StatefulDataPrev<DisplacementDim> const& SD_prev,
        std::optional<MicroPorosityParameters> const& micro_porosity_parameters,
        MaterialLib::Solids::MechanicsBase<DisplacementDim> const&
            solid_material,
        ProcessLib::ThermoRichardsMechanics::MaterialStateData<DisplacementDim>&
            material_state_data)
{
    auto const& liquid_phase = medium->phase("AqueousLiquid");
    auto const& solid_phase = medium->phase("Solid");
 
    auto const& identity2 = MathLib::KelvinVector::Invariants<
        MathLib::KelvinVector::kelvin_vector_dimensions(
            DisplacementDim)>::identity2;
 
    double const temperature = T_data();
    double const p_cap_ip = p_cap_data.p_cap;
    double const p_cap_prev_ip = p_cap_data.p_cap_prev;
 
    auto const& eps = std::get<StrainData<DisplacementDim>>(SD);
    auto& S_L =
        std::get<ProcessLib::ThermoRichardsMechanics::SaturationData>(SD).S_L;
    auto const S_L_prev =
        std::get<
            PrevState<ProcessLib::ThermoRichardsMechanics::SaturationData>>(
            SD_prev)
            ->S_L;
    auto const alpha =
        medium->property(MPL::PropertyType::biot_coefficient)
            .template value<double>(variables, x_position, t, dt);
    *std::get<ProcessLib::ThermoRichardsMechanics::BiotData>(CD) = alpha;
 
    auto const C_el = ip_data.computeElasticTangentStiffness(
        t, x_position, dt, temperature, solid_material,
        *material_state_data.material_state_variables);
 
    auto const beta_SR =
        (1 - alpha) / solid_material.getBulkModulus(t, x_position, &C_el);
    variables.grain_compressibility = beta_SR;
    std::get<ProcessLib::ThermoRichardsMechanics::SolidCompressibilityData>(CD)
        .beta_SR = beta_SR;
 
    auto const rho_LR =
        liquid_phase.property(MPL::PropertyType::density)
            .template value<double>(variables, x_position, t, dt);
    variables.density = rho_LR;
    *std::get<LiquidDensity>(CD) = rho_LR;
 
    S_L = medium->property(MPL::PropertyType::saturation)
              .template value<double>(variables, x_position, t, dt);
    variables.liquid_saturation = S_L;
    variables_prev.liquid_saturation = S_L_prev;
 
    // tangent derivative for Jacobian
    double const dS_L_dp_cap =
        medium->property(MPL::PropertyType::saturation)
            .template dValue<double>(variables,
                                     MPL::Variable::capillary_pressure,
                                     x_position, t, dt);
    std::get<ProcessLib::ThermoRichardsMechanics::SaturationDataDeriv>(CD)
        .dS_L_dp_cap = dS_L_dp_cap;
    // secant derivative from time discretization for storage
    // use tangent, if secant is not available
    double const DeltaS_L_Deltap_cap =
        (p_cap_ip == p_cap_prev_ip)
            ? dS_L_dp_cap
            : (S_L - S_L_prev) / (p_cap_ip - p_cap_prev_ip);
    std::get<SaturationSecantDerivative>(CD).DeltaS_L_Deltap_cap =
        DeltaS_L_Deltap_cap;
 
    auto const chi = [medium, x_position, t, dt](double const S_L)
    {
        MPL::VariableArray vs;
        vs.liquid_saturation = S_L;
        return medium->property(MPL::PropertyType::bishops_effective_stress)
            .template value<double>(vs, x_position, t, dt);
    };
    double const chi_S_L = chi(S_L);
    std::get<ProcessLib::ThermoRichardsMechanics::BishopsData>(CD).chi_S_L =
        chi_S_L;
    double const chi_S_L_prev = chi(S_L_prev);
    std::get<PrevState<ProcessLib::ThermoRichardsMechanics::BishopsData>>(CD)
        ->chi_S_L = chi_S_L_prev;
 
    auto const dchi_dS_L =
        medium->property(MPL::PropertyType::bishops_effective_stress)
            .template dValue<double>(
                variables, MPL::Variable::liquid_saturation, x_position, t, dt);
    std::get<ProcessLib::ThermoRichardsMechanics::BishopsData>(CD).dchi_dS_L =
        dchi_dS_L;
 
    double const p_FR = -chi_S_L * p_cap_ip;
    variables.effective_pore_pressure = p_FR;
    variables_prev.effective_pore_pressure = -chi_S_L_prev * p_cap_prev_ip;
 
    // Set volumetric strain rate for the general case without swelling.
    variables.volumetric_strain = Invariants::trace(eps.eps);
    // TODO (CL) changed that, using eps_prev for the moment, not B * u_prev
    // variables_prev.volumetric_strain = Invariants::trace(B * u_prev);
    variables_prev.volumetric_strain = Invariants::trace(
        std::get<PrevState<StrainData<DisplacementDim>>>(SD_prev)->eps);
 
    auto& phi =
        std::get<ProcessLib::ThermoRichardsMechanics::PorosityData>(SD).phi;
    {  // Porosity update
        auto const phi_prev =
            std::get<
                PrevState<ProcessLib::ThermoRichardsMechanics::PorosityData>>(
                SD_prev)
                ->phi;
        variables_prev.porosity = phi_prev;
        phi = medium->property(MPL::PropertyType::porosity)
                  .template value<double>(variables, variables_prev, x_position,
                                          t, dt);
        variables.porosity = phi;
    }
    std::get<ProcessLib::ThermoRichardsMechanics::PorosityData>(CD).phi = phi;
 
    if (alpha < phi)
    {
        auto const eid =
            x_position.getElementID()
                ? static_cast<std::ptrdiff_t>(*x_position.getElementID())
                : static_cast<std::ptrdiff_t>(-1);
        OGS_FATAL(
            "RichardsMechanics: Biot-coefficient {} is smaller than porosity "
            "{} in element {}.",
            alpha, phi, eid);
    }
 
    auto const mu = liquid_phase.property(MPL::PropertyType::viscosity)
                        .template value<double>(variables, x_position, t, dt);
    *std::get<ProcessLib::ThermoRichardsMechanics::LiquidViscosityData>(CD) =
        mu;
 
