assumedstress.hh

Go to the documentation of this file.

// 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 <dune/localfefunctions/derivativetransformators.hh>
  #include <dune/localfefunctions/linearAlgebraHelper.hh>
  #include <dune/localfefunctions/meta.hh>
 
  #include <ikarus/finiteelements/fehelper.hh>
  #include <ikarus/finiteelements/ferequirements.hh>
  #include <ikarus/finiteelements/mechanics/assumedstress/asfunctions.hh>
  #include <ikarus/finiteelements/mechanics/assumedstress/asvariants.hh>
  #include <ikarus/finiteelements/mechanics/materials/strainconversions.hh>
  #include <ikarus/finiteelements/mechanics/materials/stressconversions.hh>
  #include <ikarus/finiteelements/mechanics/materials/tags.hh>
  #include <ikarus/utils/broadcaster/broadcastermessages.hh>
  #include <ikarus/utils/concepts.hh>
  #include <ikarus/utils/linearalgebrahelper.hh>
 
namespace Ikarus {
 
template <typename PreFE, typename FE, typename ASType>
class AssumedStress;
 
template <typename ASType>
struct AssumedStressPre
{
  int numberOfParameters{};
 
  template <typename PreFE, typename FE>
  using Skill = AssumedStress<PreFE, FE, ASType>;
};
 
template <typename PreFE, typename FE, typename ASF>
class AssumedStress
    : public std::conditional_t<std::same_as<ASF, PS::LinearStress>,
                                ResultTypeBase<ResultTypes::linearStress, ResultTypes::linearStressFull>,
                                ResultTypeBase<ResultTypes::PK2Stress, ResultTypes::PK2StressFull,
                                               ResultTypes::kirchhoffStress, ResultTypes::cauchyStress>>
 
{
public:
  using Traits                = PreFE::Traits;
  using Requirement           = FERequirements<FESolutions::displacement, FEParameter::loadfactor>;
  using LocalView             = typename Traits::LocalView;
  using Geometry              = typename Traits::Geometry;
  using GridView              = typename Traits::GridView;
  using Pre                   = AssumedStressPre<ASF>;
  using AssumedStressFunction = ASF;
 
  template <typename ST>
  using VectorXOptRef = std::optional<std::reference_wrapper<const Eigen::VectorX<ST>>>;
 
  template <template <typename, int, int> class RT>
  using RTWrapperType = ResultWrapper<RT<typename Traits::ctype, Traits::mydim, Traits::worlddim>, ResultShape::Vector>;
 
  static constexpr int myDim     = Traits::mydim;
  static constexpr int strainDim = myDim * (myDim + 1) / 2;
  using StrainVector             = Eigen::Vector<double, strainDim>;
  using MaterialMatrix           = Eigen::Matrix<double, strainDim, strainDim>;
 
  explicit AssumedStress(const Pre& pre) {
    static_assert(Concepts::Formulations::TotalLagrangian<FE::strainType, FE::stressType>,
                  "PS method is only implemented for the total Lagrangian setting.");
    static_assert(not(FE::strainType == StrainTags::linear) or (std::same_as<ASF, PS::LinearStress>),
                  "If FE::strainType is linear, then the assumed stress must also be linear.");
    asVariant_.setAssumedStressType(pre.numberOfParameters);
  }
 
  const auto& asVariant() const { return asVariant_; }
 
  auto numberOfInternalVariables() const { return asVariant_.numberOfInternalVariables(); }
 
  template <template <typename, int, int> class RT>
  requires(AssumedStress::template supportsResultType<RT>())
  auto calculateAtImpl(const Requirement& req, const Dune::FieldVector<double, Traits::mydim>& local,
                       Dune::PriorityTag<2>) const {
    using namespace Dune::DerivativeDirections;
    using Ikarus::transformStrain;
    using Ikarus::transformStress;
    const auto geo   = underlying().localView().element().geometry();
    const auto ufunc = underlying().displacementFunction(req);
    auto disp        = Dune::viewAsFlatEigenVector(ufunc.coefficientsRef());
    const auto H     = ufunc.evaluateDerivative(local, Dune::wrt(spatialAll), Dune::on(gridElement));
    const auto F     = transformStrain<StrainTags::displacementGradient, StrainTags::deformationGradient>(H).eval();
 
