LinearElasticIsotropicPhaseField.cpp

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#include "LinearElasticIsotropicPhaseField.h"
 
namespace MaterialLib::Solids::Phasefield
{
double evaluateHTensSpectral(
    int const i, int const j,
    Eigen::Matrix<double, 3, 1> const& principal_strain)
{
    if (i == j)
    {
        return 0.0;
    }
    if (std::fabs(principal_strain[i] - principal_strain[j]) <
        std::numeric_limits<double>::epsilon())
    {
        return 2 * heaviside(principal_strain[i]);
    }
    return 2 *
           (macaulayTensile(principal_strain[i]) -
            macaulayTensile(principal_strain[j])) /
           (principal_strain[i] - principal_strain[j]);
}
 
double evaluateHCompSpectral(
    int const i, int const j,
    Eigen::Matrix<double, 3, 1> const& principal_strain)
{
    if (i == j)
    {
        return 0.0;
    }
    double num_zero = 1.e-14;
 
    if (std::fabs(principal_strain[i] - principal_strain[j]) < num_zero)
    {
        return 2 * (1 - heaviside(principal_strain[i]));
    }
    return 2 *
           (macaulayCompressive(principal_strain[i]) -
            macaulayCompressive(principal_strain[j])) /
           (principal_strain[i] - principal_strain[j]);
}

 
template <>
MathLib::KelvinVector::KelvinMatrixType<3> aOdotB<3>(
    MathLib::KelvinVector::KelvinVectorType<3> const& A,
    MathLib::KelvinVector::KelvinVectorType<3> const& B)
{
    MathLib::KelvinVector::KelvinMatrixType<3> result;
 
    result(0, 0) = A(0) * B(0);
    result(0, 1) = result(1, 0) = A(3) * B(3) / 2.;
    result(0, 2) = result(2, 0) = A(5) * B(5) / 2.;
    result(0, 3) = result(3, 0) = (A(0) * B(3) + A(3) * B(0)) / 2;
    result(0, 4) = result(4, 0) =
        (A(3) * B(5) + A(5) * B(3)) / (2. * std::sqrt(2.));
    result(0, 5) = result(5, 0) = (A(0) * B(5) + A(5) * B(0)) / 2;
 
    result(1, 1) = A(1) * B(1);
    result(1, 2) = result(2, 1) = A(4) * B(4) / 2.;
    result(1, 3) = result(3, 1) = (A(1) * B(3) + A(3) * B(1)) / 2.;
    result(1, 4) = result(4, 1) = (A(1) * B(4) + A(4) * B(1)) / 2.;
    result(1, 5) = result(5, 1) =
        (A(3) * B(4) + A(4) * B(3)) / (2. * std::sqrt(2.));
 
    result(2, 2) = A(2) * B(2);
    result(2, 3) = result(3, 2) =
        (A(4) * B(5) + A(5) * B(4)) / (2. * std::sqrt(2.));
    result(2, 4) = result(4, 2) = (A(2) * B(4) + A(4) * B(2)) / 2.;
    result(2, 5) = result(5, 2) = (A(2) * B(5) + A(5) * B(2)) / 2.;
 
    result(3, 3) = (A(0) * B(1) + A(1) * B(0) + A(3) * B(3)) / 2.;
    result(3, 4) = result(4, 3) =
        (A(3) * B(4) + A(4) * B(3)) / 4. +
        (A(1) * B(5) + A(5) * B(1)) / (2. * std::sqrt(2.));
    result(3, 5) = result(5, 3) =
        (A(3) * B(5) + A(5) * B(3)) / 4. +
        (A(0) * B(4) + A(4) * B(0)) / (2. * std::sqrt(2.));
 
    result(4, 4) = (A(1) * B(2) + A(2) * B(1) + A(4) * B(4)) / 2.;
    result(4, 5) = result(5, 4) =
        (A(4) * B(5) + A(5) * B(4)) / 4. +
        (A(2) * B(3) + A(3) * B(2)) / (2. * std::sqrt(2.));
 
    result(5, 5) = (A(0) * B(2) + A(2) * B(0) + A(5) * B(5)) / 2.;
    return result;
}
 
template <>
MathLib::KelvinVector::KelvinMatrixType<2> aOdotB<2>(
    MathLib::KelvinVector::KelvinVectorType<2> const& A,
    MathLib::KelvinVector::KelvinVectorType<2> const& B)
{
    MathLib::KelvinVector::KelvinMatrixType<2> result;
 
    result(0, 0) = A(0) * B(0);
    result(0, 1) = result(1, 0) = A(3) * B(3) / 2.;
    result(0, 2) = result(2, 0) = 0;
    result(0, 3) = result(3, 0) = (A(0) * B(3) + A(3) * B(0)) / 2;
 
    result(1, 1) = A(1) * B(1);
    result(1, 2) = result(2, 1) = 0;
    result(1, 3) = result(3, 1) = (A(1) * B(3) + A(3) * B(1)) / 2.;
 
    result(2, 2) = A(2) * B(2);
    result(2, 3) = result(3, 2) = 0;
 
    result(3, 3) = (A(0) * B(1) + A(1) * B(0) + A(3) * B(3)) / 2.;
 
    return result;
}
 
}  // namespace MaterialLib::Solids::Phasefield