HookeElement.hpp

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/**
 * \file HookeElement.hpp
 * \example HookeElement.hpp
 *
 * \brief Operators and data structures for linear elastic
 * analysis
 *
 * Implemention of operators for Hooke material. Implementation is extended to
 * the case when the mesh is moving as results of topological changes, also the
 * calculation of material forces and associated tangent matrices are added to
 * implementation.
 *
 * In other words, spatial deformation is small but topological changes large.
 */
 
/*
 * This file is part of MoFEM.
 * MoFEM is free software: you can redistribute it and/or modify it under
 * the terms of the GNU Lesser General Public License as published by the
 * Free Software Foundation, either version 3 of the License, or (at your
 * option) any later version.
 *
 * MoFEM is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 * License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with MoFEM. If not, see <http://www.gnu.org/licenses/>. */
 
#ifndef __HOOKE_ELEMENT_HPP
#define __HOOKE_ELEMENT_HPP
 
#ifndef __BASICFINITEELEMENTS_HPP__
#include <BasicFiniteElements.hpp>
#endif // __BASICFINITEELEMENTS_HPP__
 
#ifndef __NONLINEAR_ELASTIC_HPP
 
struct NonlinearElasticElement {
 
  /** \brief data for calculation heat conductivity and heat capacity elements
   * \ingroup nonlinear_elastic_elem
   */
  struct BlockData {
    int iD;
    double E;
    double PoissonRatio;
    Range tEts; ///< constrains elements in block set
    Range forcesOnlyOnEntitiesRow;
    Range forcesOnlyOnEntitiesCol;
  };
};
 
#endif // __NONLINEAR_ELASTIC_HPP
 
/** \brief structure grouping operators and data used for calculation of
 * nonlinear elastic element \ingroup nonlinear_elastic_elem
 *
 * In order to assemble matrices and right hand vectors, the loops over
 * elements, entities over that elements and finally loop over integration
 * points are executed.
 *
 * Following implementation separate those three categories of loops and to each
 * loop attach operator.
 *
 */
 
#ifndef __CONVECTIVE_MASS_ELEMENT_HPP
struct ConvectiveMassElement {
  /** \brief data for calculation inertia forces
   * \ingroup user_modules
   */
  struct BlockData {
    double rho0;     ///< reference density
    VectorDouble a0; ///< constant acceleration
    Range tEts;      ///< elements in block set
  };
}
 
#endif //__CONVECTIVE_MASS_ELEMENT_HPP
struct HookeElement {
 
  using BlockData = NonlinearElasticElement::BlockData;
  using MassBlockData = ConvectiveMassElement::BlockData;
 
  using EntData = EntitiesFieldData::EntData;
  using UserDataOperator = ForcesAndSourcesCore::UserDataOperator;
  using VolUserDataOperator =
      VolumeElementForcesAndSourcesCore::UserDataOperator;
 
  struct DataAtIntegrationPts {
 
    boost::shared_ptr<MatrixDouble> smallStrainMat;
    boost::shared_ptr<MatrixDouble> hMat;
    boost::shared_ptr<MatrixDouble> FMat;
 
    boost::shared_ptr<MatrixDouble> HMat;
    boost::shared_ptr<VectorDouble> detHVec;
    boost::shared_ptr<MatrixDouble> invHMat;
 
    boost::shared_ptr<MatrixDouble> cauchyStressMat;
    boost::shared_ptr<MatrixDouble> stiffnessMat;
    boost::shared_ptr<VectorDouble> energyVec;
    boost::shared_ptr<MatrixDouble> eshelbyStressMat;
 
    boost::shared_ptr<MatrixDouble> eshelbyStress_dx;
 
    DataAtIntegrationPts() {
 
      smallStrainMat = boost::shared_ptr<MatrixDouble>(new MatrixDouble());
      hMat = boost::shared_ptr<MatrixDouble>(new MatrixDouble());
      FMat = boost::shared_ptr<MatrixDouble>(new MatrixDouble());
 
      HMat = boost::shared_ptr<MatrixDouble>(new MatrixDouble());
      detHVec = boost::shared_ptr<VectorDouble>(new VectorDouble());
      invHMat = boost::shared_ptr<MatrixDouble>(new MatrixDouble());
 
      cauchyStressMat = boost::shared_ptr<MatrixDouble>(new MatrixDouble());
      stiffnessMat = boost::shared_ptr<MatrixDouble>(new MatrixDouble());
      energyVec = boost::shared_ptr<VectorDouble>(new VectorDouble());
      eshelbyStressMat = boost::shared_ptr<MatrixDouble>(new MatrixDouble());
 
      eshelbyStress_dx = boost::shared_ptr<MatrixDouble>(new MatrixDouble());
    }
 
    Range forcesOnlyOnEntitiesRow;
    Range forcesOnlyOnEntitiesCol;
  };
 
  template <bool D = false>
  struct OpCalculateStrain : public VolUserDataOperator {
 
    OpCalculateStrain(const std::string row_field, const std::string col_field,
                      boost::shared_ptr<DataAtIntegrationPts> &data_at_pts);
 
    MoFEMErrorCode doWork(int row_side, EntityType row_type, EntData &row_data);
 
  private:
    boost::shared_ptr<DataAtIntegrationPts> dataAtPts;
  };
 
  struct OpCalculateStrainAle : public VolUserDataOperator {
 
    OpCalculateStrainAle(const std::string row_field,
                         const std::string col_field,
                         boost::shared_ptr<DataAtIntegrationPts> &data_at_pts);
 
    MoFEMErrorCode doWork(int row_side, EntityType row_type, EntData &row_data);
 
  private:
    boost::shared_ptr<DataAtIntegrationPts> dataAtPts;
  };
 
#define MAT_TO_DDG(SM)                                                         \
  &(*SM)(0, 0), &(*SM)(1, 0), &(*SM)(2, 0), &(*SM)(3, 0), &(*SM)(4, 0),        \
      &(*SM)(5, 0), &(*SM)(6, 0), &(*SM)(7, 0), &(*SM)(8, 0), &(*SM)(9, 0),    \
      &(*SM)(10, 0), &(*SM)(11, 0), &(*SM)(12, 0), &(*SM)(13, 0),              \
      &(*SM)(14, 0), &(*SM)(15, 0), &(*SM)(16, 0), &(*SM)(17, 0),              \
      &(*SM)(18, 0), &(*SM)(19, 0), &(*SM)(20, 0), &(*SM)(21, 0),              \
      &(*SM)(22, 0), &(*SM)(23, 0), &(*SM)(24, 0), &(*SM)(25, 0),              \
      &(*SM)(26, 0), &(*SM)(27, 0), &(*SM)(28, 0), &(*SM)(29, 0),              \
      &(*SM)(30, 0), &(*SM)(31, 0), &(*SM)(32, 0), &(*SM)(33, 0),              \
      &(*SM)(34, 0), &(*SM)(35, 0)
 
  template <int S = 0> struct OpCalculateStress : public VolUserDataOperator {
 
    OpCalculateStress(const std::string row_field, const std::string col_field,
                      boost::shared_ptr<DataAtIntegrationPts> data_at_pts);
 
    MoFEMErrorCode doWork(int row_side, EntityType row_type, EntData &row_data);
 
  protected:
    boost::shared_ptr<DataAtIntegrationPts> dataAtPts;
  };
 
  struct OpCalculateEnergy : public VolUserDataOperator {
 
    OpCalculateEnergy(const std::string row_field, const std::string col_field,
                      boost::shared_ptr<DataAtIntegrationPts> data_at_pts,
                      SmartPetscObj<Vec> ghost_vec = SmartPetscObj<Vec>());
 
