traction.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 <dune/fufem/boundarypatch.hh>
 
#include <ikarus/finiteelements/ferequirements.hh>
#include <ikarus/utils/defaultfunctions.hh>
 
namespace Ikarus {
 
  template <typename DisplacementBasedElement, typename Traits>
  class Traction {
  public:
    using FERequirementType       = typename Traits::FERequirementType;
    using LocalView               = typename Traits::LocalView;
    using GridView                = typename Traits::GridView;
    static constexpr int myDim    = Traits::mydim;
    static constexpr int worldDim = Traits::worlddim;
 
    template <typename NeumannBoundaryLoad>
    explicit Traction(const BoundaryPatch<GridView>* p_neumannBoundary, NeumannBoundaryLoad p_neumannBoundaryLoad)
        : neumannBoundary{p_neumannBoundary} {
      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!");
    }
 
    double calculateScalar(const FERequirementType& req) const { return calculateScalarImpl<double>(req); }
 
    void calculateVector(const FERequirementType& req, typename Traits::template VectorType<> force) const {
      calculateVectorImpl<double>(req, force);
    }
    void calculateMatrix(const FERequirementType& req, typename Traits::template MatrixType<> K) const {
      calculateMatrixImpl<double>(req, K);
    }
 
  protected:
    template <typename ScalarType>
    auto calculateScalarImpl(const FERequirementType& par, const std::optional<const Eigen::VectorX<ScalarType>>& dx
                                                           = std::nullopt) const -> ScalarType {
      if (not neumannBoundary and not neumannBoundaryLoad) return 0.0;
      ScalarType energy    = 0.0;
      const auto uFunction = dbElement().displacementFunction(par, dx);
      const auto& lambda   = par.getParameter(Ikarus::FEParameter::loadfactor);
      auto& element        = dbElement().localView().element();
 
      for (auto&& intersection : intersections(neumannBoundary->gridView(), element)) {
        if (not neumannBoundary->contains(intersection)) continue;
 
        const auto& quadLine = Dune::QuadratureRules<double, myDim - 1>::rule(intersection.type(), dbElement().order());
 
        for (const auto& curQuad : quadLine) {
          // Local position of the quadrature point
          const Dune::FieldVector<double, myDim>& quadPos = intersection.geometryInInside().global(curQuad.position());
 
          const double integrationElement = intersection.geometry().integrationElement(curQuad.position());
 
          // The value of the local function
          const auto uVal = uFunction.evaluate(quadPos);
 
          // Value of the Neumann data at the current position
          auto neumannValue = neumannBoundaryLoad(intersection.geometry().global(curQuad.position()), lambda);
 
          energy -= neumannValue.dot(uVal) * curQuad.weight() * integrationElement;
        }
      }
      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 {
      if (not neumannBoundary and not neumannBoundaryLoad) return;
      using namespace Dune::DerivativeDirections;
      using namespace Dune;
      const auto uFunction = dbElement().displacementFunction(par, dx);
      const auto& lambda   = par.getParameter(Ikarus::FEParameter::loadfactor);
      auto& element        = dbElement().localView().element();
 
      for (auto&& intersection : intersections(neumannBoundary->gridView(), element)) {
        if (not neumannBoundary->contains(intersection)) continue;
 
        const auto& quadLine = Dune::QuadratureRules<double, myDim - 1>::rule(intersection.type(), dbElement().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());
 
          for (size_t i = 0; i < dbElement().numberOfNodes(); ++i) {
            const auto udCi = uFunction.evaluateDerivative(quadPos, wrt(coeff(i)));
 
            auto neumannValue = neumannBoundaryLoad(intersection.geometry().global(curQuad.position()), lambda);
            force.template segment<worldDim>(worldDim * i) -= udCi * neumannValue * curQuad.weight() * intElement;
          }
        }
      }
    }
 
    template <typename ScalarType>
    void calculateMatrixImpl(const FERequirementType& par, typename Traits::template MatrixType<> K,
                             const std::optional<const Eigen::VectorX<ScalarType>>& dx = std::nullopt) const {}
 
  private:
    std::function<Eigen::Vector<double, worldDim>(const Dune::FieldVector<double, worldDim>&, const double&)>
        neumannBoundaryLoad;
    const BoundaryPatch<GridView>* neumannBoundary;
 
    constexpr const DisplacementBasedElement& dbElement() const {
      return static_cast<DisplacementBasedElement const&>(*this);
    }
  };
}  // namespace Ikarus