ThermoMechanicalPhaseFieldFEM-impl.h

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#pragma once
 
#include "ThermoMechanicalPhaseFieldFEM.h"
 
#include "NumLib/DOF/DOFTableUtil.h"
#include "ProcessLib/CoupledSolutionsForStaggeredScheme.h"
 
namespace ProcessLib
{
namespace ThermoMechanicalPhaseField
{
template <typename ShapeFunction, typename IntegrationMethod,
          int DisplacementDim>
void ThermoMechanicalPhaseFieldLocalAssembler<ShapeFunction, IntegrationMethod,
                                              DisplacementDim>::
    assembleWithJacobianForStaggeredScheme(
        double const t, double const dt, Eigen::VectorXd const& local_x,
        Eigen::VectorXd const& local_xdot, const double /*dxdot_dx*/,
        const double /*dx_dx*/, int const process_id,
        std::vector<double>& /*local_M_data*/,
        std::vector<double>& /*local_K_data*/,
        std::vector<double>& local_b_data, std::vector<double>& local_Jac_data)
{
    if (process_id == _phase_field_process_id)
    {
        assembleWithJacobianForPhaseFieldEquations(t, local_x, local_b_data,
                                                   local_Jac_data);
        return;
    }
 
    if (process_id == _heat_conduction_process_id)
    {
        assembleWithJacobianForHeatConductionEquations(
            t, dt, local_x, local_xdot, local_b_data, local_Jac_data);
        return;
    }
 
    // For the equations with deformation
    assembleWithJacobianForDeformationEquations(t, dt, local_x, local_b_data,
                                                local_Jac_data);
}
 
template <typename ShapeFunction, typename IntegrationMethod,
          int DisplacementDim>
void ThermoMechanicalPhaseFieldLocalAssembler<ShapeFunction, IntegrationMethod,
                                              DisplacementDim>::
    assembleWithJacobianForDeformationEquations(
        double const t, double const dt, Eigen::VectorXd const& local_x,
        std::vector<double>& local_b_data, std::vector<double>& local_Jac_data)
{
    assert(local_x.size() ==
           phasefield_size + displacement_size + temperature_size);
 
    auto const d = local_x.template segment<phasefield_size>(phasefield_index);
    auto const u =
        local_x.template segment<displacement_size>(displacement_index);
    auto const T =
        local_x.template segment<temperature_size>(temperature_index);
 
    auto local_Jac = MathLib::createZeroedMatrix<
        typename ShapeMatricesType::template MatrixType<displacement_size,
                                                        displacement_size>>(
        local_Jac_data, displacement_size, displacement_size);
 
    auto local_rhs = MathLib::createZeroedVector<
        typename ShapeMatricesType::template VectorType<displacement_size>>(
        local_b_data, displacement_size);
 
    ParameterLib::SpatialPosition x_position;
    x_position.setElementID(_element.getID());
 
    int const n_integration_points = _integration_method.getNumberOfPoints();
    for (int ip = 0; ip < n_integration_points; ip++)
    {
        x_position.setIntegrationPoint(ip);
        auto const& w = _ip_data[ip].integration_weight;
        auto const& N = _ip_data[ip].N;
        auto const& dNdx = _ip_data[ip].dNdx;
 
        auto const x_coord =
            NumLib::interpolateXCoordinate<ShapeFunction, ShapeMatricesType>(
                _element, N);
        auto const& B =
            LinearBMatrix::computeBMatrix<DisplacementDim,
                                          ShapeFunction::NPOINTS,
                                          typename BMatricesType::BMatrixType>(
                dNdx, N, x_coord, _is_axially_symmetric);
 
        auto& eps = _ip_data[ip].eps;
 
        auto const& C_tensile = _ip_data[ip].C_tensile;
        auto const& C_compressive = _ip_data[ip].C_compressive;
 
        auto const& sigma = _ip_data[ip].sigma;
 
