finiteelements/mechanics/nonlinearelastic.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
 
#if HAVE_DUNE_LOCALFEFUNCTIONS
#  include <dune/fufem/boundarypatch.hh>
#  include <dune/geometry/quadraturerules.hh>
#  include <dune/geometry/type.hh>
#  include <dune/localfefunctions/cachedlocalBasis/cachedlocalBasis.hh>
#  include <dune/localfefunctions/expressions/greenLagrangeStrains.hh>
#  include <dune/localfefunctions/impl/standardLocalFunction.hh>
#  include <dune/localfefunctions/manifolds/realTuple.hh>
 
#  include <ikarus/finiteelements/febases/powerbasisfe.hh>
#  include <ikarus/finiteelements/fehelper.hh>
#  include <ikarus/finiteelements/ferequirements.hh>
#  include <ikarus/finiteelements/mechanics/loads.hh>
#  include <ikarus/finiteelements/mechanics/materials/tags.hh>
#  include <ikarus/finiteelements/physicshelper.hh>
#  include <ikarus/utils/defaultfunctions.hh>
#  include <ikarus/utils/eigendunetransformations.hh>
#  include <ikarus/utils/linearalgebrahelper.hh>
 
namespace Ikarus {
 
  template <typename Basis_, typename Material_, typename FERequirements_ = FERequirements<>, bool useEigenRef = false>
  class NonLinearElastic : public PowerBasisFE<typename Basis_::FlatBasis>,
                           public Volume<NonLinearElastic<Basis_, Material_, FERequirements_, useEigenRef>,
                                         TraitsFromFE<Basis_, FERequirements_, useEigenRef>>,
                           public Traction<NonLinearElastic<Basis_, Material_, FERequirements_, useEigenRef>,
                                           TraitsFromFE<Basis_, FERequirements_, useEigenRef>> {
  public:
    using Traits                 = TraitsFromFE<Basis_, FERequirements_, useEigenRef>;
    using Basis                  = typename Traits::Basis;
    using FlatBasis              = typename Traits::FlatBasis;
    using FERequirementType      = typename Traits::FERequirementType;
    using LocalView              = typename Traits::LocalView;
    using Geometry               = typename Traits::Geometry;
    using GridView               = typename Traits::GridView;
    using Element                = typename Traits::Element;
    using ResultRequirementsType = typename Traits::ResultRequirementsType;
    using BasePowerFE            = PowerBasisFE<FlatBasis>;  // Handles globalIndices function
    using Material               = Material_;
    using VolumeType             = Volume<NonLinearElastic<Basis_, Material_, FERequirements_, useEigenRef>, Traits>;
    using TractionType           = Traction<NonLinearElastic<Basis_, Material_, FERequirements_, useEigenRef>, Traits>;
    using LocalBasisType         = decltype(std::declval<LocalView>().tree().child(0).finiteElement().localBasis());
 
    static constexpr int myDim       = Traits::mydim;
    static constexpr auto strainType = StrainTags::greenLagrangian;
 
    template <typename VolumeLoad = utils::LoadDefault, typename NeumannBoundaryLoad = utils::LoadDefault>
    NonLinearElastic(const Basis& globalBasis, const typename LocalView::Element& element, const Material& p_mat,
                     VolumeLoad p_volumeLoad = {}, const BoundaryPatch<GridView>* p_neumannBoundary = nullptr,
                     NeumannBoundaryLoad p_neumannBoundaryLoad = {})
        : BasePowerFE(globalBasis.flat(), element),
          VolumeType(p_volumeLoad),
          TractionType(p_neumannBoundary, p_neumannBoundaryLoad),
          mat{p_mat} {
      this->localView().bind(element);
      auto& first_child = this->localView().tree().child(0);
      const auto& fe    = first_child.finiteElement();
      geo_              = std::make_shared<const Geometry>(this->localView().element().geometry());
      numberOfNodes_    = fe.size();
      order_            = 2 * (fe.localBasis().order());
      localBasis        = Dune::CachedLocalBasis(fe.localBasis());
      if constexpr (requires { this->localView().element().impl().getQuadratureRule(order_); })
        if (this->localView().element().impl().isTrimmed())
          localBasis.bind(this->localView().element().impl().getQuadratureRule(order_), Dune::bindDerivatives(0, 1));
        else
          localBasis.bind(Dune::QuadratureRules<double, myDim>::rule(this->localView().element().type(), order_),
                          Dune::bindDerivatives(0, 1));
      else
        localBasis.bind(Dune::QuadratureRules<double, myDim>::rule(this->localView().element().type(), order_),
                        Dune::bindDerivatives(0, 1));
    }
 
