vanishingstress.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
 
// SPDX-License-Identifier: LGPL-3.0-or-later
 
#pragma once
 
#include <ikarus/finiteelements/mechanics/materials/interface.hh>
#include <ikarus/solver/nonlinearsolver/newtonraphson.hh>
#include <ikarus/utils/nonlinearoperator.hh>
 
namespace Ikarus {
 
namespace Impl {
 
  struct StressIndexPair
  {
    Eigen::Index row; 
    Eigen::Index col; 
  };
 
  template <size_t size>
  consteval auto createfreeVoigtIndices(const std::array<StressIndexPair, size>& fixed) {
    std::array<size_t, 6 - size> res{};
    std::array<size_t, size> voigtFixedIndices;
    std::ranges::transform(fixed, voigtFixedIndices.begin(), [](auto pair) { return toVoigt(pair.row, pair.col); });
    std::ranges::sort(voigtFixedIndices);
    std::ranges::set_difference(std::ranges::iota_view(size_t(0), size_t(6)), voigtFixedIndices, res.begin());
    std::ranges::sort(res);
    return res;
  }
 
  template <size_t size>
  consteval auto createFixedVoigtIndices(const std::array<StressIndexPair, size>& fixed) {
    std::array<size_t, size> fixedIndices;
    std::ranges::transform(fixed, fixedIndices.begin(), [](auto pair) { return toVoigt(pair.row, pair.col); });
    std::ranges::sort(fixedIndices);
    return fixedIndices;
  }
 
  template <size_t size>
  constexpr size_t countDiagonalIndices(const std::array<StressIndexPair, size>& fixed) {
    size_t count = 0;
    for (auto v : fixed) {
      if (v.col == v.row)
        ++count;
    }
    return count;
  }
 
} // namespace Impl
 
template <auto stressIndexPair, typename MI>
struct VanishingStress : public Material<VanishingStress<stressIndexPair, MI>>
{
  explicit VanishingStress(MI mat, typename MI::ScalarType tol = 1e-12)
      : matImpl_{mat},
        tol_{tol} {}
 
  using Underlying = MI; 
 
  static constexpr auto fixedPairs        = stressIndexPair;                     
  static constexpr auto freeVoigtIndices  = createfreeVoigtIndices(fixedPairs);  
  static constexpr auto fixedVoigtIndices = createFixedVoigtIndices(fixedPairs); 
  static constexpr auto fixedDiagonalVoigtIndicesSize =
      countDiagonalIndices(fixedPairs);                                
  static constexpr auto freeStrains = freeVoigtIndices.size();         
  using ScalarType                  = typename Underlying::ScalarType; 
 
  [[nodiscard]] constexpr std::string nameImpl() const noexcept {
    auto matName = matImpl_.name() + "_Vanishing(";
    for (auto p : fixedPairs)
      matName += "(" + std::to_string(p.row) + std::to_string(p.col) + ")";
    matName += ")";
    return matName;
  }
 
  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 derivativeFactor = 1;                              
 
  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_);
  }
 
private:
  template <typename Derived>
  decltype(auto) maybeFromVoigt(const Eigen::MatrixBase<Derived>& E) const {
    if constexpr (Concepts::EigenVector<Derived>) { // receiving vector means Voigt notation
      return fromVoigt(E.derived(), true);
    } else
      return E.derived();
  }
 
  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 = 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 = [&](auto&) {
      auto S = matImpl_.template stresses<Underlying::strainTag, true>(E);
      return S(fixedDiagonalVoigtIndices).eval();
    };
    auto df = [&](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>();
    auto nonOp = Ikarus::NonLinearOperator(functions(f, df), parameter(Er));
    auto nr    = Ikarus::makeNewtonRaphson(
        nonOp, [&](auto& r, auto& A) { return (A.inverse() * r).eval(); },
        [&](auto& /* Ex33 */, auto& ecomps) {
          for (int ri = 0; auto i : fixedDiagonalVoigtIndices) {
            auto indexPair = fromVoigt(i);
            E(indexPair[0], indexPair[1]) += ecomps(ri++);
          }
        });
    nr->setup({.tol = tol_, .maxIter = 100});
    if (!static_cast<bool>(nr->solve()))
      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(nonOp, E);
  }
 
  Underlying matImpl_; 
  double tol_{};       
};
 
template <Impl::StressIndexPair... 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<Impl::StressIndexPair{2, 1}, Impl::StressIndexPair{2, 0}, Impl::StressIndexPair{2, 2}>(
      mat, tol);
}
 
template <typename MaterialImpl>
auto shellMaterial(const MaterialImpl& mat, typename MaterialImpl::ScalarType tol = 1e-8) {
  return makeVanishingStress<Impl::StressIndexPair{2, 2}>(mat, tol);
}
 
template <typename MaterialImpl>
auto beamMaterial(const MaterialImpl& mat, typename MaterialImpl::ScalarType tol = 1e-8) {
  return makeVanishingStress<Impl::StressIndexPair{1, 1}, Impl::StressIndexPair{2, 2}>(mat, tol);
}
} // namespace Ikarus