SmallDeformationLocalAssemblerMatrix-impl.h

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// SPDX-FileCopyrightText: Copyright (c) OpenGeoSys Community (opengeosys.org)
// SPDX-License-Identifier: BSD-3-Clause
 
#pragma once
 
#include <Eigen/Core>
#include <vector>
 
#include "IntegrationPointDataMatrix.h"
#include "MaterialLib/PhysicalConstant.h"
#include "MaterialLib/SolidModels/SelectSolidConstitutiveRelation.h"
#include "MathLib/KelvinVector.h"
#include "MathLib/LinAlg/Eigen/EigenMapTools.h"
#include "NumLib/Fem/InitShapeMatrices.h"
#include "NumLib/Fem/ShapeMatrixPolicy.h"
#include "ProcessLib/Deformation/BMatrixPolicy.h"
#include "ProcessLib/Deformation/LinearBMatrix.h"
#include "ProcessLib/LIE/SmallDeformation/SmallDeformationProcessData.h"
#include "ProcessLib/Utils/SetOrGetIntegrationPointData.h"
#include "SecondaryData.h"
#include "SmallDeformationLocalAssemblerInterface.h"
#include "SmallDeformationLocalAssemblerMatrix.h"
 
namespace ProcessLib
{
namespace LIE
{
namespace SmallDeformation
{
template <typename ShapeFunction, int DisplacementDim>
SmallDeformationLocalAssemblerMatrix<ShapeFunction, DisplacementDim>::
    SmallDeformationLocalAssemblerMatrix(
        MeshLib::Element const& e,
        std::size_t const /*local_matrix_size*/,
        NumLib::GenericIntegrationMethod const& integration_method,
        bool const is_axially_symmetric,
        SmallDeformationProcessData<DisplacementDim>& process_data)
    : _process_data(process_data),
      _integration_method(integration_method),
      _element(e),
      _is_axially_symmetric(is_axially_symmetric)
{
    unsigned const n_integration_points =
        _integration_method.getNumberOfPoints();
 
    _ip_data.reserve(n_integration_points);
    _secondary_data.N.resize(n_integration_points);
 
    auto const shape_matrices =
        NumLib::initShapeMatrices<ShapeFunction, ShapeMatricesType,
                                  DisplacementDim>(e, is_axially_symmetric,
                                                   _integration_method);
 
    auto& solid_material = MaterialLib::Solids::selectSolidConstitutiveRelation(
        _process_data.solid_materials, _process_data.material_ids, e.getID());
 
    for (unsigned ip = 0; ip < n_integration_points; ip++)
    {
        _ip_data.emplace_back(solid_material);
        auto& ip_data = _ip_data[ip];
        auto const& sm = shape_matrices[ip];
        ip_data.N_u = sm.N;
        ip_data.dNdx_u = sm.dNdx;
        ip_data.integration_weight =
            _integration_method.getWeightedPoint(ip).getWeight() *
            sm.integralMeasure * sm.detJ;
 
        // Initialize current time step values
        static const int kelvin_vector_size =
            MathLib::KelvinVector::kelvin_vector_dimensions(DisplacementDim);
        ip_data._sigma.setZero(kelvin_vector_size);
        ip_data._eps.setZero(kelvin_vector_size);
 
        // Previous time step values are not initialized and are set later.
        ip_data._sigma_prev.resize(kelvin_vector_size);
        ip_data._eps_prev.resize(kelvin_vector_size);
 
        ip_data._C.resize(kelvin_vector_size, kelvin_vector_size);
 
        _secondary_data.N[ip] = sm.N;
    }
}
 
template <typename ShapeFunction, int DisplacementDim>
void SmallDeformationLocalAssemblerMatrix<ShapeFunction, 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_b_data,
                         std::vector<double>& local_Jac_data)
{
    assert(_element.getDimension() == DisplacementDim);
 
    auto const local_matrix_size = local_x.size();
 
    auto local_Jac = MathLib::createZeroedMatrix<StiffnessMatrixType>(
        local_Jac_data, local_matrix_size, local_matrix_size);
 
    auto local_b = MathLib::createZeroedVector<NodalDisplacementVectorType>(
        local_b_data, local_matrix_size);
 
    unsigned const n_integration_points =
        _integration_method.getNumberOfPoints();
 
    MPL::VariableArray variables;
    MPL::VariableArray variables_prev;
 
    auto const B_dil_bar = getDilatationalBBarMatrix();
 
    for (unsigned ip = 0; ip < n_integration_points; ip++)
    {
        auto const& w = _ip_data[ip].integration_weight;
 
        auto const& N = _ip_data[ip].N_u;
        auto const& dNdx = _ip_data[ip].dNdx_u;
 
