vanishingstress.hh

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// SPDX-FileCopyrightText: 2021-2025 The Ikarus Developers ikarus@ibb.uni-stuttgart.de
// SPDX-License-Identifier: LGPL-3.0-or-later
 
#pragma once
 
#include "materialhelpers.hh"
 
#include <ikarus/finiteelements/mechanics/materials/interface.hh>
#include <ikarus/solver/nonlinearsolver/newtonraphson.hh>
#include <ikarus/solver/nonlinearsolver/nonlinearsolverfactory.hh>
#include <ikarus/utils/concepts.hh>
#include <ikarus/utils/differentiablefunction.hh>
#include <ikarus/utils/tensorutils.hh>
 
namespace Ikarus::Materials {
 
template <auto stressIndexPair, typename MI>
struct VanishingStress : public Material<VanishingStress<stressIndexPair, MI>>
{
  using Underlying         = MI; 
  using MaterialParameters = typename Underlying::MaterialParameters;
  using StrainMatrix       = typename Underlying::StrainMatrix;
  using StressMatrix       = typename Underlying::StressMatrix;
  using MaterialTensor     = typename Underlying::MaterialTensor;
  static constexpr int dim = Underlying::dim;
 
  static constexpr auto fixedPairs        = stressIndexPair; 
  static constexpr auto freeVoigtIndices  = Impl::createfreeVoigtIndices(fixedPairs);  
  static constexpr auto fixedVoigtIndices = Impl::createFixedVoigtIndices(fixedPairs); 
  static constexpr auto fixedDiagonalVoigtIndicesSize =
      Impl::countDiagonalIndices(fixedPairs);                          
  static constexpr auto freeStrains = freeVoigtIndices.size();         
  using ScalarType                  = typename Underlying::ScalarType; 
  static constexpr bool isAutoDiff  = Concepts::AutodiffScalar<ScalarType>;
 
  static constexpr auto strainTag              = Underlying::strainTag;            
  static constexpr auto stressTag              = Underlying::stressTag;            
  static constexpr auto tangentModuliTag       = Underlying::tangentModuliTag;     
  static constexpr bool energyAcceptsVoigt     = Underlying::energyAcceptsVoigt;   
  static constexpr bool stressToVoigt          = true;                             
  static constexpr bool stressAcceptsVoigt     = true;                             
  static constexpr bool moduliToVoigt          = true;                             
  static constexpr bool moduliAcceptsVoigt     = true;                             
  static constexpr double derivativeFactorImpl = Underlying::derivativeFactorImpl; 
 
  explicit VanishingStress(MI mat, typename MI::ScalarType tol = 1e-12)
      : matImpl_{mat},
        tol_{tol} {}
 
  [[nodiscard]] constexpr static std::string nameImpl() noexcept {
    auto matName = MI::name() + "_VanishingStress(";
    for (auto p : fixedPairs)
      matName += "(" + std::to_string(p.row) + std::to_string(p.col) + ")";
    matName += ")";
    return matName;
  }
 
  MaterialParameters materialParametersImpl() const { return matImpl_.materialParametersImpl(); }
 
  template <typename Derived>
  ScalarType storedEnergyImpl(const Eigen::MatrixBase<Derived>& E) const {
    const auto [nonOp, Esol] = reduceStress(E);
    return matImpl_.storedEnergyImpl(Esol);
  }
 
  template <bool voigt, typename Derived>
  auto stressesImpl(const Eigen::MatrixBase<Derived>& E) const {
    const auto [nonOp, Esol] = reduceStress(E);
    auto stressesRed         = matImpl_.template stresses<Underlying::strainTag, true>(Esol);
 
    if constexpr (voigt) {
      return removeCol(stressesRed, fixedVoigtIndices);
    } else
      return fromVoigt(stressesRed, false);
  }
 
  template <bool voigt, typename Derived>
  auto tangentModuliImpl(const Eigen::MatrixBase<Derived>& E) const {
    const auto [nonOp, Esol] = reduceStress(E);
    auto C                   = matImpl_.template tangentModuli<Underlying::strainTag, true>(Esol);
    if constexpr (voigt)
      return staticCondensation(C, fixedVoigtIndices);
    else
      return fromVoigt(C);
  }
 
  template <typename ScalarTypeOther>
  auto rebind() const {
    auto reboundMatImpl = matImpl_.template rebind<ScalarTypeOther>();
    return VanishingStress<stressIndexPair, decltype(reboundMatImpl)>(reboundMatImpl, tol_);
  }
 
  auto& underlying() const { return matImpl_; }
 
  template <typename Derived>
  auto materialInversionImpl(const Eigen::MatrixBase<Derived>& Sraw) const {
    static_assert(Concepts::EigenMatrix22<decltype(Sraw)>);
    // Enlarge S
    auto S                       = Eigen::Matrix<typename Derived::Scalar, 3, 3>::Zero().eval();
    S.template block<2, 2>(0, 0) = Sraw;
 
    auto [D, E] = matImpl_.template materialInversion<Underlying::strainTag, true>(S);
 
