linearandglstrains.hh

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// SPDX-FileCopyrightText: 2021-2025 The Ikarus Developers mueller@ibb.uni-stuttgart.de
// SPDX-License-Identifier: LGPL-3.0-or-later
 
#pragma once
 
#include <ikarus/finiteelements/mechanics/strainenhancements/easvariants/helperfunctions.hh>
#include <ikarus/utils/tensorutils.hh>
 
namespace Ikarus::EAS {
 
template <typename GEO, int ess>
struct EX
{
  static constexpr int myDim              = GEO::mydimension;
  static constexpr int strainSize         = myDim * (myDim + 1) / 2;
  static constexpr int enhancedStrainSize = ess;
  using AnsatzType                        = Eigen::Matrix<double, strainSize, enhancedStrainSize>;
  using DType                             = Eigen::Matrix<double, enhancedStrainSize, enhancedStrainSize>;
 
  EX() = default;
  explicit EX(const GEO& geometry)
      : geometry_{std::make_optional<GEO>(geometry)},
        T0InverseTransformed_{Impl::transformationMatrixAtCenterWithDetJ(geometry).inverse()} {}
 
protected:
  std::optional<GEO> geometry_;
  Eigen::Matrix<double, strainSize, strainSize> T0InverseTransformed_;
};
 
template <typename GEO>
struct E0 : EX<GEO, 0>
{
  using Base                              = EX<GEO, 0>;
  static constexpr int myDim              = Base::myDim;
  static constexpr int strainSize         = Base::strainSize;
  static constexpr int enhancedStrainSize = Base::enhancedStrainSize;
  using AnsatzType                        = typename Base::AnsatzType;
  using DType                             = typename Base::DType;
 
  E0() = default;
  explicit E0(const GEO& geo)
      : Base(geo) {}
 
  // returns an Eigen zero expression for optimization purposes
  auto operator()(const Dune::FieldVector<double, myDim>& /*quadPos*/) const { return AnsatzType::Zero(); }
};
 
template <typename GEO>
struct E4 : EX<GEO, 4>
{
  using Base                              = EX<GEO, 4>;
  static constexpr int myDim              = Base::myDim;
  static constexpr int strainSize         = Base::strainSize;
  static constexpr int enhancedStrainSize = Base::enhancedStrainSize;
  using AnsatzType                        = typename Base::AnsatzType;
  using DType                             = typename Base::DType;
 
  E4() = default;
  explicit E4(const GEO& geo)
      : Base(geo) {}
 
  AnsatzType operator()(const Dune::FieldVector<double, myDim>& quadPos) const {
    AnsatzType M;
    M.setZero(strainSize, enhancedStrainSize);
    const double xi   = quadPos[0];
    const double eta  = quadPos[1];
    M(0, 0)           = 2 * xi - 1.0;
    M(1, 1)           = 2 * eta - 1.0;
    M(2, 2)           = 2 * xi - 1.0;
    M(2, 3)           = 2 * eta - 1.0;
    const double detJ = this->geometry_->integrationElement(quadPos);
    M                 = this->T0InverseTransformed_ / detJ * M;
    return M;
  }
};
 
template <typename GEO>
struct E5 : EX<GEO, 5>
{
  using Base                              = EX<GEO, 5>;
  static constexpr int myDim              = Base::myDim;
  static constexpr int strainSize         = Base::strainSize;
  static constexpr int enhancedStrainSize = Base::enhancedStrainSize;
  using AnsatzType                        = typename Base::AnsatzType;
  using DType                             = typename Base::DType;
 
