linearelastic.hh

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// SPDX-FileCopyrightText: 2021-2026 The Ikarus Developers ikarus@ibb.uni-stuttgart.de
// SPDX-License-Identifier: LGPL-3.0-or-later
 
#pragma once
 
#if HAVE_DUNE_LOCALFEFUNCTIONS
 
  #include <optional>
  #include <type_traits>
 
  #include <dune/geometry/quadraturerules.hh>
  #include <dune/localfefunctions/expressions/linearStrainsExpr.hh>
  #include <dune/localfefunctions/impl/standardLocalFunction.hh>
 
  #include <ikarus/finiteelements/fehelper.hh>
  #include <ikarus/finiteelements/ferequirements.hh>
  #include <ikarus/finiteelements/feresulttypes.hh>
  #include <ikarus/finiteelements/mechanics/materials.hh>
  #include <ikarus/finiteelements/mechanics/materials/tags.hh>
  #include <ikarus/finiteelements/mechanics/strainenhancements/easfunctions.hh>
  #include <ikarus/finiteelements/physicshelper.hh>
  #include <ikarus/utils/quadraturerulehelper.hh>
 
namespace Ikarus {
 
template <typename PreFE, typename FE, typename PRE>
class LinearElastic;
 
template <Concepts::GeometricallyLinearMaterial MAT>
struct LinearElasticPre
{
  using Material = MAT;
  MAT material;
 
  template <typename PreFE, typename FE>
  using Skill = LinearElastic<PreFE, FE, LinearElasticPre>;
};
 
template <typename PreFE, typename FE, typename PRE>
class LinearElastic : public ResultTypeBase<ResultTypes::linearStress, ResultTypes::linearStressFull>
{
public:
  using Traits       = PreFE::Traits;
  using BasisHandler = typename Traits::BasisHandler;
  using FlatBasis    = typename Traits::FlatBasis;
  using Requirement  = FERequirements<FESolutions::displacement, FEParameter::loadfactor>;
  using LocalView    = typename Traits::LocalView;
  using Geometry     = typename Traits::Geometry;
  using GridView     = typename Traits::GridView;
  using Element      = typename Traits::Element;
  using Material     = PRE::Material;
  using Pre          = PRE;
 
  using LocalBasisType = decltype(std::declval<LocalView>().tree().child(0).finiteElement().localBasis());
 
  template <typename ST>
  using VectorXOptRef = std::optional<std::reference_wrapper<const Eigen::VectorX<ST>>>;
 
  static constexpr int myDim       = Traits::mydim;
  static constexpr int strainDim   = myDim * (myDim + 1) / 2;
  static constexpr auto strainType = StrainTags::linear;
  static constexpr auto stressType = StressTags::linear;
 
  template <template <typename, int, int> class RT>
  using RTWrapperType = ResultWrapper<RT<typename Traits::ctype, myDim, Traits::worlddim>, ResultShape::Vector>;
 
  template <typename ST = double>
  using StrainType = Eigen::Vector<ST, strainDim>;
 
  template <typename ST = double>
  using BopType = Eigen::Matrix<ST, strainDim, myDim>;
 
  template <typename ST = double>
  using KgType = Eigen::Matrix<ST, myDim, myDim>;
 
  explicit LinearElastic(const Pre& pre)
      : mat_{pre.material} {}
 
protected:
  void bindImpl() {
    const auto& localView = underlying().localView();
    const auto& element   = localView.element();
    auto& firstChild      = localView.tree().child(0);
    const auto& fe        = firstChild.finiteElement();
    geo_                  = std::make_shared<const Geometry>(element.geometry());
    numberOfNodes_        = fe.size();
    order_                = fe.localBasis().order();
    localBasis_           = Dune::CachedLocalBasis(fe.localBasis());
    if (underlying().quadratureRule())
      localBasis_.bind(underlying().quadratureRule().value(), Dune::bindDerivatives(0, 1));
    else
      localBasis_.bind(defaultQuadratureRule<myDim>(element, 2 * order_), Dune::bindDerivatives(0, 1));
  }
 
public:
  template <typename ScalarType = double>
  auto displacementFunction(const Requirement& par, const VectorXOptRef<ScalarType>& dx = std::nullopt) const {
    const auto& d = par.globalSolution();
    auto disp     = Ikarus::FEHelper::localSolutionBlockVector<Traits>(d, underlying().localView(), dx);
    Dune::StandardLocalFunction uFunction(localBasis_, disp, geo_);
    return uFunction;
  }
  template <class ScalarType = double>
  auto strainFunction(const Requirement& par, const VectorXOptRef<ScalarType>& dx = std::nullopt) const {
    return Dune::linearStrains(displacementFunction(par, dx));
  }
 