    template <typename ScalarType = double>
    auto displacementFunction(const FERequirementType& par,
                              const std::optional<const Eigen::VectorX<ScalarType>>& dx = std::nullopt) const {
      const auto& d = par.getGlobalSolution(Ikarus::FESolutions::displacement);
      auto disp     = Ikarus::FEHelper::localSolutionBlockVector<Traits>(d, this->localView(), dx);
      Dune::StandardLocalFunction uFunction(localBasis, disp, geo_);
      return uFunction;
    }
 
    template <typename ScalarType = double>
    inline auto strainFunction(const FERequirementType& par,
                               const std::optional<const Eigen::VectorX<ScalarType>>& dx = std::nullopt) const {
      return Dune::greenLagrangeStrains(displacementFunction(par, dx));
    }
 
    template <typename ScalarType, int strainDim, bool voigt = true>
    auto materialTangent(const Eigen::Vector<ScalarType, strainDim>& strain) const {
      if constexpr (std::is_same_v<ScalarType, double>)
        return mat.template tangentModuli<strainType, voigt>(strain);
      else {
        decltype(auto) matAD = mat.template rebind<ScalarType>();
        return matAD.template tangentModuli<strainType, voigt>(strain);
      }
    }
 
    template <typename ScalarType, int strainDim>
    auto getInternalEnergy(const Eigen::Vector<ScalarType, strainDim>& strain) const {
      if constexpr (std::is_same_v<ScalarType, double>)
        return mat.template storedEnergy<strainType>(strain);
      else {
        decltype(auto) matAD = mat.template rebind<ScalarType>();
        return matAD.template storedEnergy<strainType>(strain);
      }
    }
 
    template <typename ScalarType, int strainDim, bool voigt = true>
    auto getStress(const Eigen::Vector<ScalarType, strainDim>& strain) const {
      if constexpr (std::is_same_v<ScalarType, double>)
        return mat.template stresses<strainType, voigt>(strain);
      else {
        decltype(auto) matAD = mat.template rebind<ScalarType>();
        return matAD.template stresses<strainType, voigt>(strain);
      }
    }
 
    const Geometry& geometry() const { return *geo_; }
    [[nodiscard]] size_t numberOfNodes() const { return numberOfNodes_; }
    [[nodiscard]] int order() const { return order_; }
 
    double calculateScalar(const FERequirementType& par) const { return calculateScalarImpl<double>(par); }
 
    void calculateVector(const FERequirementType& par, typename Traits::template VectorType<> force) const {
      calculateVectorImpl<double>(par, force);
    }
 
    void calculateMatrix(const FERequirementType& par, typename Traits::template MatrixType<> K) const {
      using namespace Dune::DerivativeDirections;
      using namespace Dune;
      const auto eps = strainFunction(par);
      for (const auto& [gpIndex, gp] : eps.viewOverIntegrationPoints()) {
        const double intElement = geo_->integrationElement(gp.position()) * gp.weight();
        const auto EVoigt       = (eps.evaluate(gpIndex, on(gridElement))).eval();
        const auto C            = materialTangent(EVoigt);
        const auto stresses     = getStress(EVoigt);
        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));
            const auto kgIJ = eps.evaluateDerivative(gpIndex, wrt(coeff(i, j)), along(stresses), on(gridElement));
            K.template block<myDim, myDim>(i * myDim, j * myDim) += (bopI.transpose() * C * bopJ + kgIJ) * intElement;
          }
        }
      }
 