        auto const k = _process_data.residual_stiffness(t, x_position)[0];
        auto rho_sr = _process_data.solid_density(t, x_position)[0];
        auto const alpha = _process_data.linear_thermal_expansion_coefficient(
            t, x_position)[0];
        double const T0 = _process_data.reference_temperature;
        auto const& b = _process_data.specific_body_force;
 
        double const T_ip = N.dot(T);
        double const delta_T = T_ip - T0;
        // calculate real density
        double const rho_s = rho_sr / (1 + 3 * alpha * delta_T);
 
        double const d_ip = N.dot(d);
        double const degradation = d_ip * d_ip * (1 - k) + k;
 
        auto const C_eff = degradation * C_tensile + C_compressive;
        eps.noalias() = B * u;
        _ip_data[ip].updateConstitutiveRelation(t, x_position, dt, u, alpha,
                                                delta_T, degradation);
 
        typename ShapeMatricesType::template MatrixType<DisplacementDim,
                                                        displacement_size>
            N_u = ShapeMatricesType::template MatrixType<
                DisplacementDim, displacement_size>::Zero(DisplacementDim,
                                                          displacement_size);
 
        for (int i = 0; i < DisplacementDim; ++i)
        {
            N_u.template block<1, displacement_size / DisplacementDim>(
                   i, i * displacement_size / DisplacementDim)
                .noalias() = N;
        }
 
        local_Jac.noalias() += B.transpose() * C_eff * B * w;
 
        local_rhs.noalias() -=
            (B.transpose() * sigma - N_u.transpose() * rho_s * b) * w;
    }
}
 
template <typename ShapeFunction, typename IntegrationMethod,
          int DisplacementDim>
void ThermoMechanicalPhaseFieldLocalAssembler<ShapeFunction, IntegrationMethod,
                                              DisplacementDim>::
    assembleWithJacobianForHeatConductionEquations(
        double const t, double const dt, Eigen::VectorXd const& local_x,
        Eigen::VectorXd const& local_xdot, std::vector<double>& local_b_data,
        std::vector<double>& local_Jac_data)
{
    assert(local_x.size() ==
           phasefield_size + displacement_size + temperature_size);
 
    auto const d = local_x.template segment<phasefield_size>(phasefield_index);
    auto const T =
        local_x.template segment<temperature_size>(temperature_index);
    auto const T_dot =
        local_xdot.template segment<temperature_size>(temperature_index);
    auto local_Jac = MathLib::createZeroedMatrix<
        typename ShapeMatricesType::template MatrixType<temperature_size,
                                                        temperature_size>>(
        local_Jac_data, temperature_size, temperature_size);
 
    auto local_rhs = MathLib::createZeroedVector<
        typename ShapeMatricesType::template VectorType<temperature_size>>(
        local_b_data, temperature_size);
 
    ParameterLib::SpatialPosition x_position;
    x_position.setElementID(_element.getID());
 
    int const n_integration_points = _integration_method.getNumberOfPoints();
    for (int ip = 0; ip < n_integration_points; ip++)
    {
        x_position.setIntegrationPoint(ip);
        auto const& w = _ip_data[ip].integration_weight;
        auto const& N = _ip_data[ip].N;
        auto const& dNdx = _ip_data[ip].dNdx;
 
        auto& eps_m = _ip_data[ip].eps_m;
        auto& heatflux = _ip_data[ip].heatflux;
 
        auto rho_sr = _process_data.solid_density(t, x_position)[0];
        auto const alpha = _process_data.linear_thermal_expansion_coefficient(
            t, x_position)[0];
        double const c = _process_data.specific_heat_capacity(t, x_position)[0];
        auto const lambda =
            _process_data.thermal_conductivity(t, x_position)[0];
        auto const lambda_res =
            _process_data.residual_thermal_conductivity(t, x_position)[0];
        double const T0 = _process_data.reference_temperature;
 
