LinearElasticOrthotropic.cpp

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#include "LinearElasticOrthotropic.h"
 
#include <Eigen/LU>
 
#include "MaterialLib/MPL/Utils/GetSymmetricTensor.h"
 
namespace MPL = MaterialPropertyLib;
 
namespace MaterialLib
{
namespace Solids
{
template <int DisplacementDim>
std::optional<std::tuple<typename MechanicsBase<DisplacementDim>::KelvinVector,
                         std::unique_ptr<typename MechanicsBase<
                             DisplacementDim>::MaterialStateVariables>,
                         typename MechanicsBase<DisplacementDim>::KelvinMatrix>>
LinearElasticOrthotropic<DisplacementDim>::integrateStress(
    MaterialPropertyLib::VariableArray const& variable_array_prev,
    MaterialPropertyLib::VariableArray const& variable_array, double const t,
    ParameterLib::SpatialPosition const& x, double const /*dt*/,
    typename MechanicsBase<DisplacementDim>::
        MaterialStateVariables const& /*material_state_variables*/) const
{
    auto const& eps_m = std::get<MPL::SymmetricTensor<DisplacementDim>>(
        variable_array.mechanical_strain);
    auto const& eps_m_prev = std::get<MPL::SymmetricTensor<DisplacementDim>>(
        variable_array_prev.mechanical_strain);
    auto const& sigma_prev = std::get<MPL::SymmetricTensor<DisplacementDim>>(
        variable_array_prev.stress);
    auto const& T = variable_array_prev.temperature;
 
    KelvinMatrix C = getElasticTensor(t, x, T);
 
    KelvinVector sigma = sigma_prev + C * (eps_m - eps_m_prev);
 
    return {std::make_tuple(
        sigma,
        std::make_unique<
            typename MechanicsBase<DisplacementDim>::MaterialStateVariables>(),
        C)};
}
 
template <int DisplacementDim>
typename LinearElasticOrthotropic<DisplacementDim>::KelvinMatrix
LinearElasticOrthotropic<DisplacementDim>::getElasticTensor(
    double const t, ParameterLib::SpatialPosition const& x,
    double const /*T*/) const
{
    using namespace MathLib::KelvinVector;
 
    auto const& mp = _mp.evaluate(t, x);
    auto const E = [&mp](int const i) { return mp.E(i); };
    auto const G = [&mp](int const i, int const j) { return mp.G(i, j); };
    auto const nu = [&mp](int const i, int const j) { return mp.nu(i, j); };
 
    KelvinMatrixType<3> S_ortho = KelvinMatrixType<3>::Zero();
    // clang-format off
    S_ortho.template topLeftCorner<3, 3>() <<
               1. / E(1), -nu(2, 1) / E(2), -nu(3, 1) / E(3),
        -nu(1, 2) / E(1),        1. / E(2), -nu(3, 2) / E(3),
        -nu(1, 3) / E(1), -nu(2, 3) / E(2),        1. / E(3);
 
    S_ortho.template bottomRightCorner<3, 3>().diagonal() <<
        1. / (2 * G(1, 2)),
        1. / (2 * G(2, 3)),
        1. / (2 * G(1, 3));
    // clang-format on
 
    KelvinMatrixType<3> const C_ortho = S_ortho.inverse();
    auto const Q = [this, &x]() -> KelvinMatrixType<3>
    {
        if (!_local_coordinate_system)
        {
            return KelvinMatrixType<3>::Identity();
        }
        Eigen::Matrix3d R = Eigen::Matrix3d::Identity();
        R.template topLeftCorner<DisplacementDim, DisplacementDim>().noalias() =
            _local_coordinate_system->transformation<DisplacementDim>(x);
        return fourthOrderRotationMatrix(R);
    }();
 
    // Rotate the forth-order tenser in Kelvin mapping with Q*C_ortho*Q^T and
    // return the top left corner block of size 4x4 for two-dimensional case or
    // the full 6x6 matrix is returned in the three-dimensional case.
    return (Q * C_ortho * Q.transpose())
        .template topLeftCorner<kelvin_vector_dimensions(DisplacementDim),
                                kelvin_vector_dimensions(DisplacementDim)>();
}
 
template class LinearElasticOrthotropic<2>;
template class LinearElasticOrthotropic<3>;
 
}  // namespace Solids
}  // namespace MaterialLib