svk.hh

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// SPDX-FileCopyrightText: 2021-2024 The Ikarus Developers mueller@ibb.uni-stuttgart.de
// SPDX-License-Identifier: LGPL-3.0-or-later
 
// SPDX-License-Identifier: LGPL-3.0-or-later
 
#pragma once
 
#include <ikarus/finiteelements/mechanics/materials/interface.hh>
#include <ikarus/utils/tensorutils.hh>
 
namespace Ikarus {
 
template <typename ST>
struct StVenantKirchhoffT : public Material<StVenantKirchhoffT<ST>>
{
  [[nodiscard]] constexpr std::string nameImpl() const { return "StVenantKirchhoff"; }
 
  explicit StVenantKirchhoffT(const LamesFirstParameterAndShearModulus& mpt)
      : materialParameter_{mpt} {}
 
  using ScalarType                    = ST;
  static constexpr int worldDimension = 3;
  using StrainMatrix                  = Eigen::Matrix<ScalarType, worldDimension, worldDimension>;
  using StressMatrix                  = StrainMatrix;
 
  static constexpr auto strainTag          = StrainTags::greenLagrangian;
  static constexpr auto stressTag          = StressTags::PK2;
  static constexpr auto tangentModuliTag   = TangentModuliTags::Material;
  static constexpr bool energyAcceptsVoigt = true;
  static constexpr bool stressToVoigt      = true;
  static constexpr bool stressAcceptsVoigt = true;
  static constexpr bool moduliToVoigt      = true;
  static constexpr bool moduliAcceptsVoigt = true;
  // this factor denotes the differences between the returned stresses and moduli and the passed strain
  // for neoHooke the inserted quantity is C the Green-Lagrangian strain tensor,
  // the function relation between the energy and the stresses is S = 1\partial \psi(E)/ \partial E.
  // This factor is pre factor, which is the difference to the actual derivative is written here
  static constexpr double derivativeFactor = 1;
 
  template <typename Derived>
  ScalarType storedEnergyImpl(const Eigen::MatrixBase<Derived>& E) const {
    static_assert(Concepts::EigenMatrixOrVoigtNotation3<Derived>);
    if constexpr (Concepts::EigenVector<Derived>) {
      const ScalarType traceE = E.template segment<3>(0).sum();
      const ScalarType squaredNorm =
          E.template segment<3>(0).squaredNorm() + E.template segment<3>(3).squaredNorm() / ScalarType(2.0);
      return materialParameter_.lambda / ScalarType(2.0) * traceE * traceE + materialParameter_.mu * squaredNorm;
    } else {
      const auto traceE = E.trace();
      return materialParameter_.lambda / ScalarType(2.0) * traceE * traceE + materialParameter_.mu * E.squaredNorm();
    }
  }
 
  template <bool voigt, typename Derived>
  auto stressesImpl(const Eigen::MatrixBase<Derived>& E) const {
    static_assert(Concepts::EigenMatrixOrVoigtNotation3<decltype(E.eval())>);
    const auto& Ed = E.derived();
    if constexpr (!voigt) {
      if constexpr (Concepts::EigenVector<Derived>) {
        static_assert(Concepts::EigenVector6<Derived>);
        Eigen::Matrix<ScalarType, 3, 3> S;
        const ScalarType traceE = Ed.template segment<3>(0).sum();
        S.diagonal().array() =
            materialParameter_.lambda * traceE + 2 * materialParameter_.mu * Ed.template segment<3>(0).array();
        S(1, 2) = S(2, 1) = materialParameter_.mu * Ed(3);
        S(0, 2) = S(2, 0) = materialParameter_.mu * Ed(4);
        S(0, 1) = S(1, 0) = materialParameter_.mu * Ed(5); // no two since E voigt has 2* on off-diagonal terms
        return S;
      } else {
        static_assert(Concepts::EigenMatrix33<Derived>);
        return (materialParameter_.lambda * Ed.trace() * StrainMatrix::Identity() + 2 * materialParameter_.mu * Ed)
            .eval();
      }
    } else {
      if constexpr (Concepts::EigenVector<Derived>) {
        static_assert(Concepts::EigenVector6<Derived>);
        Eigen::Matrix<ScalarType, 6, 1> S;
        const ScalarType traceE          = Ed.template segment<3>(0).sum();
        S.template segment<3>(0).array() = traceE * materialParameter_.lambda;
        S.template segment<3>(0) += materialParameter_.mu * 2 * Ed.template segment<3>(0);
        S.template segment<3>(3) =
            materialParameter_.mu * Ed.template segment<3>(3); // no two since E voigt has 2* on off-diagonal terms
        return S;
      } else {
        Eigen::Matrix<ScalarType, 6, 1> S;
        S.template segment<3>(0).array() = Ed.trace() * materialParameter_.lambda;
        S.template segment<3>(0) += 2 * materialParameter_.mu * Ed.diagonal();
        S(3) = 2 * materialParameter_.mu * Ed(1, 2);
        S(4) = 2 * materialParameter_.mu * Ed(0, 2);
        S(5) = 2 * materialParameter_.mu * Ed(0, 1);
        return S;
      }
    }
  }
 
  template <bool voigt, typename Derived>
  auto tangentModuliImpl([[maybe_unused]] const Eigen::MatrixBase<Derived>& E) const {
    static_assert(Concepts::EigenMatrixOrVoigtNotation3<Derived>);
    if constexpr (!voigt) {
      Eigen::TensorFixedSize<ScalarType, Eigen::Sizes<3, 3, 3, 3>> moduli;
      moduli = materialParameter_.lambda * identityFourthOrder() +
               2 * materialParameter_.mu * symmetricIdentityFourthOrder();
      return moduli;
    } else {
      Eigen::Matrix<ScalarType, 6, 6> moduli;
      moduli.setZero();
      moduli.template block<3, 3>(0, 0).array() = materialParameter_.lambda;
      moduli.template block<3, 3>(0, 0).diagonal().array() += 2 * materialParameter_.mu;
      moduli.template block<3, 3>(3, 3).diagonal().array() = materialParameter_.mu;
      return moduli;
    }
  }
 
  template <typename ScalarTypeOther>
  auto rebind() const {
    return StVenantKirchhoffT<ScalarTypeOther>(materialParameter_);
  }
 
private:
  LamesFirstParameterAndShearModulus materialParameter_;
};
 
using StVenantKirchhoff = StVenantKirchhoffT<double>;
 
} // namespace Ikarus