    MoFEMErrorCode doWork(int row_side, EntityType row_type, EntData &row_data);
 
  protected:
    boost::shared_ptr<DataAtIntegrationPts> dataAtPts;
    SmartPetscObj<Vec> ghostVec;
  };
 
  struct OpCalculateEshelbyStress : public VolUserDataOperator {
 
    OpCalculateEshelbyStress(
        const std::string row_field, const std::string col_field,
        boost::shared_ptr<DataAtIntegrationPts> data_at_pts);
 
    MoFEMErrorCode doWork(int row_side, EntityType row_type, EntData &row_data);
 
  protected:
    boost::shared_ptr<DataAtIntegrationPts> dataAtPts;
  };
 
  template <int S = 0>
  struct OpCalculateHomogeneousStiffness : public VolUserDataOperator {
 
    OpCalculateHomogeneousStiffness(
        const std::string row_field, const std::string col_field,
        boost::shared_ptr<map<int, BlockData>> &block_sets_ptr,
        boost::shared_ptr<DataAtIntegrationPts> data_at_pts);
 
    MoFEMErrorCode doWork(int row_side, EntityType row_type, EntData &row_data);
 
  protected:
    boost::shared_ptr<map<int, BlockData>>
        blockSetsPtr; ///< Structure keeping data about problem, like
                      ///< material parameters
    boost::shared_ptr<DataAtIntegrationPts> dataAtPts;
  };
 
  /** * @brief Assemble mass matrix for elastic element TODO: CHANGE FORMULA *
   * \f[
   * {\bf{M}} = \int\limits_\Omega
   * \f]
   *
   */
  struct OpCalculateMassMatrix
      : public VolumeElementForcesAndSourcesCore::UserDataOperator {
 
    MatrixDouble locK;
    MatrixDouble translocK;
    BlockData &dAta;
    MassBlockData &massData;
 
    boost::shared_ptr<DataAtIntegrationPts> commonData;
 
    OpCalculateMassMatrix(const std::string row_field,
                          const std::string col_field, BlockData &data,
                          MassBlockData &mass_data,
                          boost::shared_ptr<DataAtIntegrationPts> &common_data,
                          bool symm = true)
        : VolumeElementForcesAndSourcesCore::UserDataOperator(
              row_field, col_field, OPROWCOL, symm),
          commonData(common_data), dAta(data), massData(mass_data) {}
 
    PetscErrorCode doWork(int row_side, int col_side, EntityType row_type,
                          EntityType col_type,
                          EntitiesFieldData::EntData &row_data,
                          EntitiesFieldData::EntData &col_data) {
      MoFEMFunctionBegin;
 
      auto get_tensor2 = [](MatrixDouble &m, const int r, const int c) {
        return FTensor::Tensor2<double *, 3, 3>(
            &m(3 * r + 0, 3 * c + 0), &m(3 * r + 0, 3 * c + 1),
            &m(3 * r + 0, 3 * c + 2), &m(3 * r + 1, 3 * c + 0),
            &m(3 * r + 1, 3 * c + 1), &m(3 * r + 1, 3 * c + 2),
            &m(3 * r + 2, 3 * c + 0), &m(3 * r + 2, 3 * c + 1),
            &m(3 * r + 2, 3 * c + 2));
      };
 
      const int row_nb_dofs = row_data.getIndices().size();
      if (!row_nb_dofs)
        MoFEMFunctionReturnHot(0);
      const int col_nb_dofs = col_data.getIndices().size();
      if (!col_nb_dofs)
        MoFEMFunctionReturnHot(0);
      if (dAta.tEts.find(getFEEntityHandle()) == dAta.tEts.end()) {
        MoFEMFunctionReturnHot(0);
      }
      if (massData.tEts.find(getFEEntityHandle()) == massData.tEts.end()) {
        MoFEMFunctionReturnHot(0);
      }
 
      const bool diagonal_block =
          (row_type == col_type) && (row_side == col_side);
      // get number of integration points
      // Set size can clear local tangent matrix
      locK.resize(row_nb_dofs, col_nb_dofs, false);
      locK.clear();
 
      const int row_nb_gauss_pts = row_data.getN().size1();
      const int row_nb_base_functions = row_data.getN().size2();
 
      FTensor::Index<'i', 3> i;
      FTensor::Index<'j', 3> j;
      FTensor::Index<'k', 3> k;
      FTensor::Index<'l', 3> l;
 
      double density = massData.rho0;
 
      // get integration weights
      auto t_w = getFTensor0IntegrationWeight();
 
      // integrate local matrix for entity block
      for (int gg = 0; gg != row_nb_gauss_pts; gg++) {
 
        auto t_row_base_func = row_data.getFTensor0N(gg, 0);
 
        // Get volume and integration weight
        double w = getVolume() * t_w;
 
        for (int row_bb = 0; row_bb != row_nb_dofs / 3; row_bb++) {
          auto t_col_base_func = col_data.getFTensor0N(gg, 0);
          for (int col_bb = 0; col_bb != col_nb_dofs / 3; col_bb++) {
            auto t_assemble = get_tensor2(locK, row_bb, col_bb);
            t_assemble(i, j) += density * t_row_base_func * t_col_base_func * w;
            // Next base function for column
            ++t_col_base_func;
          }
          // Next base function for row
          ++t_row_base_func;
        }
        // Next integration point for getting weight
        ++t_w;
      }
 
      CHKERR MatSetValues(getKSPB(), row_data, col_data, &locK(0, 0),
                          ADD_VALUES);
 
      // is symmetric
      if (row_type != col_type || row_side != col_side) {
        translocK.resize(col_nb_dofs, row_nb_dofs, false);
        noalias(translocK) = trans(locK);
 
        CHKERR MatSetValues(getKSPB(), col_data, row_data, &translocK(0, 0),
                            ADD_VALUES);
      }
 
      MoFEMFunctionReturn(0);
    }
  };
 
  struct OpCalculateStiffnessScaledByDensityField : public VolUserDataOperator {
  protected:
    boost::shared_ptr<map<int, BlockData>>
        blockSetsPtr; ///< Structure keeping data about problem, like
                      ///< material parameters
    boost::shared_ptr<DataAtIntegrationPts> dataAtPts;
 
    boost::shared_ptr<VectorDouble> rhoAtGaussPtsPtr;
    const double rhoN; ///< exponent n in E(p) = E * (p / p_0)^n
    const double rHo0; ///< p_0 reference density in E(p) = E * (p / p_0)^n
                       // // where p is density, E - youngs modulus
  public:
    OpCalculateStiffnessScaledByDensityField(
        const std::string row_field, const std::string col_field,
        boost::shared_ptr<map<int, BlockData>> &block_sets_ptr,
        boost::shared_ptr<DataAtIntegrationPts> data_at_pts,
        boost::shared_ptr<VectorDouble> rho_at_gauss_pts, const double rho_n,
        const double rho_0);
 
    MoFEMErrorCode doWork(int row_side, EntityType row_type, EntData &row_data);
  };
 
  struct OpAssemble : public VolUserDataOperator {
 
    OpAssemble(const std::string row_field, const std::string col_field,
               boost::shared_ptr<DataAtIntegrationPts> data_at_pts,
               const char type, bool symm = false);
 
    /**
     * \brief Do calculations for give operator
     * @param  row_side row side number (local number) of entity on element
     * @param  col_side column side number (local number) of entity on element
     * @param  row_type type of row entity MBVERTEX, MBEDGE, MBTRI or MBTET
     * @param  col_type type of column entity MBVERTEX, MBEDGE, MBTRI or MBTET
     * @param  row_data data for row
     * @param  col_data data for column
     * @return          error code
     */
    MoFEMErrorCode doWork(int row_side, int col_side, EntityType row_type,
                          EntityType col_type, EntData &row_data,
                          EntData &col_data);
 