    RTWrapperType<RT> resultWrapper{};
    auto calculateAtContribution = [&]<typename AssumedStressT>(const AssumedStressT& asFunction) {
      Eigen::VectorXd beta;
      beta.setZero(numberOfInternalVariables());
      if constexpr (isSameResultType<RT, ResultTypes::linearStressFull> or
                    isSameResultType<RT, ResultTypes::linearStress>) {
        const auto& Rtilde = calculateRtilde<double>(req);
        typename AssumedStressT::HType H;
        calculateHAndGMatrix(asFunction, req, H, G_);
        beta = H.inverse() * (G_ * disp);
      } else
        beta = this->beta_;
 
      const auto SVoigt = AssumedStressFunction::value(geo, local, asFunction, beta);
 
      if constexpr ((isSameResultType<RT, ResultTypes::PK2StressFull> or
                     isSameResultType<RT, ResultTypes::linearStressFull>) and
                    requires { underlying().material().underlying(); }) {
        resultWrapper = enlargeStressAnsatz(SVoigt);
      } else if constexpr (isSameResultType<RT, ResultTypes::PK2Stress> or
                           isSameResultType<RT, ResultTypes::linearStress>)
        resultWrapper = SVoigt;
      else if constexpr (isSameResultType<RT, ResultTypes::kirchhoffStress> or
                         isSameResultType<RT, ResultTypes::cauchyStress>) {
        const auto PK2StressMat = fromVoigt(SVoigt, false).eval();
        constexpr StressTags toStress =
            isSameResultType<RT, ResultTypes::kirchhoffStress> ? StressTags::Kirchhoff : StressTags::Cauchy;
        resultWrapper = toVoigt(transformStress<StressTags::PK2, toStress>(PK2StressMat, F), false);
      }
    };
    asVariant_(calculateAtContribution);
    return resultWrapper;
  }
 
  void setAssumedStressType(int numberOfInternalVariables) {
    asApplicabilityCheck();
    asVariant_.setAssumedStressType(numberOfInternalVariables);
    initializeState();
  }
 
  const auto& internalVariable() const { return beta_; }
 
protected:
  void bindImpl() {
    assert(underlying().localView().bound());
    asVariant_.bind(underlying().localView().element().geometry());
    initializeState();
  }
 
  void updateStateImpl(const Requirement& par,
                       const std::remove_reference_t<typename Traits::template VectorType<>>& correction) {
    using ScalarType = Traits::ctype;
    asApplicabilityCheck();
    auto correctbeta = [&]<typename AssumedStressT>(const AssumedStressT& asFunction) {
      if (correction.size() != par.globalSolution().size())
        DUNE_THROW(Dune::NotImplemented,
                   "Solution vector and correction vector should be of the same size. Check if DBCOption::Full is "
                   "used. The sizes are " +
                       std::to_string(par.globalSolution().size()) + " and " + std::to_string(correction.size()));
      const auto localdxBlock = Ikarus::FEHelper::localSolutionBlockVector<Traits, Eigen::VectorXd, double>(
          correction, underlying().localView());
      const auto localdx = Dune::viewAsFlatEigenVector(localdxBlock);
 
      typename AssumedStressT::HType H;
      calculateHAndGMatrix(asFunction, par, H, G_);
      const auto& Rtilde = calculateRtilde<ScalarType>(par);
      this->beta_ += H.inverse() * (Rtilde + (G_ * localdx));
    };
 
    asVariant_(correctbeta);
    calculateMaterialInversion();
  }
 
  inline void asApplicabilityCheck() const {
    const auto& numberOfNodes = underlying().numberOfNodes();
    if (not((numberOfNodes == 4 and Traits::mydim == 2) or (numberOfNodes == 8 and Traits::mydim == 3)))
      DUNE_THROW(Dune::NotImplemented, "AssumedStress is only supported for Q1 and H1 elements" +
                                           std::to_string(numberOfNodes) + std::to_string(Traits::mydim));
  }
 