    {
        // Swelling and possibly volumetric strain rate update.
        auto& sigma_sw =
            std::get<ProcessLib::ThermoRichardsMechanics::
                         ConstitutiveStress_StrainTemperature::
                             SwellingDataStateful<DisplacementDim>>(SD);
        auto const& sigma_sw_prev =
            std::get<PrevState<ProcessLib::ThermoRichardsMechanics::
                                   ConstitutiveStress_StrainTemperature::
                                       SwellingDataStateful<DisplacementDim>>>(
                SD_prev);
        auto const transport_porosity_prev = std::get<PrevState<
            ProcessLib::ThermoRichardsMechanics::TransportPorosityData>>(
            SD_prev);
        auto const phi_prev = std::get<
            PrevState<ProcessLib::ThermoRichardsMechanics::PorosityData>>(
            SD_prev);
        auto& transport_porosity = std::get<
            ProcessLib::ThermoRichardsMechanics::TransportPorosityData>(SD);
        auto& p_L_m = std::get<MicroPressure>(SD);
        auto const p_L_m_prev = std::get<PrevState<MicroPressure>>(SD_prev);
        auto& S_L_m = std::get<MicroSaturation>(SD);
        auto const S_L_m_prev = std::get<PrevState<MicroSaturation>>(SD_prev);
 
        updateSwellingStressAndVolumetricStrain<DisplacementDim>(
            *medium, solid_phase, C_el, rho_LR, mu, micro_porosity_parameters,
            alpha, phi, p_cap_ip, variables, variables_prev, x_position, t, dt,
            sigma_sw, sigma_sw_prev, transport_porosity_prev, phi_prev,
            transport_porosity, p_L_m_prev, S_L_m_prev, p_L_m, S_L_m);
    }
 
    if (medium->hasProperty(MPL::PropertyType::transport_porosity))
    {
        if (!medium->hasProperty(MPL::PropertyType::saturation_micro))
        {
            auto& transport_porosity =
                std::get<
                    ProcessLib::ThermoRichardsMechanics::TransportPorosityData>(
                    SD)
                    .phi;
            auto const transport_porosity_prev = std::get<PrevState<
                ProcessLib::ThermoRichardsMechanics::TransportPorosityData>>(
                                                     SD_prev)
                                                     ->phi;
            variables_prev.transport_porosity = transport_porosity_prev;
 
            transport_porosity =
                medium->property(MPL::PropertyType::transport_porosity)
                    .template value<double>(variables, variables_prev,
                                            x_position, t, dt);
            variables.transport_porosity = transport_porosity;
        }
    }
    else
    {
        variables.transport_porosity = phi;
    }
 
    // Set mechanical variables for the intrinsic permeability model
    // For stress dependent permeability.
    {
        // TODO mechanical constitutive relation will be evaluated afterwards
        auto const sigma_total =
            (std::get<ProcessLib::ConstitutiveRelations::EffectiveStressData<
                 DisplacementDim>>(SD)
                 .sigma_eff +
             alpha * p_FR * identity2)
                .eval();
        // For stress dependent permeability.
        variables.total_stress.emplace<SymmetricTensor>(
            MathLib::KelvinVector::kelvinVectorToSymmetricTensor(sigma_total));
    }
 
    variables.equivalent_plastic_strain =
        material_state_data.material_state_variables
            ->getEquivalentPlasticStrain();
 
    double const k_rel =
        medium->property(MPL::PropertyType::relative_permeability)
            .template value<double>(variables, x_position, t, dt);
 
    auto const K_intrinsic = MPL::formEigenTensor<DisplacementDim>(
        medium->property(MPL::PropertyType::permeability)
            .value(variables, x_position, t, dt));
 
    std::get<
        ProcessLib::ThermoRichardsMechanics::PermeabilityData<DisplacementDim>>(
        CD)
        .k_rel = k_rel;
    std::get<
        ProcessLib::ThermoRichardsMechanics::PermeabilityData<DisplacementDim>>(
        CD)
        .Ki = K_intrinsic;
 
    //
    // displacement equation, displacement part
    //
 
    {
        auto& sigma_sw =
            std::get<ProcessLib::ThermoRichardsMechanics::
                         ConstitutiveStress_StrainTemperature::
                             SwellingDataStateful<DisplacementDim>>(SD)
                .sigma_sw;
 
        auto& eps_m =
            std::get<ProcessLib::ConstitutiveRelations::MechanicalStrainData<
                DisplacementDim>>(SD)
                .eps_m;
        eps_m.noalias() =
            solid_phase.hasProperty(MPL::PropertyType::swelling_stress_rate)
                ? eps.eps + C_el.inverse() * sigma_sw
                : eps.eps;
        variables.mechanical_strain
            .emplace<MathLib::KelvinVector::KelvinVectorType<DisplacementDim>>(
                eps_m);
    }
 