    MoFEMErrorCode doWork(int row_side, EntityType row_type, EntData &row_data);
 
  protected:
    // Finite element stiffness sub-matrix K_ij
    MatrixDouble K;
    MatrixDouble transK;
    VectorDouble nF;
 
    boost::shared_ptr<DataAtIntegrationPts> dataAtPts;
 
    VectorInt rowIndices;
    VectorInt colIndices;
 
    int nbRows;           ///< number of dofs on rows
    int nbCols;           ///< number if dof on column
    int nbIntegrationPts; ///< number of integration points
    bool isDiag;          ///< true if this block is on diagonal
 
    virtual MoFEMErrorCode iNtegrate(EntData &row_data, EntData &col_data);
 
    virtual MoFEMErrorCode iNtegrate(EntData &row_data);
 
    /**
     * \brief Assemble local entity block matrix
     * @param  row_data row data (consist base functions on row entity)
     * @param  col_data column data (consist base functions on column
     * entity)
     * @return          error code
     */
    MoFEMErrorCode aSsemble(EntData &row_data, EntData &col_data);
 
    /**
     * \brief Assemble local entity right-hand vector
     * @param  row_data row data (consist base functions on row entity)
     * @param  col_data column data (consist base functions on column
     * entity)
     * @return          error code
     */
    MoFEMErrorCode aSsemble(EntData &row_data);
  };
 
  struct OpRhs_dx : public OpAssemble {
 
    OpRhs_dx(const std::string row_field, const std::string col_field,
             boost::shared_ptr<DataAtIntegrationPts> &data_at_pts);
 
  protected:
    MoFEMErrorCode iNtegrate(EntData &row_data);
  };
 
  template <int S = 0> struct OpLhs_dx_dx : public OpAssemble {
 
    OpLhs_dx_dx(const std::string row_field, const std::string col_field,
                boost::shared_ptr<DataAtIntegrationPts> &data_at_pts);
 
  protected:
    /**
     * \brief Integrate B^T D B operator
     * @param  row_data row data (consist base functions on row entity)
     * @param  col_data column data (consist base functions on column entity)
     * @return error code
     */
    MoFEMErrorCode iNtegrate(EntData &row_data, EntData &col_data);
  };
 
  struct OpAleRhs_dx : public OpAssemble {
 
    OpAleRhs_dx(const std::string row_field, const std::string col_field,
                boost::shared_ptr<DataAtIntegrationPts> &data_at_pts);
 
  protected:
    MoFEMErrorCode iNtegrate(EntData &row_data);
  };
 
  template <int S = 0> struct OpAleLhs_dx_dx : public OpAssemble {
 
    OpAleLhs_dx_dx(const std::string row_field, const std::string col_field,
                   boost::shared_ptr<DataAtIntegrationPts> &data_at_pts);
 
  protected:
    /**
     * \brief Integrate B^T D B operator
     * @param  row_data row data (consist base functions on row entity)
     * @param  col_data column data (consist base functions on column entity)
     * @return error code
     */
    MoFEMErrorCode iNtegrate(EntData &row_data, EntData &col_data);
  };
 
  template <int S = 0> struct OpAleLhs_dx_dX : public OpAssemble {
 
    OpAleLhs_dx_dX(const std::string row_field, const std::string col_field,
                   boost::shared_ptr<DataAtIntegrationPts> &data_at_pts);
 
  protected:
    /**
     * \brief Integrate tangent stiffness for spatial momentum
     * @param  row_data row data (consist base functions on row entity)
     * @param  col_data column data (consist base functions on column entity)
     * @return error code
     */
    MoFEMErrorCode iNtegrate(EntData &row_data, EntData &col_data);
  };
 
  struct OpAleLhsWithDensity_dx_dX : public OpAssemble {
 
    boost::shared_ptr<VectorDouble> rhoAtGaussPtsPtr;
    boost::shared_ptr<MatrixDouble> rhoGradAtGaussPtsPtr;
    const double rhoN;
    const double rHo0;
 
    OpAleLhsWithDensity_dx_dX(
        const std::string row_field, const std::string col_field,
        boost::shared_ptr<DataAtIntegrationPts> &data_at_pts,
        boost::shared_ptr<VectorDouble> rho_at_gauss_pts,
        boost::shared_ptr<MatrixDouble> rho_grad_at_gauss_pts,
        const double rho_n, const double rho_0);
 
  protected:
    /**
     * \brief Integrate tangent stiffness for spatial momentum
     * @param  row_data row data (consist base functions on row entity)
     * @param  col_data column data (consist base functions on column entity)
     * @return error code
     */
    MoFEMErrorCode iNtegrate(EntData &row_data, EntData &col_data);
  };
 
  struct OpAleLhsWithDensity_dX_dX : public OpAssemble {
 
    boost::shared_ptr<VectorDouble> rhoAtGaussPtsPtr;
    boost::shared_ptr<MatrixDouble> rhoGradAtGaussPtsPtr;
    const double rhoN;
    const double rHo0;
 
    OpAleLhsWithDensity_dX_dX(
        const std::string row_field, const std::string col_field,
        boost::shared_ptr<DataAtIntegrationPts> &data_at_pts,
        boost::shared_ptr<VectorDouble> rho_at_gauss_pts,
        boost::shared_ptr<MatrixDouble> rho_grad_at_gauss_pts,
        const double rho_n, const double rho_0);
 
  protected:
    /**
     * \brief Integrate tangent stiffness for material momentum
     * @param  row_data row data (consist base functions on row entity)
     * @param  col_data column data (consist base functions on column entity)
     * @return error code
     */
    MoFEMErrorCode iNtegrate(EntData &row_data, EntData &col_data);
  };
 
  struct OpAleRhs_dX : public OpAssemble {
 
    OpAleRhs_dX(const std::string row_field, const std::string col_field,
                boost::shared_ptr<DataAtIntegrationPts> &data_at_pts);
 
  protected:
    MoFEMErrorCode iNtegrate(EntData &row_data);
  };
 
  template <int S = 0> struct OpAleLhs_dX_dX : public OpAssemble {
 
    OpAleLhs_dX_dX(const std::string row_field, const std::string col_field,
                   boost::shared_ptr<DataAtIntegrationPts> &data_at_pts);
 
  protected:
    /**
     * \brief Integrate tangent stiffness for material momentum
     * @param  row_data row data (consist base functions on row entity)
     * @param  col_data column data (consist base functions on column entity)
     * @return error code
     */
    MoFEMErrorCode iNtegrate(EntData &row_data, EntData &col_data);
  };
 
  template <int S = 0> struct OpAleLhsPre_dX_dx : public VolUserDataOperator {
 
    OpAleLhsPre_dX_dx(const std::string row_field, const std::string col_field,
                      boost::shared_ptr<DataAtIntegrationPts> &data_at_pts);
 
    MoFEMErrorCode doWork(int row_side, EntityType row_type, EntData &row_data);
 
  private:
    boost::shared_ptr<DataAtIntegrationPts> dataAtPts;
  };
 
  struct OpAleLhs_dX_dx : public OpAssemble {
 
    OpAleLhs_dX_dx(const std::string row_field, const std::string col_field,
                   boost::shared_ptr<DataAtIntegrationPts> &data_at_pts)
        : OpAssemble(row_field, col_field, data_at_pts, OPROWCOL, false) {}
 
  protected:
    /**
     * \brief Integrate tangent stiffness for material momentum
     * @param  row_data row data (consist base functions on row entity)
     * @param  col_data column data (consist base functions on column entity)
     * @return error code
     */
    MoFEMErrorCode iNtegrate(EntData &row_data, EntData &col_data);
  };
 
  template <int S> struct OpAnalyticalInternalStrain_dx : public OpAssemble {
 
    typedef boost::function<
 
        FTensor::Tensor2_symmetric<double, 3>(
 
            FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> &t_coords
 
            )
 