        double const d_ip = N.dot(d);
        double const T_ip = N.dot(T);
        double const T_dot_ip = N.dot(T_dot);
        double const delta_T = T_ip - T0;
        // calculate real density
        double const rho_s = rho_sr / (1 + 3 * alpha * delta_T);
        // calculate effective thermal conductivity
        auto const lambda_eff =
            d_ip * d_ip * lambda + (1 - d_ip) * (1 - d_ip) * lambda_res;
 
        using Invariants = MathLib::KelvinVector::Invariants<
            MathLib::KelvinVector::kelvin_vector_dimensions(DisplacementDim)>;
 
        double const eps_m_trace = Invariants::trace(eps_m);
        if (eps_m_trace >= 0)
        {
            local_Jac.noalias() += (dNdx.transpose() * lambda_eff * dNdx +
                                    N.transpose() * rho_s * c * N / dt) *
                                   w;
 
            local_rhs.noalias() -= (N.transpose() * rho_s * c * T_dot_ip +
                                    dNdx.transpose() * lambda_eff * dNdx * T) *
                                   w;
 
            heatflux.noalias() = -(lambda_eff * dNdx * T) * w;
        }
        else
        {
            local_Jac.noalias() += (dNdx.transpose() * lambda * dNdx +
                                    N.transpose() * rho_s * c * N / dt) *
                                   w;
 
            local_rhs.noalias() -= (N.transpose() * rho_s * c * T_dot_ip +
                                    dNdx.transpose() * lambda * dNdx * T) *
                                   w;
 
            heatflux.noalias() = -(lambda * dNdx * T) * w;
        }
    }
}
 
template <typename ShapeFunction, typename IntegrationMethod,
          int DisplacementDim>
void ThermoMechanicalPhaseFieldLocalAssembler<ShapeFunction, IntegrationMethod,
                                              DisplacementDim>::
    assembleWithJacobianForPhaseFieldEquations(
        double const t, Eigen::VectorXd const& local_x,
        std::vector<double>& local_b_data, std::vector<double>& local_Jac_data)
{
    assert(local_x.size() ==
           phasefield_size + displacement_size + temperature_size);
 
    auto const d = local_x.template segment<phasefield_size>(phasefield_index);
 
    auto local_Jac = MathLib::createZeroedMatrix<
        typename ShapeMatricesType::template MatrixType<phasefield_size,
                                                        phasefield_size>>(
        local_Jac_data, phasefield_size, phasefield_size);
 
    auto local_rhs = MathLib::createZeroedVector<
        typename ShapeMatricesType::template VectorType<phasefield_size>>(
        local_b_data, phasefield_size);
 
    ParameterLib::SpatialPosition x_position;
    x_position.setElementID(_element.getID());
 
    int const n_integration_points = _integration_method.getNumberOfPoints();
    for (int ip = 0; ip < n_integration_points; ip++)
    {
        x_position.setIntegrationPoint(ip);
        auto const& w = _ip_data[ip].integration_weight;
        auto const& N = _ip_data[ip].N;
        auto const& dNdx = _ip_data[ip].dNdx;
 
        auto const& strain_energy_tensile = _ip_data[ip].strain_energy_tensile;
 
        auto const gc = _process_data.crack_resistance(t, x_position)[0];
        auto const ls = _process_data.crack_length_scale(t, x_position)[0];
 
        double const d_ip = N.dot(d);
 
        local_Jac.noalias() += (dNdx.transpose() * gc * ls * dNdx +
                                N.transpose() * 2 * strain_energy_tensile * N +
                                N.transpose() * gc / ls * N) *
                               w;
 
        local_rhs.noalias() -=
            (dNdx.transpose() * gc * ls * dNdx * d +
             N.transpose() * d_ip * 2 * strain_energy_tensile -
             N.transpose() * gc / ls * (1 - d_ip)) *
            w;
    }
}
 
}  // namespace ThermoMechanicalPhaseField
}  // namespace ProcessLib