      // Update due to displacement-dependent external loads, e.g., follower loads
      VolumeType::calculateMatrix(par, K);
      TractionType::calculateMatrix(par, K);
    }
 
    void calculateAt(const ResultRequirementsType& req, const Dune::FieldVector<double, Traits::mydim>& local,
                     ResultTypeMap<double>& result) const {
      using namespace Dune::DerivativeDirections;
      using namespace Dune;
 
      const auto uFunction = displacementFunction(req.getFERequirements());
      const auto H         = uFunction.evaluateDerivative(local, Dune::wrt(spatialAll), Dune::on(gridElement));
      const auto E         = (0.5 * (H.transpose() + H + H.transpose() * H)).eval();
      const auto EVoigt    = toVoigt(E);
      auto PK2             = mat.template stresses<StrainTags::greenLagrangian>(EVoigt);
 
      if (req.isResultRequested(ResultType::PK2Stress))
        result.insertOrAssignResult(ResultType::PK2Stress, PK2);
      else
        DUNE_THROW(Dune::NotImplemented, "The requested result type is NOT implemented.");
    }
 
  private:
    std::shared_ptr<const Geometry> geo_;
    Dune::CachedLocalBasis<std::remove_cvref_t<LocalBasisType>> localBasis;
    Material mat;
    size_t numberOfNodes_{0};
    int order_{};
 
  protected:
    template <typename ScalarType>
    auto calculateScalarImpl(const FERequirementType& par, const std::optional<const Eigen::VectorX<ScalarType>>& dx
                                                           = std::nullopt) const -> ScalarType {
      using namespace Dune::DerivativeDirections;
      using namespace Dune;
      const auto uFunction = displacementFunction(par, dx);
      const auto eps       = strainFunction(par, dx);
      const auto& lambda   = par.getParameter(Ikarus::FEParameter::loadfactor);
      ScalarType energy    = 0.0;
 
      for (const auto& [gpIndex, gp] : eps.viewOverIntegrationPoints()) {
        const auto EVoigt         = (eps.evaluate(gpIndex, on(gridElement))).eval();
        const auto internalEnergy = getInternalEnergy(EVoigt);
        energy += internalEnergy * geo_->integrationElement(gp.position()) * gp.weight();
      }
 
      // External forces volume forces over the domain
      energy += VolumeType::calculateScalarImpl(par, dx);
 
      // line or surface loads, i.e., neumann boundary
      energy += TractionType::calculateScalarImpl(par, dx);
      return energy;
    }
 
    template <typename ScalarType>
    void calculateVectorImpl(const FERequirementType& par, typename Traits::template VectorType<ScalarType> force,
                             const std::optional<const Eigen::VectorX<ScalarType>>& dx = std::nullopt) const {
      using namespace Dune::DerivativeDirections;
      using namespace Dune;
      const auto eps = strainFunction(par, dx);
 
      // Internal forces
      for (const auto& [gpIndex, gp] : eps.viewOverIntegrationPoints()) {
        const double intElement = geo_->integrationElement(gp.position()) * gp.weight();
        const auto EVoigt       = (eps.evaluate(gpIndex, on(gridElement))).eval();
        const auto stresses     = getStress(EVoigt);
        for (size_t i = 0; i < numberOfNodes_; ++i) {
          const auto bopI = eps.evaluateDerivative(gpIndex, wrt(coeff(i)), on(gridElement));
          force.template segment<myDim>(myDim * i) += bopI.transpose() * stresses * intElement;
        }
      }
 
      // External forces volume forces over the domain
      VolumeType::calculateVectorImpl(par, force, dx);
 
      // External forces, boundary forces, i.e., at the Neumann boundary
      TractionType::calculateVectorImpl(par, force, dx);
    }
  };
}  // namespace Ikarus
 
#else
#  error NonLinearElastic depends on dune-localfefunctions, which is not included
#endif