        >
        StrainFunction;
 
    OpAnalyticalInternalStrain_dx(
        const std::string row_field,
        boost::shared_ptr<DataAtIntegrationPts> data_at_pts,
        StrainFunction strain_fun);
 
  protected:
    MoFEMErrorCode iNtegrate(EntData &row_data);
    StrainFunction strainFun;
  };
 
  template <int S> struct OpAnalyticalInternalAleStrain_dX : public OpAssemble {
 
    typedef boost::function<
 
        FTensor::Tensor2_symmetric<double, 3>(
 
            FTensor::Tensor1<FTensor::PackPtr<double *, 1>, 3> &t_coords
 
            )
 
        >
        StrainFunction;
 
    OpAnalyticalInternalAleStrain_dX(
        const std::string row_field,
        boost::shared_ptr<DataAtIntegrationPts> &data_at_pts,
        StrainFunction strain_fun,
        boost::shared_ptr<MatrixDouble> mat_pos_at_pts_ptr);
 
  protected:
    MoFEMErrorCode iNtegrate(EntData &row_data);
    StrainFunction strainFun;
    boost::shared_ptr<MatrixDouble> matPosAtPtsPtr;
  };
 
  template <int S> struct OpAnalyticalInternalAleStrain_dx : public OpAssemble {
 
    typedef boost::function<
 
        FTensor::Tensor2_symmetric<double, 3>(
 
            FTensor::Tensor1<FTensor::PackPtr<double *, 1>, 3> &t_coords
 
            )
 
        >
        StrainFunction;
 
    OpAnalyticalInternalAleStrain_dx(
        const std::string row_field,
        boost::shared_ptr<DataAtIntegrationPts> &data_at_pts,
        StrainFunction strain_fun,
        boost::shared_ptr<MatrixDouble> mat_pos_at_pts_ptr);
 
  protected:
    MoFEMErrorCode iNtegrate(EntData &row_data);
    StrainFunction strainFun;
    boost::shared_ptr<MatrixDouble> matPosAtPtsPtr;
  };
 
  template <class ELEMENT>
  struct OpPostProcHookeElement : public ELEMENT::UserDataOperator {
    boost::shared_ptr<DataAtIntegrationPts> dataAtPts;
    map<int, BlockData>
        &blockSetsPtr; // FIXME: (works only with the first block)
    moab::Interface &postProcMesh;
    std::vector<EntityHandle> &mapGaussPts;
    bool isALE;
    bool isFieldDisp;
 
    OpPostProcHookeElement(const string row_field,
                           boost::shared_ptr<DataAtIntegrationPts> data_at_pts,
                           map<int, BlockData> &block_sets_ptr,
                           moab::Interface &post_proc_mesh,
                           std::vector<EntityHandle> &map_gauss_pts,
                           bool is_ale = false, bool is_field_disp = true);
 
    MoFEMErrorCode doWork(int side, EntityType type,
                          EntitiesFieldData::EntData &data);
  };
 
  static MoFEMErrorCode
  setBlocks(MoFEM::Interface &m_field,
            boost::shared_ptr<map<int, BlockData>> &block_sets_ptr);
 
  static MoFEMErrorCode
  addElasticElement(MoFEM::Interface &m_field,
                    boost::shared_ptr<map<int, BlockData>> &block_sets_ptr,
                    const std::string element_name, const std::string x_field,
                    const std::string X_field, const bool ale);
 
  static MoFEMErrorCode
  setOperators(boost::shared_ptr<ForcesAndSourcesCore> fe_lhs_ptr,
               boost::shared_ptr<ForcesAndSourcesCore> fe_rhs_ptr,
               boost::shared_ptr<map<int, BlockData>> block_sets_ptr,
               const std::string x_field, const std::string X_field,
               const bool ale, const bool field_disp,
               const EntityType type = MBTET,
               boost::shared_ptr<DataAtIntegrationPts> data_at_pts = nullptr);
 
  static MoFEMErrorCode
  calculateEnergy(DM dm, boost::shared_ptr<map<int, BlockData>> block_sets_ptr,
                  const std::string x_field, const std::string X_field,
                  const bool ale, const bool field_disp,
                  SmartPetscObj<Vec> &v_energy_ptr);
 
private:
  MatrixDouble invJac;
};
 
template <bool D>
HookeElement::OpCalculateStrain<D>::OpCalculateStrain(
    const std::string row_field, const std::string col_field,
    boost::shared_ptr<DataAtIntegrationPts> &data_at_pts)
    : VolUserDataOperator(row_field, col_field, OPROW, true),
      dataAtPts(data_at_pts) {
  std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
}
 
template <bool D>
MoFEMErrorCode HookeElement::OpCalculateStrain<D>::doWork(int row_side,
                                                          EntityType row_type,
                                                          EntData &row_data) {
  MoFEMFunctionBegin;
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  // get number of integration points
  const int nb_integration_pts = getGaussPts().size2();
  dataAtPts->smallStrainMat->resize(6, nb_integration_pts, false);
  auto t_strain = getFTensor2SymmetricFromMat<3>(*(dataAtPts->smallStrainMat));
  auto t_h = getFTensor2FromMat<3, 3>(*(dataAtPts->hMat));
 
  for (int gg = 0; gg != nb_integration_pts; ++gg) {
    t_strain(i, j) = (t_h(i, j) || t_h(j, i)) / 2.;
 
    // If displacement field, not field o spatial positons is given
    if (!D) {
      t_strain(0, 0) -= 1;
      t_strain(1, 1) -= 1;
      t_strain(2, 2) -= 1;
    }
 
    ++t_strain;
    ++t_h;
  }
  MoFEMFunctionReturn(0);
}
 
template <int S>
HookeElement::OpAleLhs_dx_dx<S>::OpAleLhs_dx_dx(
    const std::string row_field, const std::string col_field,
    boost::shared_ptr<DataAtIntegrationPts> &data_at_pts)
    : OpAssemble(row_field, col_field, data_at_pts, OPROWCOL, true) {}
 
template <int S>
MoFEMErrorCode HookeElement::OpAleLhs_dx_dx<S>::iNtegrate(EntData &row_data,
                                                          EntData &col_data) {
  MoFEMFunctionBegin;
 
  // get sub-block (3x3) of local stiffens matrix, here represented by
  // second order tensor
  auto get_tensor2 = [](MatrixDouble &m, const int r, const int c) {
    return FTensor::Tensor2<FTensor::PackPtr<double *, 3>, 3, 3>(
        &m(r + 0, c + 0), &m(r + 0, c + 1), &m(r + 0, c + 2), &m(r + 1, c + 0),
        &m(r + 1, c + 1), &m(r + 1, c + 2), &m(r + 2, c + 0), &m(r + 2, c + 1),
        &m(r + 2, c + 2));
  };
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
 
  // get element volume
  double vol = getVolume();
 
  // get intergrayion weights
  auto t_w = getFTensor0IntegrationWeight();
 
  // get derivatives of base functions on rows
  auto t_row_diff_base = row_data.getFTensor1DiffN<3>();
  const int row_nb_base_fun = row_data.getN().size2();
 
