neohooke.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
 
#pragma once
 
#include <ikarus/finiteelements/mechanics/materials/interface.hh>
#include <ikarus/utils/tensorutils.hh>
 
namespace Ikarus {
 
  template <typename ScalarType_>
  struct NeoHookeT : public Material<NeoHookeT<ScalarType_>> {
    [[nodiscard]] constexpr std::string nameImpl() const noexcept { return "NeoHooke"; }
 
    explicit NeoHookeT(const LamesFirstParameterAndShearModulus& mpt) : lambdaAndmu{mpt} {}
 
    using ScalarType                    = ScalarType_;
    static constexpr int worldDimension = 3;
    using StrainMatrix                  = Eigen::Matrix<ScalarType, worldDimension, worldDimension>;
    using StressMatrix                  = StrainMatrix;
 
    static constexpr auto strainTag          = StrainTags::rightCauchyGreenTensor;
    static constexpr auto stressTag          = StressTags::PK2;
    static constexpr auto tangentModuliTag   = TangentModuliTags::Material;
    static constexpr bool energyAcceptsVoigt = false;
    static constexpr bool stressToVoigt      = false;
    static constexpr bool stressAcceptsVoigt = false;
    static constexpr bool moduliToVoigt      = false;
    static constexpr bool moduliAcceptsVoigt = false;
    static constexpr double derivativeFactor = 2;
 
    template <typename Derived>
    ScalarType storedEnergyImpl(const Eigen::MatrixBase<Derived>& C) const noexcept {
      static_assert(Concepts::EigenMatrixOrVoigtNotation3<Derived>);
      if constexpr (!Concepts::EigenVector<Derived>) {
        const auto traceC  = C.trace();
        const auto logdetF = log(sqrt(C.determinant()));
        return lambdaAndmu.mu / 2.0 * (traceC - 3 - 2 * logdetF) + lambdaAndmu.lambda / 2.0 * logdetF * logdetF;
      } else
        static_assert(!Concepts::EigenVector<Derived>,
                      "NeoHooke energy can only be called with a matrix and not a vector in Voigt notation");
    }
 
    template <bool voigt, typename Derived>
    auto stressesImpl(const Eigen::MatrixBase<Derived>& C) const {
      static_assert(Concepts::EigenMatrixOrVoigtNotation3<Derived>);
      if constexpr (!voigt) {
        if constexpr (!Concepts::EigenVector<Derived>) {
          const auto logdetF = log(sqrt(C.determinant()));
          const auto invC    = C.inverse().eval();
          return (lambdaAndmu.mu * (StrainMatrix::Identity() - invC) + lambdaAndmu.lambda * logdetF * invC).eval();
        } else
          static_assert(!Concepts::EigenVector<Derived>,
                        "NeoHooke can only be called with a matrix and not a vector in Voigt notation");
      } else
        static_assert(voigt == false, "NeoHooke does not support returning stresses in Voigt notation");
    }
 
    template <bool voigt, typename Derived>
    auto tangentModuliImpl(const Eigen::MatrixBase<Derived>& C) const {
      static_assert(Concepts::EigenMatrixOrVoigtNotation3<Derived>);
      if constexpr (!voigt) {
        const auto invC    = C.inverse().eval();
        const auto logdetF = log(sqrt(C.determinant()));
        const auto CTinv   = tensorView(invC, std::array<Eigen::Index, 2>({3, 3}));
        static_assert(Eigen::TensorFixedSize<ScalarType, Eigen::Sizes<3, 3>>::NumIndices == 2);
        Eigen::TensorFixedSize<ScalarType, Eigen::Sizes<3, 3, 3, 3>> moduli
            = (lambdaAndmu.lambda * dyadic(CTinv, CTinv)
               + 2 * (lambdaAndmu.mu - lambdaAndmu.lambda * logdetF) * symTwoSlots(fourthOrderIKJL(invC, invC), {2, 3}))
                  .eval();
        return moduli;
      } else
        static_assert(voigt == false, "NeoHooke does not support returning tangent moduli in Voigt notation");
    }
 
    template <typename ScalarTypeOther>
    auto rebind() const {
      return NeoHookeT<ScalarTypeOther>(lambdaAndmu);
    }
 
    LamesFirstParameterAndShearModulus lambdaAndmu;
  };
 
  typedef NeoHookeT<double> NeoHooke;
 
}  // namespace Ikarus