  E5() = default;
  explicit E5(const GEO& geo)
      : Base(geo) {}
 
  AnsatzType operator()(const Dune::FieldVector<double, myDim>& quadPos) const {
    AnsatzType M;
    M.setZero();
    const double xi   = quadPos[0];
    const double eta  = quadPos[1];
    M(0, 0)           = 2 * xi - 1.0;
    M(1, 1)           = 2 * eta - 1.0;
    M(2, 2)           = 2 * xi - 1.0;
    M(2, 3)           = 2 * eta - 1.0;
    M(2, 4)           = (2 * xi - 1.0) * (2 * eta - 1.0);
    const double detJ = this->geometry_->integrationElement(quadPos);
    M                 = this->T0InverseTransformed_ / detJ * M;
    return M;
  }
};
 
template <typename GEO>
struct E7 : EX<GEO, 7>
{
  using Base                              = EX<GEO, 7>;
  static constexpr int myDim              = Base::myDim;
  static constexpr int strainSize         = Base::strainSize;
  static constexpr int enhancedStrainSize = Base::enhancedStrainSize;
  using AnsatzType                        = typename Base::AnsatzType;
  using DType                             = typename Base::DType;
 
  E7() = default;
  explicit E7(const GEO& geo)
      : Base(geo) {}
 
  AnsatzType operator()(const Dune::FieldVector<double, myDim>& quadPos) const {
    AnsatzType M;
    M.setZero();
    const double xi   = quadPos[0];
    const double eta  = quadPos[1];
    M(0, 0)           = 2 * xi - 1.0;
    M(1, 1)           = 2 * eta - 1.0;
    M(2, 2)           = 2 * xi - 1.0;
    M(2, 3)           = 2 * eta - 1.0;
    M(0, 4)           = (2 * xi - 1.0) * (2 * eta - 1.0);
    M(1, 5)           = (2 * xi - 1.0) * (2 * eta - 1.0);
    M(2, 6)           = (2 * xi - 1.0) * (2 * eta - 1.0);
    const double detJ = this->geometry_->integrationElement(quadPos);
    M                 = this->T0InverseTransformed_ / detJ * M;
    return M;
  }
};
 
template <typename GEO>
struct E11 : EX<GEO, 11>
{
  using Base                              = EX<GEO, 11>;
  static constexpr int myDim              = Base::myDim;
  static constexpr int strainSize         = Base::strainSize;
  static constexpr int enhancedStrainSize = Base::enhancedStrainSize;
  using AnsatzType                        = typename Base::AnsatzType;
  using DType                             = typename Base::DType;
 
  E11() = default;
  explicit E11(const GEO& geo)
      : Base(geo) {}
 
  AnsatzType operator()(const Dune::FieldVector<double, myDim>& quadPos) const {
    AnsatzType M;
    M.setZero();
    const double xi    = quadPos[0];
    const double eta   = quadPos[1];
    const double xi_t  = 2 * xi - 1;
    const double eta_t = 2 * eta - 1;
 
    const double xi2    = xi_t * xi_t;
    const double eta2   = eta_t * eta_t;
    const double xi_eta = xi_t * eta_t;
 
    M(0, 0) = 1 - 3 * xi2;
    M(0, 1) = eta_t - 3 * xi2 * eta_t;
    M(0, 2) = eta2 - 3 * xi2 * eta2;
 
    M(1, 3) = 1 - 3 * eta2;
    M(1, 4) = xi_t - 3 * xi_t * eta2;
    M(1, 5) = xi2 - 3 * xi2 * eta2;
 
    M(2, 6)  = 1 - 3 * xi2;
    M(2, 7)  = 1 - 3 * eta2;
    M(2, 8)  = eta_t - 3 * xi2 * eta_t;
    M(2, 9)  = xi_t - 3 * xi_t * eta2;
    M(2, 10) = 1 - 3 * (xi2 + eta2) + 9 * xi2 * eta2;
 
    const double detJ = this->geometry_->integrationElement(quadPos);
    M                 = this->T0InverseTransformed_ / detJ * M;
    return M;
  }
};
 
template <typename GEO>
struct E9 : EX<GEO, 9>
{
  using Base                              = EX<GEO, 9>;
  static constexpr int myDim              = Base::myDim;
  static constexpr int strainSize         = Base::strainSize;
  static constexpr int enhancedStrainSize = Base::enhancedStrainSize;
  using AnsatzType                        = typename Base::AnsatzType;
  using DType                             = typename Base::DType;
 