  // Elastic stiffness tensor (4th rank tensor with minor and major
  // symmetry)
  FTensor::Ddg<FTensor::PackPtr<double *, S>, 3, 3> t_D(
      MAT_TO_DDG(dataAtPts->stiffnessMat));
 
  auto t_invH = getFTensor2FromMat<3, 3>(*dataAtPts->invHMat);
  auto &det_H = *dataAtPts->detHVec;
 
  // iterate over integration points
  for (int gg = 0; gg != nbIntegrationPts; ++gg) {
 
    // calculate scalar weight times element volume
    double a = t_w * vol * det_H[gg];
 
    // iterate over row base functions
    int rr = 0;
    for (; rr != nbRows / 3; ++rr) {
 
      // get sub matrix for the row
      auto t_m = get_tensor2(K, 3 * rr, 0);
 
      FTensor::Tensor1<double, 3> t_row_diff_base_pulled;
      t_row_diff_base_pulled(i) = t_row_diff_base(j) * t_invH(j, i);
 
      FTensor::Christof<double, 3, 3> t_rowD;
      // I mix up the indices here so that it behaves like a
      // Dg.  That way I don't have to have a separate wrapper
      // class Christof_Expr, which simplifies things.
      t_rowD(l, j, k) = t_D(i, j, k, l) * (a * t_row_diff_base_pulled(i));
 
      // get derivatives of base functions for columns
      auto t_col_diff_base = col_data.getFTensor1DiffN<3>(gg, 0);
 
      // iterate column base functions
      for (int cc = 0; cc != nbCols / 3; ++cc) {
 
        FTensor::Tensor1<double, 3> t_col_diff_base_pulled;
        t_col_diff_base_pulled(j) = t_col_diff_base(i) * t_invH(i, j);
 
        // integrate block local stiffens matrix
        t_m(i, j) += t_rowD(i, j, k) * t_col_diff_base_pulled(k);
 
        // move to next column base function
        ++t_col_diff_base;
 
        // move to next block of local stiffens matrix
        ++t_m;
      }
 
      // move to next row base function
      ++t_row_diff_base;
    }
 
    for (; rr != row_nb_base_fun; ++rr)
      ++t_row_diff_base;
 
    // move to next integration weight
    ++t_w;
    ++t_D;
    ++t_invH;
  }
 
  MoFEMFunctionReturn(0);
}
 
template <int S>
HookeElement::OpCalculateHomogeneousStiffness<S>::
    OpCalculateHomogeneousStiffness(
        const std::string row_field, const std::string col_field,
        boost::shared_ptr<map<int, BlockData>> &block_sets_ptr,
        boost::shared_ptr<DataAtIntegrationPts> data_at_pts)
    : VolUserDataOperator(row_field, col_field, OPROW, true),
      blockSetsPtr(block_sets_ptr), dataAtPts(data_at_pts) {
  std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
}
 
template <int S>
MoFEMErrorCode HookeElement::OpCalculateHomogeneousStiffness<S>::doWork(
    int row_side, EntityType row_type, EntData &row_data) {
  MoFEMFunctionBegin;
 
  for (auto &m : (*blockSetsPtr)) {
    if (m.second.tEts.find(getFEEntityHandle()) != m.second.tEts.end()) {
 
      dataAtPts->stiffnessMat->resize(36, 1, false);
      FTensor::Ddg<FTensor::PackPtr<double *, S>, 3, 3> t_D(
          MAT_TO_DDG(dataAtPts->stiffnessMat));
      const double young = m.second.E;
      const double poisson = m.second.PoissonRatio;
 
      // coefficient used in intermediate calculation
      const double coefficient = young / ((1 + poisson) * (1 - 2 * poisson));
 
      FTensor::Index<'i', 3> i;
      FTensor::Index<'j', 3> j;
      FTensor::Index<'k', 3> k;
      FTensor::Index<'l', 3> l;
 
      t_D(i, j, k, l) = 0.;
 
      t_D(0, 0, 0, 0) = 1 - poisson;
      t_D(1, 1, 1, 1) = 1 - poisson;
      t_D(2, 2, 2, 2) = 1 - poisson;
 
      t_D(0, 1, 0, 1) = 0.5 * (1 - 2 * poisson);
      t_D(0, 2, 0, 2) = 0.5 * (1 - 2 * poisson);
      t_D(1, 2, 1, 2) = 0.5 * (1 - 2 * poisson);
 
      t_D(0, 0, 1, 1) = poisson;
      t_D(1, 1, 0, 0) = poisson;
      t_D(0, 0, 2, 2) = poisson;
      t_D(2, 2, 0, 0) = poisson;
      t_D(1, 1, 2, 2) = poisson;
      t_D(2, 2, 1, 1) = poisson;
 
      t_D(i, j, k, l) *= coefficient;
 
      break;
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
template <int S>
HookeElement::OpCalculateStress<S>::OpCalculateStress(
    const std::string row_field, const std::string col_field,
    boost::shared_ptr<DataAtIntegrationPts> data_at_pts)
    : VolUserDataOperator(row_field, col_field, OPROW, true),
      dataAtPts(data_at_pts) {
  std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
}
 
template <int S>
MoFEMErrorCode HookeElement::OpCalculateStress<S>::doWork(int row_side,
                                                          EntityType row_type,
                                                          EntData &row_data) {
  MoFEMFunctionBegin;
  // get number of integration points
  const int nb_integration_pts = getGaussPts().size2();
  auto t_strain = getFTensor2SymmetricFromMat<3>(*(dataAtPts->smallStrainMat));
  dataAtPts->cauchyStressMat->resize(6, nb_integration_pts, false);
  auto t_cauchy_stress =
      getFTensor2SymmetricFromMat<3>(*(dataAtPts->cauchyStressMat));
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
 
  // elastic stiffness tensor (4th rank tensor with minor and major
  // symmetry)
  FTensor::Ddg<FTensor::PackPtr<double *, S>, 3, 3> t_D(
      MAT_TO_DDG(dataAtPts->stiffnessMat));
  for (int gg = 0; gg != nb_integration_pts; ++gg) {
    t_cauchy_stress(i, j) = t_D(i, j, k, l) * t_strain(k, l);
    ++t_strain;
    ++t_cauchy_stress;
    ++t_D;
  }
  MoFEMFunctionReturn(0);
}
 
template <int S>
HookeElement::OpLhs_dx_dx<S>::OpLhs_dx_dx(
    const std::string row_field, const std::string col_field,
    boost::shared_ptr<DataAtIntegrationPts> &data_at_pts)
    : OpAssemble(row_field, col_field, data_at_pts, OPROWCOL, true) {}
 
template <int S>
MoFEMErrorCode HookeElement::OpLhs_dx_dx<S>::iNtegrate(EntData &row_data,
                                                       EntData &col_data) {
  MoFEMFunctionBegin;
 
  // get sub-block (3x3) of local stiffens matrix, here represented by
  // second order tensor
  auto get_tensor2 = [](MatrixDouble &m, const int r, const int c) {
    return FTensor::Tensor2<FTensor::PackPtr<double *, 3>, 3, 3>(
        &m(r + 0, c + 0), &m(r + 0, c + 1), &m(r + 0, c + 2), &m(r + 1, c + 0),
        &m(r + 1, c + 1), &m(r + 1, c + 2), &m(r + 2, c + 0), &m(r + 2, c + 1),
        &m(r + 2, c + 2));
  };
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
 
  // get element volume
  double vol = getVolume();
 
  // get intergrayion weights
  auto t_w = getFTensor0IntegrationWeight();
 
  // get derivatives of base functions on rows
  auto t_row_diff_base = row_data.getFTensor1DiffN<3>();
  const int row_nb_base_fun = row_data.getN().size2();
 