        ParameterLib::SpatialPosition const x_position{
            std::nullopt, this->_element.getID(),
            MathLib::Point3d(NumLib::interpolateCoordinates<ShapeFunction,
                                                            ShapeMatricesType>(
                this->_element, N))};
 
        auto const x_coord =
            x_position.getCoordinates().value()[0];  // r for axisymmetry
        auto const B = LinearBMatrix::computeBMatrixPossiblyWithBbar<
            DisplacementDim, ShapeFunction::NPOINTS, BBarMatrixType,
            typename BMatricesType::BMatrixType>(dNdx, N, B_dil_bar, x_coord,
                                                 this->_is_axially_symmetric);
 
        auto const& eps_prev = _ip_data[ip]._eps_prev;
        auto const& sigma_prev = _ip_data[ip]._sigma_prev;
 
        auto& eps = _ip_data[ip]._eps;
        auto& sigma = _ip_data[ip]._sigma;
        auto& state = _ip_data[ip]._material_state_variables;
 
        eps.noalias() =
            B * Eigen::Map<typename BMatricesType::NodalForceVectorType const>(
                    local_x.data(), ShapeFunction::NPOINTS * DisplacementDim);
 
        variables.mechanical_strain
            .emplace<MathLib::KelvinVector::KelvinVectorType<DisplacementDim>>(
                eps);
        variables_prev.stress
            .emplace<MathLib::KelvinVector::KelvinVectorType<DisplacementDim>>(
                sigma_prev);
        variables_prev.mechanical_strain
            .emplace<MathLib::KelvinVector::KelvinVectorType<DisplacementDim>>(
                eps_prev);
        variables_prev.temperature = _process_data.reference_temperature;
 
        auto&& solution = _ip_data[ip]._solid_material.integrateStress(
            variables_prev, variables, t, x_position, dt, *state);
 
        if (!solution)
        {
            OGS_FATAL("Computation of local constitutive relation failed.");
        }
 
        MathLib::KelvinVector::KelvinMatrixType<DisplacementDim> C;
        std::tie(sigma, state, C) = std::move(*solution);
 
        local_b.noalias() -= B.transpose() * sigma * w;
        local_Jac.noalias() += B.transpose() * C * B * w;
    }
}
 
template <typename ShapeFunction, int DisplacementDim>
void SmallDeformationLocalAssemblerMatrix<ShapeFunction, DisplacementDim>::
    computeSecondaryVariableConcreteWithVector(
        double const /*t*/, Eigen::VectorXd const& /*local_x*/)
{
    // Compute average value per element
    using KV = MathLib::KelvinVector::KelvinVectorType<DisplacementDim>;
    KV sigma_avg = KV::Zero();
    auto const e_id = _element.getID();
 
    unsigned const n_integration_points =
        _integration_method.getNumberOfPoints();
    for (unsigned ip = 0; ip < n_integration_points; ip++)
    {
        sigma_avg += _ip_data[ip]._sigma;
    }
    sigma_avg /= n_integration_points;
 
    Eigen::Map<KV>(
        &(*_process_data.element_stresses)[e_id * KV::RowsAtCompileTime]) =
        MathLib::KelvinVector::kelvinVectorToSymmetricTensor(sigma_avg);
}
 
template <typename ShapeFunction, int DisplacementDim>
std::vector<double> const&
SmallDeformationLocalAssemblerMatrix<ShapeFunction, DisplacementDim>::
    getIntPtSigma(
        const double /*t*/,
        std::vector<GlobalVector*> const& /*x*/,
        std::vector<NumLib::LocalToGlobalIndexMap const*> const& /*dof_table*/,
        std::vector<double>& cache) const
{
    return ProcessLib::getIntegrationPointKelvinVectorData<DisplacementDim>(
        _ip_data, &IntegrationPointDataType::_sigma, cache);
}
template <typename ShapeFunction, int DisplacementDim>
std::vector<double> const&
SmallDeformationLocalAssemblerMatrix<ShapeFunction, DisplacementDim>::
    getIntPtEpsilon(
        const double /*t*/,
        std::vector<GlobalVector*> const& /*x*/,
        std::vector<NumLib::LocalToGlobalIndexMap const*> const& /*dof_table*/,
        std::vector<double>& cache) const
{
    return ProcessLib::getIntegrationPointKelvinVectorData<DisplacementDim>(
        _ip_data, &IntegrationPointDataType::_eps, cache);
}
 
}  // namespace SmallDeformation
}  // namespace LIE
}  // namespace ProcessLib