  E9() = default;
  explicit E9(const GEO& geo)
      : Base(geo) {}
 
  AnsatzType operator()(const Dune::FieldVector<double, myDim>& quadPos) const {
    AnsatzType M;
    M.setZero();
    const double xi   = quadPos[0];
    const double eta  = quadPos[1];
    const double zeta = quadPos[2];
    M(0, 0)           = 2 * xi - 1.0;
    M(1, 1)           = 2 * eta - 1.0;
    M(2, 2)           = 2 * zeta - 1.0;
    M(3, 3)           = 2 * eta - 1.0;
    M(3, 4)           = 2 * zeta - 1.0;
    M(4, 5)           = 2 * xi - 1.0;
    M(4, 6)           = 2 * zeta - 1.0;
    M(5, 7)           = 2 * xi - 1.0;
    M(5, 8)           = 2 * eta - 1.0;
    const double detJ = this->geometry_->integrationElement(quadPos);
    M                 = this->T0InverseTransformed_ / detJ * M;
    return M;
  }
};
 
template <typename GEO>
struct E21 : EX<GEO, 21>
{
  using Base                              = EX<GEO, 21>;
  static constexpr int myDim              = Base::myDim;
  static constexpr int strainSize         = Base::strainSize;
  static constexpr int enhancedStrainSize = Base::enhancedStrainSize;
  using AnsatzType                        = typename Base::AnsatzType;
  using DType                             = typename Base::DType;
 
  E21() = default;
  explicit E21(const GEO& geo)
      : Base(geo) {}
 
  AnsatzType operator()(const Dune::FieldVector<double, myDim>& quadPos) const {
    AnsatzType M;
    M.setZero();
    const double xi   = quadPos[0];
    const double eta  = quadPos[1];
    const double zeta = quadPos[2];
    M(0, 0)           = 2 * xi - 1.0;
    M(1, 1)           = 2 * eta - 1.0;
    M(2, 2)           = 2 * zeta - 1.0;
    M(3, 3)           = 2 * eta - 1.0;
    M(3, 4)           = 2 * zeta - 1.0;
    M(4, 5)           = 2 * xi - 1.0;
    M(4, 6)           = 2 * zeta - 1.0;
    M(5, 7)           = 2 * xi - 1.0;
    M(5, 8)           = 2 * eta - 1.0;
 
    M(3, 9)  = (2 * xi - 1.0) * (2 * eta - 1.0);
    M(3, 10) = (2 * xi - 1.0) * (2 * zeta - 1.0);
    M(4, 11) = (2 * xi - 1.0) * (2 * eta - 1.0);
    M(4, 12) = (2 * eta - 1.0) * (2 * zeta - 1.0);
    M(5, 13) = (2 * xi - 1.0) * (2 * zeta - 1.0);
    M(5, 14) = (2 * eta - 1.0) * (2 * zeta - 1.0);
 
    M(0, 15) = (2 * xi - 1.0) * (2 * eta - 1.0);
    M(0, 16) = (2 * xi - 1.0) * (2 * zeta - 1.0);
    M(1, 17) = (2 * xi - 1.0) * (2 * eta - 1.0);
    M(1, 18) = (2 * eta - 1.0) * (2 * zeta - 1.0);
    M(2, 19) = (2 * xi - 1.0) * (2 * zeta - 1.0);
    M(2, 20) = (2 * eta - 1.0) * (2 * zeta - 1.0);
 
    const double detJ = this->geometry_->integrationElement(quadPos);
    M                 = this->T0InverseTransformed_ / detJ * M;
    return M;
  }
};
 
} // namespace Ikarus::EAS