  // Elastic stiffness tensor (4th rank tensor with minor and major
  // symmetry)
  FTensor::Ddg<FTensor::PackPtr<double *, S>, 3, 3> t_D(
      MAT_TO_DDG(dataAtPts->stiffnessMat));
 
  // iterate over integration points
  for (int gg = 0; gg != nbIntegrationPts; ++gg) {
 
    // calculate scalar weight times element volume
    double a = t_w * vol;
 
    // iterate over row base functions
    int rr = 0;
    for (; rr != nbRows / 3; ++rr) {
 
      // get sub matrix for the row
      auto t_m = get_tensor2(K, 3 * rr, 0);
 
      // get derivatives of base functions for columns
      auto t_col_diff_base = col_data.getFTensor1DiffN<3>(gg, 0);
 
      FTensor::Christof<double, 3, 3> t_rowD;
      // I mix up the indices here so that it behaves like a
      // Dg.  That way I don't have to have a separate wrapper
      // class Christof_Expr, which simplifies things.
      t_rowD(l, j, k) = t_D(i, j, k, l) * (a * t_row_diff_base(i));
 
      // iterate column base functions
      for (int cc = 0; cc != nbCols / 3; ++cc) {
 
        // integrate block local stiffens matrix
        t_m(i, j) += t_rowD(i, j, k) * t_col_diff_base(k);
 
        // move to next column base function
        ++t_col_diff_base;
 
        // move to next block of local stiffens matrix
        ++t_m;
      }
 
      // move to next row base function
      ++t_row_diff_base;
    }
 
    for (; rr != row_nb_base_fun; ++rr)
      ++t_row_diff_base;
 
    // move to next integration weight
    ++t_w;
    ++t_D;
  }
 
  MoFEMFunctionReturn(0);
}
 
template <int S>
HookeElement::OpAleLhs_dx_dX<S>::OpAleLhs_dx_dX(
    const std::string row_field, const std::string col_field,
    boost::shared_ptr<DataAtIntegrationPts> &data_at_pts)
    : OpAssemble(row_field, col_field, data_at_pts, OPROWCOL, false) {}
 
template <int S>
MoFEMErrorCode HookeElement::OpAleLhs_dx_dX<S>::iNtegrate(EntData &row_data,
                                                          EntData &col_data) {
  MoFEMFunctionBegin;
 
  // get sub-block (3x3) of local stiffens matrix, here represented by
  // second order tensor
  auto get_tensor2 = [](MatrixDouble &m, const int r, const int c) {
    return FTensor::Tensor2<FTensor::PackPtr<double *, 3>, 3, 3>(
        &m(r + 0, c + 0), &m(r + 0, c + 1), &m(r + 0, c + 2), &m(r + 1, c + 0),
        &m(r + 1, c + 1), &m(r + 1, c + 2), &m(r + 2, c + 0), &m(r + 2, c + 1),
        &m(r + 2, c + 2));
  };
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
  FTensor::Index<'m', 3> m;
  FTensor::Index<'n', 3> n;
 
  // get element volume
  double vol = getVolume();
 
  // get intergrayion weights
  auto t_w = getFTensor0IntegrationWeight();
 
  // get derivatives of base functions on rows
  auto t_row_diff_base = row_data.getFTensor1DiffN<3>();
  const int row_nb_base_fun = row_data.getN().size2();
 
  // Elastic stiffness tensor (4th rank tensor with minor and major
  // symmetry)
  FTensor::Ddg<FTensor::PackPtr<double *, S>, 3, 3> t_D(
      MAT_TO_DDG(dataAtPts->stiffnessMat));
 
  auto t_cauchy_stress =
      getFTensor2SymmetricFromMat<3>(*(dataAtPts->cauchyStressMat));
  auto t_h = getFTensor2FromMat<3, 3>(*dataAtPts->hMat);
  auto t_invH = getFTensor2FromMat<3, 3>(*dataAtPts->invHMat);
  auto &det_H = *dataAtPts->detHVec;
 
  // iterate over integration points
  for (int gg = 0; gg != nbIntegrationPts; ++gg) {
 
    // calculate scalar weight times element volume
    double a = t_w * vol * det_H[gg];
 
    FTensor::Tensor4<double, 3, 3, 3, 3> t_F_dX;
    t_F_dX(i, j, k, l) = -(t_h(i, m) * t_invH(m, k)) * t_invH(l, j);
 
    // iterate over row base functions
    int rr = 0;
    for (; rr != nbRows / 3; ++rr) {
 
      // get sub matrix for the row
      auto t_m = get_tensor2(K, 3 * rr, 0);
 
      FTensor::Tensor1<double, 3> t_row_diff_base_pulled;
      t_row_diff_base_pulled(i) = t_row_diff_base(j) * t_invH(j, i);
 
      FTensor::Tensor1<double, 3> t_row_stress;
      t_row_stress(i) = a * t_row_diff_base_pulled(j) * t_cauchy_stress(i, j);
 
      FTensor::Tensor3<double, 3, 3, 3> t_row_diff_base_pulled_dX;
      t_row_diff_base_pulled_dX(j, k, l) =
          -(t_invH(i, k) * t_row_diff_base(i)) * t_invH(l, j);
 
      FTensor::Tensor3<double, 3, 3, 3> t_row_dX_stress;
      t_row_dX_stress(i, k, l) =
          a * (t_row_diff_base_pulled_dX(j, k, l) * t_cauchy_stress(j, i));
 
      FTensor::Christof<double, 3, 3> t_row_D;
      t_row_D(l, j, k) = (a * t_row_diff_base_pulled(i)) * t_D(i, j, k, l);
 
      FTensor::Tensor3<double, 3, 3, 3> t_row_stress_dX;
      // FIXME: This operator is not implemented, doing operation by hand
      // t_row_stress_dX(i, m, n) = t_row_D(i, k, l) * t_F_dX(k, l, m, n);
      t_row_stress_dX(i, j, k) = 0;
      for (int ii = 0; ii != 3; ++ii)
        for (int mm = 0; mm != 3; ++mm)
          for (int nn = 0; nn != 3; ++nn) {
            auto &v = t_row_stress_dX(ii, mm, nn);
            for (int kk = 0; kk != 3; ++kk)
              for (int ll = 0; ll != 3; ++ll)
                v += t_row_D(ii, kk, ll) * t_F_dX(kk, ll, mm, nn);
          }
 
      // get derivatives of base functions for columns
      auto t_col_diff_base = col_data.getFTensor1DiffN<3>(gg, 0);
 
      // iterate column base functions
      for (int cc = 0; cc != nbCols / 3; ++cc) {
 
        t_m(i, k) += t_row_stress(i) * (t_invH(j, k) * t_col_diff_base(j));
        t_m(i, k) += t_row_dX_stress(i, k, l) * t_col_diff_base(l);
        t_m(i, k) += t_row_stress_dX(i, k, l) * t_col_diff_base(l);
 
        // move to next column base function
        ++t_col_diff_base;
 
        // move to next block of local stiffens matrix
        ++t_m;
      }
 
      // move to next row base function
      ++t_row_diff_base;
    }
 
    for (; rr != row_nb_base_fun; ++rr)
      ++t_row_diff_base;
 
    // move to next integration weight
    ++t_w;
    ++t_D;
    ++t_cauchy_stress;
    ++t_invH;
    ++t_h;
  }
 
  MoFEMFunctionReturn(0);
}
 
template <int S>
HookeElement::OpAleLhs_dX_dX<S>::OpAleLhs_dX_dX(
    const std::string row_field, const std::string col_field,
    boost::shared_ptr<DataAtIntegrationPts> &data_at_pts)
    : OpAssemble(row_field, col_field, data_at_pts, OPROWCOL, true) {}
 
template <int S>
MoFEMErrorCode HookeElement::OpAleLhs_dX_dX<S>::iNtegrate(EntData &row_data,
                                                          EntData &col_data) {
  MoFEMFunctionBegin;
 