    {
        auto& sigma_eff =
            std::get<ProcessLib::ConstitutiveRelations::EffectiveStressData<
                DisplacementDim>>(SD);
        auto const& sigma_eff_prev =
            std::get<PrevState<ProcessLib::ConstitutiveRelations::
                                   EffectiveStressData<DisplacementDim>>>(
                SD_prev);
        auto const& eps_m =
            std::get<ProcessLib::ConstitutiveRelations::MechanicalStrainData<
                DisplacementDim>>(SD);
        auto& eps_m_prev =
            std::get<PrevState<ProcessLib::ConstitutiveRelations::
                                   MechanicalStrainData<DisplacementDim>>>(
                SD_prev);
 
        auto C = ip_data.updateConstitutiveRelation(
            variables, t, x_position, dt, temperature, sigma_eff,
            sigma_eff_prev, eps_m, eps_m_prev, solid_material,
            material_state_data.material_state_variables);
 
        *std::get<StiffnessTensor<DisplacementDim>>(CD) = std::move(C);
    }
 
    // p_SR
    variables.solid_grain_pressure =
        p_FR - std::get<ProcessLib::ConstitutiveRelations::EffectiveStressData<
                   DisplacementDim>>(SD)
                       .sigma_eff.dot(identity2) /
                   (3 * (1 - phi));
    auto const rho_SR =
        solid_phase.property(MPL::PropertyType::density)
            .template value<double>(variables, x_position, t, dt);
 
    double const rho = rho_SR * (1 - phi) + S_L * phi * rho_LR;
    *std::get<Density>(CD) = rho;
}
                                     ShapeFunctionPressure, DisplacementDim>:: {…}
 
template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
          int DisplacementDim>
void RichardsMechanicsLocalAssembler<ShapeFunctionDisplacement,
                                     ShapeFunctionPressure, DisplacementDim>::
    assembleWithJacobian(double const t, double const dt,
                         std::vector<double> const& local_x,
                         std::vector<double> const& local_x_prev,
                         std::vector<double>& local_rhs_data,
                         std::vector<double>& local_Jac_data)
{
    assert(local_x.size() == pressure_size + displacement_size);
 
    auto const [p_L, u] = localDOF(local_x);
    auto const [p_L_prev, u_prev] = localDOF(local_x_prev);
 
    auto local_Jac = MathLib::createZeroedMatrix<
        typename ShapeMatricesTypeDisplacement::template MatrixType<
            displacement_size + pressure_size,
            displacement_size + pressure_size>>(
        local_Jac_data, displacement_size + pressure_size,
        displacement_size + pressure_size);
 
    auto local_rhs = MathLib::createZeroedVector<
        typename ShapeMatricesTypeDisplacement::template VectorType<
            displacement_size + pressure_size>>(
        local_rhs_data, displacement_size + pressure_size);
 
    auto const& identity2 = MathLib::KelvinVector::Invariants<
        MathLib::KelvinVector::kelvin_vector_dimensions(
            DisplacementDim)>::identity2;
 
    typename ShapeMatricesTypePressure::NodalMatrixType laplace_p =
        ShapeMatricesTypePressure::NodalMatrixType::Zero(pressure_size,
                                                         pressure_size);
 
    typename ShapeMatricesTypePressure::NodalMatrixType storage_p_a_p =
        ShapeMatricesTypePressure::NodalMatrixType::Zero(pressure_size,
                                                         pressure_size);
 
    typename ShapeMatricesTypePressure::NodalMatrixType storage_p_a_S_Jpp =
        ShapeMatricesTypePressure::NodalMatrixType::Zero(pressure_size,
                                                         pressure_size);
 
    typename ShapeMatricesTypePressure::NodalMatrixType storage_p_a_S =
        ShapeMatricesTypePressure::NodalMatrixType::Zero(pressure_size,
                                                         pressure_size);
 
    typename ShapeMatricesTypeDisplacement::template MatrixType<
        displacement_size, pressure_size>
        Kup = ShapeMatricesTypeDisplacement::template MatrixType<
            displacement_size, pressure_size>::Zero(displacement_size,
                                                    pressure_size);
 
    typename ShapeMatricesTypeDisplacement::template MatrixType<
        pressure_size, displacement_size>
        Kpu = ShapeMatricesTypeDisplacement::template MatrixType<
            pressure_size, displacement_size>::Zero(pressure_size,
                                                    displacement_size);
 
    auto const& medium =
        this->process_data_.media_map.getMedium(this->element_.getID());
    auto const& liquid_phase = medium->phase("AqueousLiquid");
    auto const& solid_phase = medium->phase("Solid");
    MPL::VariableArray variables;
    MPL::VariableArray variables_prev;
 
    ParameterLib::SpatialPosition x_position;
    x_position.setElementID(this->element_.getID());
 
    unsigned const n_integration_points =
        this->integration_method_.getNumberOfPoints();
    for (unsigned ip = 0; ip < n_integration_points; ip++)
    {
        ConstitutiveData<DisplacementDim> CD;
        auto& SD = this->current_states_[ip];
        auto const& SD_prev = this->prev_states_[ip];
        [[maybe_unused]] auto models = createConstitutiveModels(
            this->process_data_, this->solid_material_);
 
        auto const& w = _ip_data[ip].integration_weight;
 
        auto const& N_u = _ip_data[ip].N_u;
        auto const& dNdx_u = _ip_data[ip].dNdx_u;
 
        auto const& N_p = _ip_data[ip].N_p;
        auto const& dNdx_p = _ip_data[ip].dNdx_p;
 
        auto const x_coord =
            NumLib::interpolateXCoordinate<ShapeFunctionDisplacement,
                                           ShapeMatricesTypeDisplacement>(
                this->element_, N_u);
        auto const B =
            LinearBMatrix::computeBMatrix<DisplacementDim,
                                          ShapeFunctionDisplacement::NPOINTS,
                                          typename BMatricesType::BMatrixType>(
                dNdx_u, N_u, x_coord, this->is_axially_symmetric_);
 