  template <typename ScalarType, int strainDim>
  auto internalEnergy(const Eigen::Vector<ScalarType, strainDim>& strain) const {
    const auto C = materialTangent<ScalarType, strainDim>(strain);
    return (0.5 * strain.dot(C * strain));
  }
 
  template <typename ScalarType, int strainDim, bool voigt = true>
  auto stress(const Eigen::Vector<ScalarType, strainDim>& strain) const {
    const auto C = materialTangent<ScalarType, strainDim, voigt>(strain);
    return (C * strain).eval();
  }
 
  template <typename ScalarType, int strainDim, bool voigt = true>
  auto materialTangent(
      const Eigen::Vector<ScalarType, strainDim>& strain = Eigen::Vector<ScalarType, strainDim>::Zero()) const {
    // Since that material is independent of the strains, a zero strain is passed here
    return material<ScalarType>().template tangentModuli<strainType, voigt>(strain);
  }
 
  const Geometry& geometry() const { return *geo_; }
  [[nodiscard]] size_t numberOfNodes() const { return numberOfNodes_; }
  [[nodiscard]] int order() const { return order_; }
  const Dune::CachedLocalBasis<std::remove_cvref_t<LocalBasisType>>& localBasis() const { return localBasis_; }
 
  template <typename ScalarType = double>
  decltype(auto) material() const {
    if constexpr (Concepts::AutodiffScalar<ScalarType>)
      return mat_.template rebind<ScalarType>();
    else
      return mat_;
  }
 
public:
  template <typename M>
  auto calculateStress(const M& mat, const Eigen::Vector<double, strainDim>& strainInVoigt) const {
    return mat.template stresses<strainType>(enlargeIfReduced<Material>(strainInVoigt)).eval();
  }
 
  template <template <typename, int, int> class RT>
  requires(LinearElastic::template supportsResultType<RT>())
  auto calculateAtImpl(const Requirement& req, const Dune::FieldVector<double, Traits::mydim>& local,
                       Dune::PriorityTag<1>) const {
    if constexpr (FE::isMixed())
      return RTWrapperType<RT>{};
 
    const auto eps     = strainFunction(req);
    auto epsVoigt      = eps.evaluate(local, Dune::on(Dune::DerivativeDirections::gridElement));
    decltype(auto) mat = [&]() {
      if constexpr (isSameResultType<RT, ResultTypes::linearStressFull> and requires { mat_.underlying(); })
        return mat_.underlying();
      else
        return mat_;
    }();
    const auto linearStress = calculateStress(mat, epsVoigt).eval();
    RTWrapperType<RT> resultWrapper{};
    if constexpr (isSameResultType<RT, ResultTypes::linearStress> or
                  isSameResultType<RT, ResultTypes::linearStressFull>)
      resultWrapper = linearStress;
    return resultWrapper;
  }
 
private:
  //> CRTP
  const auto& underlying() const { return static_cast<const FE&>(*this); }
  auto& underlying() { return static_cast<FE&>(*this); }
 
  std::shared_ptr<const Geometry> geo_;
  Dune::CachedLocalBasis<std::remove_cvref_t<LocalBasisType>> localBasis_;
  Material mat_;
  size_t numberOfNodes_{0};
  int order_{};
 
public:
  template <typename ST>
  auto geometricStiffnessMatrixFunction(const Requirement& par, typename Traits::template MatrixType<ST>& K,
                                        const VectorXOptRef<ST>& dx = std::nullopt) const {
    return [&](const FE::template KgType<ST>& kgIJ, const int I, const int J, const auto& gp) {
      const auto geo          = underlying().localView().element().geometry();
      const double intElement = geo.integrationElement(gp.position()) * gp.weight();
      K.template block<FE::myDim, FE::myDim>(I * FE::myDim, J * FE::myDim) += kgIJ * intElement;
    };
  }
  template <typename ST>
  auto materialStiffnessMatrixFunction(const Requirement& par, typename Traits::template MatrixType<ST>& K,
                                       const VectorXOptRef<ST>& dx = std::nullopt) const {
    return [&](const StrainType<ST>& strain, const BopType<ST>& bopI, const BopType<ST>& bopJ, const int I, const int J,
               const auto& gp) {
      const auto C            = materialTangent(strain);
      const double intElement = geo_->integrationElement(gp.position()) * gp.weight();
      K.template block<myDim, myDim>(I * myDim, J * myDim) += (bopI.transpose() * C * bopJ) * intElement;
    };
  }
 