    // Reduce D and E again
    auto Dred = reduceMatrix(D, fixedVoigtIndices);
    auto Ered = removeCol(E, fixedVoigtIndices);
 
    return std::make_pair(Dred, Ered);
  }
 
private:
  template <typename Derived>
  void initUnknownStrains(Eigen::MatrixBase<Derived>& E) const {
    for (size_t i = 0; i < fixedPairs.size(); ++i) {
      ScalarType initialVal = E(fixedPairs[i].row, fixedPairs[i].col);
      if constexpr (strainTag == StrainTags::deformationGradient or strainTag == StrainTags::rightCauchyGreenTensor) {
        if (Dune::FloatCmp::eq(initialVal, ScalarType(0.0)) and (fixedPairs[i].row == fixedPairs[i].col))
          initialVal = ScalarType(1.0);
      }
      if (fixedPairs[i].row != fixedPairs[i].col)
        initialVal = ScalarType(0.0);
      E(fixedPairs[i].row, fixedPairs[i].col) = E(fixedPairs[i].col, fixedPairs[i].row) = initialVal;
    }
  }
 
  template <typename Derived>
  auto reduceStress(const Eigen::MatrixBase<Derived>& Eraw) const {
    auto E = Impl::maybeFromVoigt(Eraw);
    initUnknownStrains(E);
 
    std::array<size_t, fixedDiagonalVoigtIndicesSize> fixedDiagonalVoigtIndices;
    for (size_t ri = 0; auto i : fixedVoigtIndices) {
      auto indexPair = fromVoigt(i);
      if (indexPair[0] == indexPair[1])
        fixedDiagonalVoigtIndices[ri++] = i;
    }
 
    auto f = [&](const auto&) {
      auto S = matImpl_.template stresses<Underlying::strainTag, true>(E);
      return S(fixedDiagonalVoigtIndices).eval();
    };
    auto df = [&](const auto&) {
      auto moduli = (matImpl_.template tangentModuli<Underlying::strainTag, true>(E)).eval();
      return (moduli(fixedDiagonalVoigtIndices, fixedDiagonalVoigtIndices) / Underlying::derivativeFactor).eval();
    };
 
    auto Er = E(fixedDiagonalVoigtIndices, fixedDiagonalVoigtIndices).eval().template cast<ScalarType>();
 
    Er.setZero();
    auto diffFunction = Ikarus::makeDifferentiableFunction(functions(f, df), Er);
 
    auto linearSolver   = [](auto& r, auto& A) { return (A.inverse() * r).eval(); };
    auto updateFunction = [&](auto&, const auto& ecomps) {
      for (int ri = 0; auto i : fixedDiagonalVoigtIndices) {
        auto indexPair = fromVoigt(i);
        E(indexPair[0], indexPair[1]) += ecomps(ri++);
      }
    };
 
    int minIter = isAutoDiff ? 1 : 0;
    NewtonRaphsonConfig nrs({.tol = tol_, .maxIter = 100, .minIter = minIter}, linearSolver, updateFunction);
 
    auto nr = createNonlinearSolver(std::move(nrs), diffFunction);
    if (!static_cast<bool>(nr->solve(Er)))
      DUNE_THROW(Dune::MathError, "The stress reduction of material " << nameImpl() << " was unsuccessful\n"
                                                                      << "The strains are\n"
                                                                      << E << "\n The stresses are\n"
                                                                      << f(Er));
    return std::make_pair(diffFunction, E);
  }
 
  Underlying matImpl_; 
  double tol_{};       
};
 
template <MatrixIndexPair... stressIndexPair, typename MaterialImpl>
auto makeVanishingStress(MaterialImpl mat, typename MaterialImpl::ScalarType p_tol = 1e-12) {
  return VanishingStress<std::to_array({stressIndexPair...}), MaterialImpl>(mat, p_tol);
}
 
template <typename MaterialImpl>
auto planeStress(const MaterialImpl& mat, typename MaterialImpl::ScalarType tol = 1e-8) {
  return makeVanishingStress<MatrixIndexPair{2, 1}, MatrixIndexPair{2, 0}, MatrixIndexPair{2, 2}>(mat, tol);
}
 
template <typename MaterialImpl>
auto shellMaterial(const MaterialImpl& mat, typename MaterialImpl::ScalarType tol = 1e-8) {
  return makeVanishingStress<MatrixIndexPair{2, 2}>(mat, tol);
}
 
template <typename MaterialImpl>
auto beamMaterial(const MaterialImpl& mat, typename MaterialImpl::ScalarType tol = 1e-8) {
  return makeVanishingStress<MatrixIndexPair{1, 1}, MatrixIndexPair{2, 2}>(mat, tol);
}
} // namespace Ikarus::Materials