        double p_cap_ip;
        NumLib::shapeFunctionInterpolate(-p_L, N_p, p_cap_ip);
 
        double p_cap_prev_ip;
        NumLib::shapeFunctionInterpolate(-p_L_prev, N_p, p_cap_prev_ip);
 
        variables.capillary_pressure = p_cap_ip;
        variables.liquid_phase_pressure = -p_cap_ip;
        // setting pG to 1 atm
        // TODO : rewrite equations s.t. p_L = pG-p_cap
        variables.gas_phase_pressure = 1.0e5;
 
        auto const temperature =
            medium->property(MPL::PropertyType::reference_temperature)
                .template value<double>(variables, x_position, t, dt);
        variables.temperature = temperature;
 
        std::get<StrainData<DisplacementDim>>(SD).eps.noalias() = B * u;
 
        assembleWithJacobianEvalConstitutiveSetting(
            t, dt, x_position, _ip_data[ip], variables, variables_prev, medium,
            TemperatureData{temperature},
            CapillaryPressureData<DisplacementDim>{
                p_cap_ip, p_cap_prev_ip,
                Eigen::Vector<double, DisplacementDim>::Zero()},
            CD, SD, SD_prev, this->process_data_.micro_porosity_parameters,
            this->solid_material_, this->material_states_[ip]);
 
        {
            auto const& C = *std::get<StiffnessTensor<DisplacementDim>>(CD);
            local_Jac
                .template block<displacement_size, displacement_size>(
                    displacement_index, displacement_index)
                .noalias() += B.transpose() * C * B * w;
        }
 
        auto const& b = this->process_data_.specific_body_force;
 
        {
            auto const& sigma_eff =
                std::get<ProcessLib::ConstitutiveRelations::EffectiveStressData<
                    DisplacementDim>>(this->current_states_[ip])
                    .sigma_eff;
            double const rho = *std::get<Density>(CD);
            local_rhs.template segment<displacement_size>(displacement_index)
                .noalias() -= (B.transpose() * sigma_eff -
                               N_u_op(N_u).transpose() * rho * b) *
                              w;
        }
 
        //
        // displacement equation, pressure part
        //
 
        double const alpha =
            *std::get<ProcessLib::ThermoRichardsMechanics::BiotData>(CD);
        double const dS_L_dp_cap =
            std::get<ProcessLib::ThermoRichardsMechanics::SaturationDataDeriv>(
                CD)
                .dS_L_dp_cap;
 
        {
            double const chi_S_L =
                std::get<ProcessLib::ThermoRichardsMechanics::BishopsData>(CD)
                    .chi_S_L;
            Kup.noalias() +=
                B.transpose() * alpha * chi_S_L * identity2 * N_p * w;
            double const dchi_dS_L =
                std::get<ProcessLib::ThermoRichardsMechanics::BishopsData>(CD)
                    .dchi_dS_L;
 
            local_Jac
                .template block<displacement_size, pressure_size>(
                    displacement_index, pressure_index)
                .noalias() -= B.transpose() * alpha *
                              (chi_S_L + dchi_dS_L * p_cap_ip * dS_L_dp_cap) *
                              identity2 * N_p * w;
        }
 
        double const phi =
            std::get<ProcessLib::ThermoRichardsMechanics::PorosityData>(CD).phi;
        double const rho_LR = *std::get<LiquidDensity>(CD);
        local_Jac
            .template block<displacement_size, pressure_size>(
                displacement_index, pressure_index)
            .noalias() +=
            N_u_op(N_u).transpose() * phi * rho_LR * dS_L_dp_cap * b * N_p * w;
 
        // For the swelling stress with double structure model the corresponding
        // Jacobian u-p entry would be required, but it does not improve
        // convergence and sometimes worsens it:
        // if (medium->hasProperty(MPL::PropertyType::saturation_micro))
        // {
        //     -B.transpose() *
        //         dsigma_sw_dS_L_m* dS_L_m_dp_cap_m*(p_L_m - p_L_m_prev) /
        //         (p_cap_ip - p_cap_prev_ip) * N_p* w;
        // }
        if (!medium->hasProperty(MPL::PropertyType::saturation_micro) &&
            solid_phase.hasProperty(MPL::PropertyType::swelling_stress_rate))
        {
            using DimMatrix = Eigen::Matrix<double, 3, 3>;
            auto const dsigma_sw_dS_L =
                MathLib::KelvinVector::tensorToKelvin<DisplacementDim>(
                    solid_phase
                        .property(MPL::PropertyType::swelling_stress_rate)
                        .template dValue<DimMatrix>(
                            variables, variables_prev,
                            MPL::Variable::liquid_saturation, x_position, t,
                            dt));
            local_Jac
                .template block<displacement_size, pressure_size>(
                    displacement_index, pressure_index)
                .noalias() +=
                B.transpose() * dsigma_sw_dS_L * dS_L_dp_cap * N_p * w;
        }
        //
        // pressure equation, displacement part.
        //
        double const S_L =
            std::get<ProcessLib::ThermoRichardsMechanics::SaturationData>(
                this->current_states_[ip])
                .S_L;
        if (this->process_data_.explicit_hm_coupling_in_unsaturated_zone)
        {
            double const chi_S_L_prev = std::get<PrevState<
                ProcessLib::ThermoRichardsMechanics::BishopsData>>(CD)
                                            ->chi_S_L;
            Kpu.noalias() += N_p.transpose() * chi_S_L_prev * rho_LR * alpha *
                             identity2.transpose() * B * w;
        }
        else
        {
            Kpu.noalias() += N_p.transpose() * S_L * rho_LR * alpha *
                             identity2.transpose() * B * w;
        }
 