  // get sub-block (3x3) of local stiffens matrix, here represented by
  // second order tensor
  auto get_tensor2 = [](MatrixDouble &m, const int r, const int c) {
    return FTensor::Tensor2<FTensor::PackPtr<double *, 3>, 3, 3>(
        &m(r + 0, c + 0), &m(r + 0, c + 1), &m(r + 0, c + 2), &m(r + 1, c + 0),
        &m(r + 1, c + 1), &m(r + 1, c + 2), &m(r + 2, c + 0), &m(r + 2, c + 1),
        &m(r + 2, c + 2));
  };
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
  FTensor::Index<'m', 3> m;
  FTensor::Index<'n', 3> n;
 
  // get element volume
  double vol = getVolume();
 
  // get intergrayion weights
  auto t_w = getFTensor0IntegrationWeight();
 
  // get derivatives of base functions on rows
  auto t_row_diff_base = row_data.getFTensor1DiffN<3>();
  const int row_nb_base_fun = row_data.getN().size2();
 
  // Elastic stiffness tensor (4th rank tensor with minor and major
  // symmetry)
  FTensor::Ddg<FTensor::PackPtr<double *, S>, 3, 3> t_D(
      MAT_TO_DDG(dataAtPts->stiffnessMat));
  auto t_cauchy_stress =
      getFTensor2SymmetricFromMat<3>(*(dataAtPts->cauchyStressMat));
  auto t_strain = getFTensor2SymmetricFromMat<3>(*(dataAtPts->smallStrainMat));
  auto t_eshelby_stress =
      getFTensor2FromMat<3, 3>(*dataAtPts->eshelbyStressMat);
  auto t_h = getFTensor2FromMat<3, 3>(*dataAtPts->hMat);
  auto t_invH = getFTensor2FromMat<3, 3>(*dataAtPts->invHMat);
  auto t_F = getFTensor2FromMat<3, 3>(*dataAtPts->FMat);
  auto &det_H = *dataAtPts->detHVec;
 
  // iterate over integration points
  for (int gg = 0; gg != nbIntegrationPts; ++gg) {
 
    // calculate scalar weight times element volume
    double a = t_w * vol * det_H[gg];
 
    FTensor::Tensor4<double, 3, 3, 3, 3> t_F_dX;
    t_F_dX(i, j, k, l) = -(t_h(i, m) * t_invH(m, k)) * t_invH(l, j);
 
    FTensor::Tensor4<double, 3, 3, 3, 3> t_D_strain_dX;
    t_D_strain_dX(i, j, m, n) = 0.;
    for (int ii = 0; ii != 3; ++ii)
      for (int jj = 0; jj != 3; ++jj)
        for (int ll = 0; ll != 3; ++ll)
          for (int kk = 0; kk != 3; ++kk) {
            auto &v = t_D_strain_dX(ii, jj, kk, ll);
            for (int mm = 0; mm != 3; ++mm)
              for (int nn = 0; nn != 3; ++nn)
                v += t_D(ii, jj, mm, nn) * t_F_dX(mm, nn, kk, ll);
          }
 
    FTensor::Tensor4<double, 3, 3, 3, 3> t_eshelby_stress_dX;
    t_eshelby_stress_dX(i, j, m, n) = t_F(k, i) * t_D_strain_dX(k, j, m, n);
 
    for (int ii = 0; ii != 3; ++ii)
      for (int jj = 0; jj != 3; ++jj)
        for (int mm = 0; mm != 3; ++mm)
          for (int nn = 0; nn != 3; ++nn) {
            auto &v = t_eshelby_stress_dX(ii, jj, mm, nn);
            for (int kk = 0; kk != 3; ++kk)
              v += t_F_dX(kk, ii, mm, nn) * t_cauchy_stress(kk, jj);
          }
 
    t_eshelby_stress_dX(i, j, k, l) *= -1;
 
    FTensor::Tensor2<double, 3, 3> t_energy_dX;
    t_energy_dX(k, l) = t_F_dX(i, j, k, l) * t_cauchy_stress(i, j);
    t_energy_dX(k, l) +=
        (t_strain(m, n) * t_D(m, n, i, j)) * t_F_dX(i, j, k, l);
    t_energy_dX(k, l) /= 2.;
 
    for (int kk = 0; kk != 3; ++kk)
      for (int ll = 0; ll != 3; ++ll) {
        auto v = t_energy_dX(kk, ll);
        for (int ii = 0; ii != 3; ++ii)
          t_eshelby_stress_dX(ii, ii, kk, ll) += v;
      }
 
    // iterate over row base functions
    int rr = 0;
    for (; rr != nbRows / 3; ++rr) {
 
      // get sub matrix for the row
      auto t_m = get_tensor2(K, 3 * rr, 0);
 
      FTensor::Tensor1<double, 3> t_row_diff_base_pulled;
      t_row_diff_base_pulled(i) = t_row_diff_base(j) * t_invH(j, i);
 
      FTensor::Tensor1<double, 3> t_row_stress;
      t_row_stress(i) = a * t_row_diff_base_pulled(j) * t_eshelby_stress(i, j);
 
      FTensor::Tensor3<double, 3, 3, 3> t_row_diff_base_pulled_dX;
      t_row_diff_base_pulled_dX(j, k, l) =
          -(t_row_diff_base(i) * t_invH(i, k)) * t_invH(l, j);
 
      FTensor::Tensor3<double, 3, 3, 3> t_row_dX_stress;
      t_row_dX_stress(i, k, l) =
          a * (t_row_diff_base_pulled_dX(j, k, l) * t_eshelby_stress(i, j));
 
      FTensor::Tensor3<double, 3, 3, 3> t_row_stress_dX;
      t_row_stress_dX(i, m, n) =
          a * t_row_diff_base_pulled(j) * t_eshelby_stress_dX(i, j, m, n);
 
      // get derivatives of base functions for columns
      auto t_col_diff_base = col_data.getFTensor1DiffN<3>(gg, 0);
 
      // iterate column base functions
      for (int cc = 0; cc != nbCols / 3; ++cc) {
 
        t_m(i, k) += t_row_stress(i) * (t_invH(j, k) * t_col_diff_base(j));
        t_m(i, k) += t_row_dX_stress(i, k, l) * t_col_diff_base(l);
        t_m(i, k) += t_row_stress_dX(i, k, l) * t_col_diff_base(l);
 
        // move to next column base function
        ++t_col_diff_base;
 
        // move to next block of local stiffens matrix
        ++t_m;
      }
 
      // move to next row base function
      ++t_row_diff_base;
    }
 
    for (; rr != row_nb_base_fun; ++rr)
      ++t_row_diff_base;
 
    // move to next integration weight
    ++t_w;
    ++t_D;
    ++t_cauchy_stress;
    ++t_strain;
    ++t_eshelby_stress;
    ++t_h;
    ++t_invH;
    ++t_F;
  }
 
