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/fetraits.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:
    using Basis                      = Basis_;
    using Material                   = Material_;
    using FlatBasis                  = typename Basis::FlatBasis;
    using BasePowerFE                = PowerBasisFE<FlatBasis>;  // Handles globalIndices function
    using FERequirementType          = FERequirements_;
    using ResultRequirementsType     = ResultRequirements<FERequirementType>;
    using LocalView                  = typename FlatBasis::LocalView;
    using Element                    = typename LocalView::Element;
    using Geometry                   = typename Element::Geometry;
    using GridView                   = typename FlatBasis::GridView;
    using Traits                     = TraitsFromLocalView<LocalView, useEigenRef>;
    static constexpr int myDim       = Traits::mydim;
    static constexpr int worldDim    = Traits::worlddim;
    static constexpr auto strainType = StrainTags::greenLagrangian;
    using LocalBasisType             = decltype(std::declval<LocalView>().tree().child(0).finiteElement().localBasis());
 
    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), neumannBoundary{p_neumannBoundary}, 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));
 
      if constexpr (!std::is_same_v<VolumeLoad, utils::LoadDefault>) volumeLoad = p_volumeLoad;
      if constexpr (!std::is_same_v<NeumannBoundaryLoad, utils::LoadDefault>)
        neumannBoundaryLoad = p_neumannBoundaryLoad;
 
      assert(((not p_neumannBoundary and not neumannBoundaryLoad) or (p_neumannBoundary and neumannBoundaryLoad))
             && "If you pass a Neumann boundary you should also pass the function for the Neumann load!");
    }
 
    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<FERequirementType>(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);
      }
    }
 
    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;
          }
        }
      }
    }
 
    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.");
    }
 
    std::shared_ptr<const Geometry> geo_;
    Dune::CachedLocalBasis<std::remove_cvref_t<LocalBasisType>> localBasis;
    std::function<Eigen::Vector<double, worldDim>(const Dune::FieldVector<double, worldDim>&, const double&)>
        volumeLoad;
    std::function<Eigen::Vector<double, worldDim>(const Dune::FieldVector<double, worldDim>&, const double&)>
        neumannBoundaryLoad;
    const BoundaryPatch<GridView>* neumannBoundary;
    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] : uFunction.viewOverIntegrationPoints()) {
        const auto EVoigt         = (eps.evaluate(gpIndex, on(gridElement))).eval();
        const auto internalEnergy = getInternalEnergy(EVoigt);
        energy += internalEnergy * geo_->integrationElement(gp.position()) * gp.weight();
      }
 
      if (volumeLoad) {
        for (const auto& [gpIndex, gp] : uFunction.viewOverIntegrationPoints()) {
          const auto u                                       = uFunction.evaluate(gpIndex);
          const Eigen::Vector<double, Traits::worlddim> fExt = volumeLoad(geo_->global(gp.position()), lambda);
          energy -= u.dot(fExt) * geo_->integrationElement(gp.position()) * gp.weight();
        }
      }
 
      // line or surface loads, i.e., neumann boundary
      if (not neumannBoundary and not neumannBoundaryLoad) return energy;
 
      const auto& element = this->localView().element();
      for (auto&& intersection : intersections(neumannBoundary->gridView(), element)) {
        if (not neumannBoundary or not neumannBoundary->contains(intersection)) continue;
 
        const auto& quadLine = Dune::QuadratureRules<double, Traits::mydim - 1>::rule(intersection.type(), order);
 
        for (const auto& curQuad : quadLine) {
          // Local position of the quadrature point
          const Dune::FieldVector<double, Traits::mydim>& quadPos
              = intersection.geometryInInside().global(curQuad.position());
 
          const double intElement = intersection.geometry().integrationElement(curQuad.position());
 
          // The value of the local function
          const auto u = uFunction.evaluate(quadPos);
 
          // Value of the Neumann data at the current position
          const auto neumannValue = neumannBoundaryLoad(intersection.geometry().global(curQuad.position()), lambda);
          energy -= neumannValue.dot(u) * curQuad.weight() * intElement;
        }
      }
      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& lambda   = par.getParameter(Ikarus::FEParameter::loadfactor);
      const auto uFunction = displacementFunction(par, dx);
      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
      if (volumeLoad) {
        for (const auto& [gpIndex, gp] : uFunction.viewOverIntegrationPoints()) {
          const double intElement                            = geo_->integrationElement(gp.position()) * gp.weight();
          const Eigen::Vector<double, Traits::worlddim> fExt = volumeLoad(geo_->global(gp.position()), lambda);
          for (size_t i = 0; i < numberOfNodes; ++i) {
            const auto udCi = uFunction.evaluateDerivative(gpIndex, wrt(coeff(i)));
            force.template segment<myDim>(myDim * i) -= udCi * fExt * intElement;
          }
        }
      }
 
      // External forces, boundary forces, i.e., at the Neumann boundary
      if (not neumannBoundary and not neumannBoundaryLoad) return;
      const auto& element = this->localView().element();
      for (auto&& intersection : intersections(neumannBoundary->gridView(), element)) {
        if (not neumannBoundary->contains(intersection)) continue;
 
        // Integration rule along the boundary
        const auto& quadLine = Dune::QuadratureRules<double, myDim - 1>::rule(intersection.type(), order);
 
        for (const auto& curQuad : quadLine) {
          const Dune::FieldVector<double, myDim>& quadPos = intersection.geometryInInside().global(curQuad.position());
 
          const double intElement = intersection.geometry().integrationElement(curQuad.position());
 
          // The value of the local function wrt the i-th coefficient
          for (size_t i = 0; i < numberOfNodes; ++i) {
            const auto udCi = uFunction.evaluateDerivative(quadPos, wrt(coeff(i)));
 
            // Value of the Neumann data at the current position
            const auto neumannValue = neumannBoundaryLoad(intersection.geometry().global(curQuad.position()), lambda);
            force.template segment<myDim>(myDim * i) -= udCi * neumannValue * curQuad.weight() * intElement;
          }
        }
      }
    }
  };
}  // namespace Ikarus
 
#else
#  error NonLinearElastic depends on dune-localfefunctions, which is not included
#endif