        //
        // pressure equation, pressure part.
        //
 
        double const k_rel =
            std::get<ProcessLib::ThermoRichardsMechanics::PermeabilityData<
                DisplacementDim>>(CD)
                .k_rel;
        auto const& K_intrinsic =
            std::get<ProcessLib::ThermoRichardsMechanics::PermeabilityData<
                DisplacementDim>>(CD)
                .Ki;
        double const mu =
            *std::get<ProcessLib::ThermoRichardsMechanics::LiquidViscosityData>(
                CD);
 
        GlobalDimMatrixType const rho_Ki_over_mu = K_intrinsic * rho_LR / mu;
 
        laplace_p.noalias() +=
            dNdx_p.transpose() * k_rel * rho_Ki_over_mu * dNdx_p * w;
 
        auto const beta_LR =
            1 / rho_LR *
            liquid_phase.property(MPL::PropertyType::density)
                .template dValue<double>(variables,
                                         MPL::Variable::liquid_phase_pressure,
                                         x_position, t, dt);
 
        double const beta_SR =
            std::get<
                ProcessLib::ThermoRichardsMechanics::SolidCompressibilityData>(
                CD)
                .beta_SR;
        double const a0 = (alpha - phi) * beta_SR;
        double const specific_storage_a_p = S_L * (phi * beta_LR + S_L * a0);
        double const specific_storage_a_S = phi - p_cap_ip * S_L * a0;
 
        double const dspecific_storage_a_p_dp_cap =
            dS_L_dp_cap * (phi * beta_LR + 2 * S_L * a0);
        double const dspecific_storage_a_S_dp_cap =
            -a0 * (S_L + p_cap_ip * dS_L_dp_cap);
 
        storage_p_a_p.noalias() +=
            N_p.transpose() * rho_LR * specific_storage_a_p * N_p * w;
 
        double const DeltaS_L_Deltap_cap =
            std::get<SaturationSecantDerivative>(CD).DeltaS_L_Deltap_cap;
        storage_p_a_S.noalias() -= N_p.transpose() * rho_LR *
                                   specific_storage_a_S * DeltaS_L_Deltap_cap *
                                   N_p * w;
 
        local_Jac
            .template block<pressure_size, pressure_size>(pressure_index,
                                                          pressure_index)
            .noalias() += N_p.transpose() * (p_cap_ip - p_cap_prev_ip) / dt *
                          rho_LR * dspecific_storage_a_p_dp_cap * N_p * w;
 
        double const S_L_prev =
            std::get<
                PrevState<ProcessLib::ThermoRichardsMechanics::SaturationData>>(
                this->prev_states_[ip])
                ->S_L;
        storage_p_a_S_Jpp.noalias() -=
            N_p.transpose() * rho_LR *
            ((S_L - S_L_prev) * dspecific_storage_a_S_dp_cap +
             specific_storage_a_S * dS_L_dp_cap) /
            dt * N_p * w;
 
        if (!this->process_data_.explicit_hm_coupling_in_unsaturated_zone)
        {
            local_Jac
                .template block<pressure_size, pressure_size>(pressure_index,
                                                              pressure_index)
                .noalias() -= N_p.transpose() * rho_LR * dS_L_dp_cap * alpha *
                              identity2.transpose() * B * (u - u_prev) / dt *
                              N_p * w;
        }
 
        double const dk_rel_dS_l =
            medium->property(MPL::PropertyType::relative_permeability)
                .template dValue<double>(variables,
                                         MPL::Variable::liquid_saturation,
                                         x_position, t, dt);
        typename ShapeMatricesTypeDisplacement::GlobalDimVectorType const
            grad_p_cap = -dNdx_p * p_L;
        local_Jac
            .template block<pressure_size, pressure_size>(pressure_index,
                                                          pressure_index)
            .noalias() += dNdx_p.transpose() * rho_Ki_over_mu * grad_p_cap *
                          dk_rel_dS_l * dS_L_dp_cap * N_p * w;
 
        local_Jac
            .template block<pressure_size, pressure_size>(pressure_index,
                                                          pressure_index)
            .noalias() += dNdx_p.transpose() * rho_LR * rho_Ki_over_mu * b *
                          dk_rel_dS_l * dS_L_dp_cap * N_p * w;
 
        local_rhs.template segment<pressure_size>(pressure_index).noalias() +=
            dNdx_p.transpose() * rho_LR * k_rel * rho_Ki_over_mu * b * w;
 
        if (medium->hasProperty(MPL::PropertyType::saturation_micro))
        {
            double const alpha_bar =
                this->process_data_.micro_porosity_parameters
                    ->mass_exchange_coefficient;
            auto const p_L_m =
                *std::get<MicroPressure>(this->current_states_[ip]);
            local_rhs.template segment<pressure_size>(pressure_index)
                .noalias() -=
                N_p.transpose() * alpha_bar / mu * (-p_cap_ip - p_L_m) * w;
 
            local_Jac
                .template block<pressure_size, pressure_size>(pressure_index,
                                                              pressure_index)
                .noalias() += N_p.transpose() * alpha_bar / mu * N_p * w;
            if (p_cap_ip != p_cap_prev_ip)
            {
                auto const p_L_m_prev = **std::get<PrevState<MicroPressure>>(
                    this->prev_states_[ip]);
                local_Jac
                    .template block<pressure_size, pressure_size>(
                        pressure_index, pressure_index)
                    .noalias() += N_p.transpose() * alpha_bar / mu *
                                  (p_L_m - p_L_m_prev) /
                                  (p_cap_ip - p_cap_prev_ip) * N_p * w;
            }
        }
    }
 
    if (this->process_data_.apply_mass_lumping)
    {
        storage_p_a_p = storage_p_a_p.colwise().sum().eval().asDiagonal();
        storage_p_a_S = storage_p_a_S.colwise().sum().eval().asDiagonal();
        storage_p_a_S_Jpp =
            storage_p_a_S_Jpp.colwise().sum().eval().asDiagonal();
    }
 