  template <typename ScalarType>
  void calculateMatrixImpl(const Requirement& par, const MatrixAffordance& affordance,
                           typename Traits::template MatrixType<> K,
                           const VectorXOptRef<ScalarType>& dx = std::nullopt) const {
    using namespace Dune;
    using namespace Dune::DerivativeDirections;
 
    if (affordance != MatrixAffordance::stiffness)
      DUNE_THROW(Dune::NotImplemented, "MatrixAffordance not implemented: " + toString(affordance));
    asApplicabilityCheck();
 
    const auto geo             = underlying().localView().element().geometry();
    const auto& strainFunction = underlying().strainFunction(par, dx);
    const auto& kGFunction     = underlying().template geometricStiffnessMatrixFunction<ScalarType>(par, K, dx);
    const auto numberOfNodes   = underlying().numberOfNodes();
    const auto& localBasis     = underlying().localBasis();
 
    auto calculateMatrixContribution = [&]<typename AssumedStressT>(const AssumedStressT& asFunction) {
      for (const auto& [gpIndex, gp] : strainFunction.viewOverIntegrationPoints()) {
        const auto SVoigt = AssumedStressFunction::value(geo, gp.position(), asFunction, beta_);
 
        for (size_t i = 0; i < numberOfNodes; ++i)
          for (size_t j = 0; j < numberOfNodes; ++j) {
            const auto E_dd =
                strainFunction.evaluateDerivative(gpIndex, wrt(coeff(i, j)), along(SVoigt), on(gridElement));
            kGFunction(E_dd, i, j, gp);
          }
      }
 
      typename AssumedStressT::HType H;
      calculateHAndGMatrix(asFunction, par, H, G_, dx);
 
      K.template triangularView<Eigen::Upper>() += G_.transpose() * H.inverse() * G_;
      K.template triangularView<Eigen::StrictlyLower>() = K.transpose();
    };
    asVariant_(calculateMatrixContribution);
  }
 
  template <typename ScalarType>
  inline ScalarType calculateScalarImpl(const Requirement& par, ScalarAffordance affordance,
                                        const VectorXOptRef<ScalarType>& dx = std::nullopt) const {
    using namespace Dune;
    using namespace Dune::DerivativeDirections;
    asApplicabilityCheck();
    ScalarType energy = 0.0;
 
    // This will not work in the context of autodiff because `AutoDiffFE` class doesn't include static condensation of
    // the internal variable
    if constexpr (not Concepts::AutodiffScalar<ScalarType>) {
      const auto geo            = underlying().localView().element().geometry();
      const auto strainFunction = underlying().strainFunction(par, dx);
 
      auto calculateScalarContribution = [&]<typename AssumedStressT>(const AssumedStressT& asFunction) {
        for (const auto& [gpIndex, gp] : strainFunction.viewOverIntegrationPoints()) {
          const auto SVoigt = AssumedStressFunction::value(geo, gp.position(), asFunction, beta_);
          const auto& Es    = strainStates_[gpIndex];
          const auto EVoigt = strainFunction.evaluate(gp.position(), on(gridElement));
 
          energy += ((SVoigt.transpose() * EVoigt - ScalarType(0.5) * (SVoigt.transpose() * Es)).eval() *
                     geo.integrationElement(gp.position()) * gp.weight())
                        .eval()[0];
        }
      };
 
      asVariant_(calculateScalarContribution);
    } else {
      DUNE_THROW(Dune::NotImplemented,
                 "AssumedStress element does not support scalar calculations for autodiff scalars");
    }
    return energy;
  }
 
  template <typename ScalarType>
  void calculateVectorImpl(const Requirement& par, VectorAffordance affordance,
                           typename Traits::template VectorType<ScalarType> force,
                           const VectorXOptRef<ScalarType>& dx = std::nullopt) const {
    using namespace Dune::DerivativeDirections;
    using namespace Dune;
 
