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/febase.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 PreFE, typename FE, typename PRE>
class NonLinearElastic;
 
template <typename MAT>
struct NonLinearElasticPre
{
  using Material = MAT;
  MAT material;
 
  template <typename PreFE, typename FE>
  using Skill = NonLinearElastic<PreFE, FE, NonLinearElasticPre>;
};
 
template <typename PreFE, typename FE, typename PRE>
class NonLinearElastic : public ResultTypeBase<ResultTypes::PK2Stress>
{
public:
  using Traits    = PreFE::Traits;
  using Basis     = typename Traits::Basis;
  using FlatBasis = typename Traits::FlatBasis;
  using Requirement =
      FERequirementsFactory<FESolutions::displacement, FEParameter::loadfactor, Traits::useEigenRef>::type;
  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());
 
  static constexpr int myDim       = Traits::mydim;
  static constexpr auto strainType = StrainTags::greenLagrangian;
 
  explicit NonLinearElastic(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_                = 2 * (fe.localBasis().order());
    localBasis_           = Dune::CachedLocalBasis(fe.localBasis());
    if constexpr (requires { element.impl().getQuadratureRule(order_); })
      if (element.impl().isTrimmed())
        localBasis_.bind(element.impl().getQuadratureRule(order_), Dune::bindDerivatives(0, 1));
      else
        localBasis_.bind(Dune::QuadratureRules<double, myDim>::rule(element.type(), order_),
                         Dune::bindDerivatives(0, 1));
    else
      localBasis_.bind(Dune::QuadratureRules<double, myDim>::rule(element.type(), order_), Dune::bindDerivatives(0, 1));
  }
 
public:
  template <typename ScalarType = double>
  auto displacementFunction(
      const Requirement& par,
      const std::optional<std::reference_wrapper<const Eigen::VectorX<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 <typename ScalarType = double>
  inline auto strainFunction(
      const Requirement& par,
      const std::optional<std::reference_wrapper<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 {
    return material<ScalarType>().template tangentModuli<strainType, voigt>(strain);
  }
 
  template <typename ScalarType, int strainDim>
  auto getInternalEnergy(const Eigen::Vector<ScalarType, strainDim>& strain) const {
    return material<ScalarType>().template storedEnergy<strainType>(strain);
  }
 
  template <typename ScalarType, int strainDim, bool voigt = true>
  auto getStress(const Eigen::Vector<ScalarType, strainDim>& strain) const {
    return material<ScalarType>().template stresses<strainType, voigt>(strain);
  }
 
  const Geometry& geometry() const { return *geo_; }
  [[nodiscard]] size_t numberOfNodes() const { return numberOfNodes_; }
  [[nodiscard]] int order() const { return order_; }
 
public:
  template <template <typename, int, int> class RT>
  requires(supportsResultType<RT>())
  auto calculateAtImpl(const Requirement& req, const Dune::FieldVector<double, Traits::mydim>& local,
                       Dune::PriorityTag<1>) const {
    using namespace Dune::DerivativeDirections;
 
    using RTWrapper = ResultWrapper<RT<typename Traits::ctype, myDim, Traits::worlddim>, ResultShape::Vector>;
    if constexpr (isSameResultType<RT, ResultTypes::PK2Stress>) {
      const auto uFunction = displacementFunction(req);
      const auto H         = uFunction.evaluateDerivative(local, Dune::wrt(spatialAll), Dune::on(gridElement));
      const auto E         = (0.5 * (H.transpose() + H + H.transpose() * H)).eval();
 
      return RTWrapper{mat_.template stresses<StrainTags::greenLagrangian>(toVoigt(E))};
    }
  }
 
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_{};
 
  template <typename ScalarType>
  decltype(auto) material() const {
    if constexpr (Concepts::AutodiffScalar<ScalarType>)
      return mat_.template rebind<ScalarType>();
    else
      return mat_;
  }
 
protected:
  template <typename ScalarType>
  void calculateMatrixImpl(
      const Requirement& par, const MatrixAffordance& affordance, typename Traits::template MatrixType<> K,
      const std::optional<std::reference_wrapper<const Eigen::VectorX<ScalarType>>>& dx = std::nullopt) const {
    using namespace Dune::DerivativeDirections;
    using namespace Dune;
    const auto uFunction = displacementFunction(par, dx);
    const auto eps       = strainFunction(par, dx);
    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 u            = (uFunction.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;
        }
      }
    }
  }
 
  template <typename ScalarType>
  auto calculateScalarImpl(const Requirement& par, ScalarAffordance affordance,
                           const std::optional<std::reference_wrapper<const Eigen::VectorX<ScalarType>>>& dx =
                               std::nullopt) const -> ScalarType {
    using namespace Dune::DerivativeDirections;
    using namespace Dune;
 
    const auto eps     = strainFunction(par, dx);
    const auto& lambda = par.parameter();
    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();
    }
 
    return energy;
  }
 
  template <typename ScalarType>
  void calculateVectorImpl(
      const Requirement& par, VectorAffordance affordance, typename Traits::template VectorType<ScalarType> force,
      const std::optional<std::reference_wrapper<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;
      }
    }
  }
};
 
template <typename MAT>
auto nonLinearElastic(const MAT& mat) {
  NonLinearElasticPre<MAT> pre(mat);
 
  return pre;
}
 
} // namespace Ikarus
 
#else
  #error NonLinearElastic depends on dune-localfefunctions, which is not included
#endif