    // pressure equation, pressure part.
    local_Jac
        .template block<pressure_size, pressure_size>(pressure_index,
                                                      pressure_index)
        .noalias() += laplace_p + storage_p_a_p / dt + storage_p_a_S_Jpp;
 
    // pressure equation, displacement part.
    local_Jac
        .template block<pressure_size, displacement_size>(pressure_index,
                                                          displacement_index)
        .noalias() = Kpu / dt;
 
    // pressure equation
    local_rhs.template segment<pressure_size>(pressure_index).noalias() -=
        laplace_p * p_L +
        (storage_p_a_p + storage_p_a_S) * (p_L - p_L_prev) / dt +
        Kpu * (u - u_prev) / dt;
 
    // displacement equation
    local_rhs.template segment<displacement_size>(displacement_index)
        .noalias() += Kup * p_L;
}
                                     ShapeFunctionPressure, DisplacementDim>:: {…}
 
template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
          int DisplacementDim>
void RichardsMechanicsLocalAssembler<ShapeFunctionDisplacement,
                                     ShapeFunctionPressure, DisplacementDim>::
    assembleWithJacobianForPressureEquations(
        const double /*t*/, double const /*dt*/,
        Eigen::VectorXd const& /*local_x*/,
        Eigen::VectorXd const& /*local_x_prev*/,
        std::vector<double>& /*local_b_data*/,
        std::vector<double>& /*local_Jac_data*/)
{
    OGS_FATAL("RichardsMechanics; The staggered scheme is not implemented.");
}
                                     ShapeFunctionPressure, DisplacementDim>:: {…}
 
template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
          int DisplacementDim>
void RichardsMechanicsLocalAssembler<ShapeFunctionDisplacement,
                                     ShapeFunctionPressure, DisplacementDim>::
    assembleWithJacobianForDeformationEquations(
        const double /*t*/, double const /*dt*/,
        Eigen::VectorXd const& /*local_x*/,
        Eigen::VectorXd const& /*local_x_prev*/,
        std::vector<double>& /*local_b_data*/,
        std::vector<double>& /*local_Jac_data*/)
{
    OGS_FATAL("RichardsMechanics; The staggered scheme is not implemented.");
}
                                     ShapeFunctionPressure, DisplacementDim>:: {…}
 
template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
          int DisplacementDim>
void RichardsMechanicsLocalAssembler<ShapeFunctionDisplacement,
                                     ShapeFunctionPressure, DisplacementDim>::
    assembleWithJacobianForStaggeredScheme(double const t, double const dt,
                                           Eigen::VectorXd const& local_x,
                                           Eigen::VectorXd const& local_x_prev,
                                           int const process_id,
                                           std::vector<double>& local_b_data,
                                           std::vector<double>& local_Jac_data)
{
    // For the equations with pressure
    if (process_id == 0)
    {
        assembleWithJacobianForPressureEquations(t, dt, local_x, local_x_prev,
                                                 local_b_data, local_Jac_data);
        return;
    }
 
    // For the equations with deformation
    assembleWithJacobianForDeformationEquations(t, dt, local_x, local_x_prev,
                                                local_b_data, local_Jac_data);
}
                                     ShapeFunctionPressure, DisplacementDim>:: {…}
 
template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
          int DisplacementDim>
void RichardsMechanicsLocalAssembler<ShapeFunctionDisplacement,
                                     ShapeFunctionPressure, DisplacementDim>::
    computeSecondaryVariableConcrete(double const t, double const dt,
                                     Eigen::VectorXd const& local_x,
                                     Eigen::VectorXd const& local_x_prev)
{
    auto const [p_L, u] = localDOF(local_x);
    auto const [p_L_prev, u_prev] = localDOF(local_x_prev);
 
    auto const& identity2 = MathLib::KelvinVector::Invariants<
        MathLib::KelvinVector::kelvin_vector_dimensions(
            DisplacementDim)>::identity2;
 
    auto const& medium =
        this->process_data_.media_map.getMedium(this->element_.getID());
    auto const& liquid_phase = medium->phase("AqueousLiquid");
    auto const& solid_phase = medium->phase("Solid");
    MPL::VariableArray variables;
    MPL::VariableArray variables_prev;
 
    ParameterLib::SpatialPosition x_position;
    x_position.setElementID(this->element_.getID());
 
    unsigned const n_integration_points =
        this->integration_method_.getNumberOfPoints();
 
    double saturation_avg = 0;
    double porosity_avg = 0;
 
    using KV = MathLib::KelvinVector::KelvinVectorType<DisplacementDim>;
    KV sigma_avg = KV::Zero();
 
    for (unsigned ip = 0; ip < n_integration_points; ip++)
    {
        auto const& N_p = _ip_data[ip].N_p;
        auto const& N_u = _ip_data[ip].N_u;
        auto const& dNdx_u = _ip_data[ip].dNdx_u;
 
        auto const x_coord =
            NumLib::interpolateXCoordinate<ShapeFunctionDisplacement,
                                           ShapeMatricesTypeDisplacement>(
                this->element_, N_u);
        auto const B =
            LinearBMatrix::computeBMatrix<DisplacementDim,
                                          ShapeFunctionDisplacement::NPOINTS,
                                          typename BMatricesType::BMatrixType>(
                dNdx_u, N_u, x_coord, this->is_axially_symmetric_);
 
        double p_cap_ip;
        NumLib::shapeFunctionInterpolate(-p_L, N_p, p_cap_ip);
 