    if (affordance != VectorAffordance::forces)
      DUNE_THROW(Dune::NotImplemented, "VectorAffordance not implemented: " + toString(affordance));
    asApplicabilityCheck();
 
    const auto geo             = underlying().localView().element().geometry();
    const auto& uFunction      = underlying().displacementFunction(par, dx);
    const auto& strainFunction = underlying().strainFunction(par, dx);
    const auto numberOfNodes   = underlying().numberOfNodes();
    const auto& localBasis     = underlying().localBasis();
    const auto fIntFunction    = underlying().template internalForcesFunction<ScalarType>(par, force, dx);
 
    auto calculateForceContribution = [&]<typename AssumedStressT>(const AssumedStressT& asFunction) {
      for (const auto& [gpIndex, gp] : uFunction.viewOverIntegrationPoints()) {
        const auto SVoigt = AssumedStressFunction::value(geo, gp.position(), asFunction, beta_);
 
        for (size_t i = 0; i < numberOfNodes; ++i) {
          const auto E_dI = strainFunction.evaluateDerivative(gpIndex, wrt(coeff(i)), on(gridElement));
          fIntFunction(SVoigt, E_dI, i, gp);
        }
      }
      typename AssumedStressT::HType H;
      calculateHAndGMatrix(asFunction, par, H, G_);
      const auto Rtilde = calculateRtilde(par, dx);
      force += G_.transpose() * H.inverse() * Rtilde;
    };
    asVariant_(calculateForceContribution);
  }
 
  template <typename MT, typename BC>
  void subscribeToImpl(BC& bc) {
    if constexpr (std::same_as<MT, NonLinearSolverMessages>) {
      using NLSState = typename BC::State;
      underlying().subscribe(bc, [&](NonLinearSolverMessages message, const NLSState& state) {
        if (message == NonLinearSolverMessages::CORRECTION_UPDATED)
          this->updateStateImpl(state.domain, state.correction);
      });
    }
  }
 
private:
  PS::AssumedStressVariant<AssumedStressFunction, Geometry> asVariant_;
  mutable Eigen::MatrixXd G_;
  Eigen::VectorXd beta_;
  std::vector<StrainVector> strainStates_;
  std::vector<MaterialMatrix> invertedMaterialStates_;
 
  //> CRTP
  const auto& underlying() const { return static_cast<const FE&>(*this); }
  auto& underlying() { return static_cast<FE&>(*this); }
 
  void initializeState() {
    beta_.resize(numberOfInternalVariables());
    beta_.setZero();
    strainStates_.resize(underlying().localBasis().integrationPointSize(), StrainVector::Zero());
    invertedMaterialStates_.resize(underlying().localBasis().integrationPointSize(), MaterialMatrix::Zero());
    calculateMaterialInversion();
  }
 
  template <typename ScalarType, int assumedStressSize>
  void calculateHAndGMatrix(const auto& asFunction, const auto& par,
                            Eigen::Matrix<double, assumedStressSize, assumedStressSize>& H,
                            Eigen::MatrixX<ScalarType>& G, const VectorXOptRef<ScalarType>& dx = std::nullopt) const {
    using namespace Dune::DerivativeDirections;
    using namespace Dune;
 
    const auto& uFunction      = underlying().displacementFunction(par);
    const auto& strainFunction = underlying().strainFunction(par, dx);
    const auto geo             = underlying().localView().element().geometry();
    const auto numberOfNodes   = underlying().numberOfNodes();
    const auto& localBasis     = underlying().localBasis();
    H.setZero();
    G.setZero(assumedStressSize, underlying().localView().size());
    for (const auto& [gpIndex, gp] : uFunction.viewOverIntegrationPoints()) {
      const double intElement = geo.integrationElement(gp.position()) * gp.weight();
 
      const auto SVoigt = AssumedStressFunction::value(geo, gp.position(), asFunction, beta_);
      const auto& D     = invertedMaterialStates_[gpIndex];
 
      const auto S_b  = AssumedStressFunction::template firstDerivative(geo, uFunction, localBasis, gpIndex,
                                                                        gp.position(), asFunction, beta_);
      const auto S_bb = AssumedStressFunction::template secondDerivative(geo, uFunction, localBasis, gpIndex,
                                                                         gp.position(), SVoigt, asFunction, beta_);
 