  template <typename ST>
  auto internalForcesFunction(const Requirement& par, typename Traits::template VectorType<ST>& force,
                              const VectorXOptRef<ST>& dx = std::nullopt) const {
    return [&](const StrainType<ST>& stresses, const BopType<ST>& bopI, const int I, const auto& gp) {
      const double intElement = geo_->integrationElement(gp.position()) * gp.weight();
      force.template segment<myDim>(myDim * I) += bopI.transpose() * stresses * intElement;
    };
  }
 
  template <typename ScalarType>
  auto energyFunction(const Requirement& par, const VectorXOptRef<ScalarType>& dx = std::nullopt) const {
    return [&]() -> ScalarType {
      using namespace Dune::DerivativeDirections;
      using namespace Dune;
      ScalarType energy = 0.0;
      const auto eps    = strainFunction(par, dx);
      for (const auto& [gpIndex, gp] : eps.viewOverIntegrationPoints()) {
        const auto epsVoigt = eps.evaluate(gpIndex, on(gridElement));
        energy += internalEnergy(epsVoigt) * geo_->integrationElement(gp.position()) * gp.weight();
      }
      return energy;
    };
  }
 
protected:
  template <typename ScalarType>
  void calculateMatrixImpl(const Requirement& par, const MatrixAffordance& affordance,
                           typename Traits::template MatrixType<> K,
                           const VectorXOptRef<ScalarType>& dx = std::nullopt) const {
    if constexpr (FE::isMixed()) {
      return;
    }
    using namespace Dune::DerivativeDirections;
    using namespace Dune;
    const auto eps       = strainFunction(par, dx);
    const auto kFunction = materialStiffnessMatrixFunction<ScalarType>(par, K, dx);
 
    for (const auto& [gpIndex, gp] : eps.viewOverIntegrationPoints()) {
      const auto epsVoigt = eps.evaluate(gpIndex, on(gridElement));
      for (size_t i = 0; i < numberOfNodes_; ++i) {
        const auto bopI = eps.evaluateDerivative(gpIndex, wrt(coeff(i)), on(gridElement));
        for (size_t j = 0; j < numberOfNodes_; ++j) {
          const auto bopJ = eps.evaluateDerivative(gpIndex, wrt(coeff(j)), on(gridElement));
          kFunction(epsVoigt, bopI, bopJ, i, j, gp);
        }
      }
    }
  }
 
  template <typename ScalarType>
  auto calculateScalarImpl(const Requirement& par, ScalarAffordance affordance,
                           const VectorXOptRef<ScalarType>& dx = std::nullopt) const -> ScalarType {
    if constexpr (FE::isMixed())
      return ScalarType{0.0};
    return energyFunction(par, dx)();
  }
 
  template <typename ScalarType>
  void calculateVectorImpl(const Requirement& par, VectorAffordance affordance,
                           typename Traits::template VectorType<ScalarType> force,
                           const VectorXOptRef<ScalarType>& dx = std::nullopt) const {
    if constexpr (FE::isMixed())
      return;
    using namespace Dune::DerivativeDirections;
    using namespace Dune;
    const auto eps          = strainFunction(par, dx);
    const auto fIntFunction = internalForcesFunction<ScalarType>(par, force, dx);
 
    // Internal forces
    for (const auto& [gpIndex, gp] : eps.viewOverIntegrationPoints()) {
      const auto epsVoigt = eps.evaluate(gpIndex, on(gridElement));
      const auto stresses = stress(epsVoigt);
      for (size_t i = 0; i < numberOfNodes_; ++i) {
        const auto bopI = eps.evaluateDerivative(gpIndex, wrt(coeff(i)), on(gridElement));
        fIntFunction(stresses, bopI, i, gp);
      }
    }
  }
};
 
template <Concepts::GeometricallyLinearMaterial MAT>
auto linearElastic(const MAT& mat) {
  LinearElasticPre<MAT> pre(mat);
 
  return pre;
}
} // namespace Ikarus
 
#else
  #error LinearElastic depends on dune-localfefunctions, which is not included
#endif