        double p_cap_prev_ip;
        NumLib::shapeFunctionInterpolate(-p_L_prev, N_p, p_cap_prev_ip);
 
        variables.capillary_pressure = p_cap_ip;
        variables.liquid_phase_pressure = -p_cap_ip;
        // setting pG to 1 atm
        // TODO : rewrite equations s.t. p_L = pG-p_cap
        variables.gas_phase_pressure = 1.0e5;
 
        auto const temperature =
            medium->property(MPL::PropertyType::reference_temperature)
                .template value<double>(variables, x_position, t, dt);
        variables.temperature = temperature;
 
        auto& eps =
            std::get<StrainData<DisplacementDim>>(this->current_states_[ip])
                .eps;
        eps.noalias() = B * u;
        auto& S_L =
            std::get<ProcessLib::ThermoRichardsMechanics::SaturationData>(
                this->current_states_[ip])
                .S_L;
        auto const S_L_prev =
            std::get<
                PrevState<ProcessLib::ThermoRichardsMechanics::SaturationData>>(
                this->prev_states_[ip])
                ->S_L;
        S_L = medium->property(MPL::PropertyType::saturation)
                  .template value<double>(variables, x_position, t, dt);
        variables.liquid_saturation = S_L;
        variables_prev.liquid_saturation = S_L_prev;
 
        auto const chi = [medium, x_position, t, dt](double const S_L)
        {
            MPL::VariableArray vs;
            vs.liquid_saturation = S_L;
            return medium->property(MPL::PropertyType::bishops_effective_stress)
                .template value<double>(vs, x_position, t, dt);
        };
        double const chi_S_L = chi(S_L);
        double const chi_S_L_prev = chi(S_L_prev);
 
        auto const alpha =
            medium->property(MPL::PropertyType::biot_coefficient)
                .template value<double>(variables, x_position, t, dt);
 
        auto const C_el = _ip_data[ip].computeElasticTangentStiffness(
            t, x_position, dt, temperature, this->solid_material_,
            *this->material_states_[ip].material_state_variables);
 
        auto const beta_SR = (1 - alpha) / this->solid_material_.getBulkModulus(
                                               t, x_position, &C_el);
        variables.grain_compressibility = beta_SR;
 
        variables.effective_pore_pressure = -chi_S_L * p_cap_ip;
        variables_prev.effective_pore_pressure = -chi_S_L_prev * p_cap_prev_ip;
 
        // Set volumetric strain rate for the general case without swelling.
        variables.volumetric_strain = Invariants::trace(eps);
        variables_prev.volumetric_strain = Invariants::trace(B * u_prev);
 
        auto& phi = std::get<ProcessLib::ThermoRichardsMechanics::PorosityData>(
                        this->current_states_[ip])
                        .phi;
        {  // Porosity update
            auto const phi_prev = std::get<PrevState<
                ProcessLib::ThermoRichardsMechanics::PorosityData>>(
                                      this->prev_states_[ip])
                                      ->phi;
            variables_prev.porosity = phi_prev;
            phi = medium->property(MPL::PropertyType::porosity)
                      .template value<double>(variables, variables_prev,
                                              x_position, t, dt);
            variables.porosity = phi;
        }
 
        auto const rho_LR =
            liquid_phase.property(MPL::PropertyType::density)
                .template value<double>(variables, x_position, t, dt);
        variables.density = rho_LR;
        auto const mu =
            liquid_phase.property(MPL::PropertyType::viscosity)
                .template value<double>(variables, x_position, t, dt);
 
        {
            // Swelling and possibly volumetric strain rate update.
            auto& sigma_sw =
                std::get<ProcessLib::ThermoRichardsMechanics::
                             ConstitutiveStress_StrainTemperature::
                                 SwellingDataStateful<DisplacementDim>>(
                    this->current_states_[ip]);
            auto const& sigma_sw_prev = std::get<
                PrevState<ProcessLib::ThermoRichardsMechanics::
                              ConstitutiveStress_StrainTemperature::
                                  SwellingDataStateful<DisplacementDim>>>(
                this->prev_states_[ip]);
            auto const transport_porosity_prev = std::get<PrevState<
                ProcessLib::ThermoRichardsMechanics::TransportPorosityData>>(
                this->prev_states_[ip]);
            auto const phi_prev = std::get<
                PrevState<ProcessLib::ThermoRichardsMechanics::PorosityData>>(
                this->prev_states_[ip]);
            auto& transport_porosity = std::get<
                ProcessLib::ThermoRichardsMechanics::TransportPorosityData>(
                this->current_states_[ip]);
            auto& p_L_m = std::get<MicroPressure>(this->current_states_[ip]);
            auto const p_L_m_prev =
                std::get<PrevState<MicroPressure>>(this->prev_states_[ip]);
            auto& S_L_m = std::get<MicroSaturation>(this->current_states_[ip]);
            auto const S_L_m_prev =
                std::get<PrevState<MicroSaturation>>(this->prev_states_[ip]);
 
            updateSwellingStressAndVolumetricStrain<DisplacementDim>(
                *medium, solid_phase, C_el, rho_LR, mu,
                this->process_data_.micro_porosity_parameters, alpha, phi,
                p_cap_ip, variables, variables_prev, x_position, t, dt,
                sigma_sw, sigma_sw_prev, transport_porosity_prev, phi_prev,
                transport_porosity, p_L_m_prev, S_L_m_prev, p_L_m, S_L_m);
        }
 
        if (medium->hasProperty(MPL::PropertyType::transport_porosity))
        {
            if (!medium->hasProperty(MPL::PropertyType::saturation_micro))
            {
                auto& transport_porosity =
                    std::get<ProcessLib::ThermoRichardsMechanics::
                                 TransportPorosityData>(
                        this->current_states_[ip])
                        .phi;
                auto const transport_porosity_prev =
                    std::get<PrevState<ProcessLib::ThermoRichardsMechanics::
                                           TransportPorosityData>>(
                        this->prev_states_[ip])
                        ->phi;
 
                variables_prev.transport_porosity = transport_porosity_prev;
 
                transport_porosity =
                    medium->property(MPL::PropertyType::transport_porosity)
                        .template value<double>(variables, variables_prev,
                                                x_position, t, dt);
                variables.transport_porosity = transport_porosity;
            }
        }
        else
        {
            variables.transport_porosity = phi;
        }
 
        auto const& sigma_eff =
            std::get<ProcessLib::ConstitutiveRelations::EffectiveStressData<
                DisplacementDim>>(this->current_states_[ip])
                .sigma_eff;
 