      H += (S_b.transpose() * D * S_b + S_bb) * intElement;
 
      for (size_t i = 0U; i < numberOfNodes; ++i) {
        const auto E_dI = strainFunction.evaluateDerivative(gpIndex, wrt(coeff(i)), on(gridElement));
 
        G.template block<assumedStressSize, Traits::worlddim>(0, myDim * i) += S_b.transpose() * E_dI * intElement;
      }
    }
  }
 
  template <typename ScalarType>
  Eigen::VectorX<ScalarType> calculateRtilde(const Requirement& par,
                                             const VectorXOptRef<ScalarType>& dx = std::nullopt) const {
    using namespace Dune;
    using namespace Dune::DerivativeDirections;
 
    const auto geo            = underlying().localView().element().geometry();
    const auto& uFunction     = underlying().displacementFunction(par, dx);
    const auto strainFunction = underlying().strainFunction(par, dx);
    const auto& localBasis    = underlying().localBasis();
 
    Eigen::VectorX<ScalarType> Rtilde;
    Rtilde.setZero(numberOfInternalVariables());
 
    auto calculateRtildeContribution = [&]<typename AssumedStressT>(const AssumedStressT& asFunction) {
      for (const auto& [gpIndex, gp] : uFunction.viewOverIntegrationPoints()) {
        const auto SVoigt = AssumedStressFunction::value(geo, gp.position(), asFunction, beta_);
        const auto S_b    = AssumedStressFunction::template firstDerivative(geo, uFunction, localBasis, gpIndex,
                                                                            gp.position(), asFunction, beta_);
 
        const auto& Es    = strainStates_[gpIndex];
        const auto EVoigt = strainFunction.evaluate(gp.position(), on(gridElement));
 
        const double intElement = geo.integrationElement(gp.position()) * gp.weight();
        Rtilde += (S_b.transpose() * (EVoigt - Es)).eval() * intElement;
      }
    };
 
    asVariant_(calculateRtildeContribution);
    return Rtilde;
  }
 
  void calculateMaterialInversion() {
    auto saveMaterialState = [&]<typename AssumedStressT>(const AssumedStressT& asFunction) {
      const auto geo = underlying().localView().element().geometry();
 
      for (const auto& [gpIndex, gp] : underlying().localBasis().viewOverIntegrationPoints()) {
        const auto SVoigt = AssumedStressFunction::value(geo, gp.position(), asFunction, beta_);
        const auto& EsOld = strainStates_[gpIndex];
        std::tie(invertedMaterialStates_[gpIndex], strainStates_[gpIndex]) =
            underlying().material().template materialInversion<FE::strainType, true>(SVoigt, EsOld);
      }
    };
    asVariant_(saveMaterialState);
  }
 
  auto enlargeStressAnsatz(const StrainVector& SVoigt, size_t qpIndexForIteration = 0) const
  requires(decltype(underlying().material())::isReduced)
  {
    auto [_, Es] = underlying().material().template materialInversion<FE::strainType, true>(
        SVoigt, strainStates_[qpIndexForIteration]);
    auto Esfull = enlargeIfReduced<decltype(underlying().material())>(Es).eval();
    return underlying().material().underlying().template stresses<FE::strainType, true>(Esfull);
  }
};
 
template <typename ASType = PS::LinearStress>
auto assumedStress(int numberOfInternalVariables) {
  return AssumedStressPre<ASType>(numberOfInternalVariables);
}
 
} // namespace Ikarus
 
#else
  #error AssumedStress depends on dune-localfefunctions, which is not included
#endif