        // Set mechanical variables for the intrinsic permeability model
        // For stress dependent permeability.
        {
            auto const sigma_total =
                (sigma_eff + alpha * chi_S_L * identity2 * p_cap_ip).eval();
            // For stress dependent permeability.
            variables.total_stress.emplace<SymmetricTensor>(
                MathLib::KelvinVector::kelvinVectorToSymmetricTensor(
                    sigma_total));
        }
 
        variables.equivalent_plastic_strain =
            this->material_states_[ip]
                .material_state_variables->getEquivalentPlasticStrain();
 
        auto const K_intrinsic = MPL::formEigenTensor<DisplacementDim>(
            medium->property(MPL::PropertyType::permeability)
                .value(variables, x_position, t, dt));
 
        double const k_rel =
            medium->property(MPL::PropertyType::relative_permeability)
                .template value<double>(variables, x_position, t, dt);
 
        GlobalDimMatrixType const K_over_mu = k_rel * K_intrinsic / mu;
 
        double const p_FR = -chi_S_L * p_cap_ip;
        // p_SR
        variables.solid_grain_pressure =
            p_FR - sigma_eff.dot(identity2) / (3 * (1 - phi));
        auto const rho_SR =
            solid_phase.property(MPL::PropertyType::density)
                .template value<double>(variables, x_position, t, dt);
        *std::get<DrySolidDensity>(this->output_data_[ip]) = (1 - phi) * rho_SR;
 
        {
            auto& SD = this->current_states_[ip];
            auto const& sigma_sw =
                std::get<ProcessLib::ThermoRichardsMechanics::
                             ConstitutiveStress_StrainTemperature::
                                 SwellingDataStateful<DisplacementDim>>(SD)
                    .sigma_sw;
            auto& eps_m =
                std::get<ProcessLib::ConstitutiveRelations::
                             MechanicalStrainData<DisplacementDim>>(SD)
                    .eps_m;
            eps_m.noalias() =
                solid_phase.hasProperty(MPL::PropertyType::swelling_stress_rate)
                    ? eps + C_el.inverse() * sigma_sw
                    : eps;
            variables.mechanical_strain.emplace<
                MathLib::KelvinVector::KelvinVectorType<DisplacementDim>>(
                eps_m);
        }
 
        {
            auto& SD = this->current_states_[ip];
            auto const& SD_prev = this->prev_states_[ip];
            auto& sigma_eff =
                std::get<ProcessLib::ConstitutiveRelations::EffectiveStressData<
                    DisplacementDim>>(SD);
            auto const& sigma_eff_prev =
                std::get<PrevState<ProcessLib::ConstitutiveRelations::
                                       EffectiveStressData<DisplacementDim>>>(
                    SD_prev);
            auto const& eps_m =
                std::get<ProcessLib::ConstitutiveRelations::
                             MechanicalStrainData<DisplacementDim>>(SD);
            auto const& eps_m_prev =
                std::get<PrevState<ProcessLib::ConstitutiveRelations::
                                       MechanicalStrainData<DisplacementDim>>>(
                    SD_prev);
 
            _ip_data[ip].updateConstitutiveRelation(
                variables, t, x_position, dt, temperature, sigma_eff,
                sigma_eff_prev, eps_m, eps_m_prev, this->solid_material_,
                this->material_states_[ip].material_state_variables);
        }
 
        auto const& b = this->process_data_.specific_body_force;
 
        // Compute the velocity
        auto const& dNdx_p = _ip_data[ip].dNdx_p;
        std::get<
            ProcessLib::ThermoRichardsMechanics::DarcyLawData<DisplacementDim>>(
            this->output_data_[ip])
            ->noalias() = -K_over_mu * dNdx_p * p_L + rho_LR * K_over_mu * b;
 
        saturation_avg += S_L;
        porosity_avg += phi;
        sigma_avg += sigma_eff;
    }
    saturation_avg /= n_integration_points;
    porosity_avg /= n_integration_points;
    sigma_avg /= n_integration_points;
 
    (*this->process_data_.element_saturation)[this->element_.getID()] =
        saturation_avg;
    (*this->process_data_.element_porosity)[this->element_.getID()] =
        porosity_avg;
 
    Eigen::Map<KV>(
        &(*this->process_data_.element_stresses)[this->element_.getID() *
                                                 KV::RowsAtCompileTime]) =
        MathLib::KelvinVector::kelvinVectorToSymmetricTensor(sigma_avg);
 
    NumLib::interpolateToHigherOrderNodes<
        ShapeFunctionPressure, typename ShapeFunctionDisplacement::MeshElement,
        DisplacementDim>(this->element_, this->is_axially_symmetric_, p_L,
                         *this->process_data_.pressure_interpolated);
}
                                     ShapeFunctionPressure, DisplacementDim>:: {…}
}  // namespace RichardsMechanics
}  // namespace ProcessLib