  MoFEMFunctionReturn(0);
}
 
template <int S>
HookeElement::OpAleLhsPre_dX_dx<S>::OpAleLhsPre_dX_dx(
    const std::string row_field, const std::string col_field,
    boost::shared_ptr<DataAtIntegrationPts> &data_at_pts)
    : VolUserDataOperator(row_field, col_field, OPROW, true),
      dataAtPts(data_at_pts) {
  std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
}
 
template <int S>
MoFEMErrorCode HookeElement::OpAleLhsPre_dX_dx<S>::doWork(int row_side,
                                                          EntityType row_type,
                                                          EntData &row_data) {
  MoFEMFunctionBegin;
 
  const int nb_integration_pts = row_data.getN().size1();
 
  auto get_eshelby_stress_dx = [this, nb_integration_pts]() {
    FTensor::Tensor4<FTensor::PackPtr<double *, 1>, 3, 3, 3, 3>
        t_eshelby_stress_dx;
    dataAtPts->eshelbyStress_dx->resize(81, nb_integration_pts, false);
    int mm = 0;
    for (int ii = 0; ii != 3; ++ii)
      for (int jj = 0; jj != 3; ++jj)
        for (int kk = 0; kk != 3; ++kk)
          for (int ll = 0; ll != 3; ++ll)
            t_eshelby_stress_dx.ptr(ii, jj, kk, ll) =
                &(*dataAtPts->eshelbyStress_dx)(mm++, 0);
    return t_eshelby_stress_dx;
  };
 
  auto t_eshelby_stress_dx = get_eshelby_stress_dx();
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
  FTensor::Index<'m', 3> m;
  FTensor::Index<'n', 3> n;
 
  // Elastic stiffness tensor (4th rank tensor with minor and major
  // symmetry)
  FTensor::Ddg<FTensor::PackPtr<double *, S>, 3, 3> t_D(
      MAT_TO_DDG(dataAtPts->stiffnessMat));
  auto t_cauchy_stress =
      getFTensor2SymmetricFromMat<3>(*(dataAtPts->cauchyStressMat));
  auto t_invH = getFTensor2FromMat<3, 3>(*dataAtPts->invHMat);
  auto t_F = getFTensor2FromMat<3, 3>(*dataAtPts->FMat);
 
  for (int gg = 0; gg != nb_integration_pts; ++gg) {
 
    t_eshelby_stress_dx(i, j, m, n) =
        (t_F(k, i) * t_D(k, j, m, l)) * t_invH(n, l);
    for (int ii = 0; ii != 3; ++ii)
      for (int jj = 0; jj != 3; ++jj)
        for (int mm = 0; mm != 3; ++mm)
          for (int nn = 0; nn != 3; ++nn) {
            auto &v = t_eshelby_stress_dx(ii, jj, mm, nn);
            v += t_invH(nn, ii) * t_cauchy_stress(mm, jj);
          }
    t_eshelby_stress_dx(i, j, k, l) *= -1;
 
    FTensor::Tensor2<double, 3, 3> t_energy_dx;
    t_energy_dx(m, n) = t_invH(n, j) * t_cauchy_stress(m, j);
 
    for (int mm = 0; mm != 3; ++mm)
      for (int nn = 0; nn != 3; ++nn) {
        auto v = t_energy_dx(mm, nn);
        for (int ii = 0; ii != 3; ++ii)
          t_eshelby_stress_dx(ii, ii, mm, nn) += v;
      }
 
    ++t_D;
    ++t_invH;
    ++t_cauchy_stress;
    ++t_eshelby_stress_dx;
    ++t_F;
  }
 
  MoFEMFunctionReturn(0);
}
 
template <class ELEMENT>
HookeElement::OpPostProcHookeElement<ELEMENT>::OpPostProcHookeElement(
    const string row_field, boost::shared_ptr<DataAtIntegrationPts> data_at_pts,
    map<int, BlockData> &block_sets_ptr, moab::Interface &post_proc_mesh,
    std::vector<EntityHandle> &map_gauss_pts, bool is_ale, bool is_field_disp)
    : ELEMENT::UserDataOperator(row_field, UserDataOperator::OPROW),
      dataAtPts(data_at_pts), blockSetsPtr(block_sets_ptr),
      postProcMesh(post_proc_mesh), mapGaussPts(map_gauss_pts), isALE(is_ale),
      isFieldDisp(is_field_disp) {}
 
template <class ELEMENT>
MoFEMErrorCode HookeElement::OpPostProcHookeElement<ELEMENT>::doWork(
    int side, EntityType type, EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
 
  if (type != MBVERTEX) {
    MoFEMFunctionReturnHot(0);
  }
 
  auto tensor_to_tensor = [](const auto &t1, auto &t2) {
    t2(0, 0) = t1(0, 0);
    t2(1, 1) = t1(1, 1);
    t2(2, 2) = t1(2, 2);
    t2(0, 1) = t2(1, 0) = t1(1, 0);
    t2(0, 2) = t2(2, 0) = t1(2, 0);
    t2(1, 2) = t2(2, 1) = t1(2, 1);
  };
 
  std::array<double, 9> def_val;
  def_val.fill(0);
 
  auto make_tag = [&](auto name, auto size) {
    Tag th;
    CHKERR postProcMesh.tag_get_handle(name, size, MB_TYPE_DOUBLE, th,
                                       MB_TAG_CREAT | MB_TAG_SPARSE,
                                       def_val.data());
    return th;
  };
 
  auto th_stress = make_tag("STRESS", 9);
  auto th_psi = make_tag("ENERGY", 1);
 
  const int nb_integration_pts = mapGaussPts.size();
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
 
  auto t_h = getFTensor2FromMat<3, 3>(*dataAtPts->hMat);
  auto t_H = getFTensor2FromMat<3, 3>(*dataAtPts->HMat);
 
  dataAtPts->stiffnessMat->resize(36, 1, false);
  FTensor::Ddg<FTensor::PackPtr<double *, 1>, 3, 3> t_D(
      MAT_TO_DDG(dataAtPts->stiffnessMat));
  for (auto &m : (blockSetsPtr)) {
    const double young = m.second.E;
    const double poisson = m.second.PoissonRatio;
 
    const double coefficient = young / ((1 + poisson) * (1 - 2 * poisson));
 
    t_D(i, j, k, l) = 0.;
    t_D(0, 0, 0, 0) = t_D(1, 1, 1, 1) = t_D(2, 2, 2, 2) = 1 - poisson;
    t_D(0, 1, 0, 1) = t_D(0, 2, 0, 2) = t_D(1, 2, 1, 2) =
        0.5 * (1 - 2 * poisson);
    t_D(0, 0, 1, 1) = t_D(1, 1, 0, 0) = t_D(0, 0, 2, 2) = t_D(2, 2, 0, 0) =
        t_D(1, 1, 2, 2) = t_D(2, 2, 1, 1) = poisson;
    t_D(i, j, k, l) *= coefficient;
 
    break; // FIXME: calculates only first block
  }
 
  double detH = 0.;
  FTensor::Tensor2<double, 3, 3> t_invH;
  FTensor::Tensor2<double, 3, 3> t_F;
  FTensor::Tensor2<double, 3, 3> t_stress;
  FTensor::Tensor2<double, 3, 3> t_small_strain;
  FTensor::Tensor2_symmetric<double, 3> t_stress_symm;
  FTensor::Tensor2_symmetric<double, 3> t_small_strain_symm;
 
  for (int gg = 0; gg != nb_integration_pts; ++gg) {
 
    if (isFieldDisp) {
      t_h(0, 0) += 1;
      t_h(1, 1) += 1;
      t_h(2, 2) += 1;
    }
 
    if (!isALE) {
      t_small_strain_symm(i, j) = (t_h(i, j) || t_h(j, i)) / 2.;
    } else {
      CHKERR determinantTensor3by3(t_H, detH);
      CHKERR invertTensor3by3(t_H, detH, t_invH);
      t_F(i, j) = t_h(i, k) * t_invH(k, j);
      t_small_strain_symm(i, j) = (t_F(i, j) || t_F(j, i)) / 2.;
      ++t_H;
    }
 
    t_small_strain_symm(0, 0) -= 1;
    t_small_strain_symm(1, 1) -= 1;
    t_small_strain_symm(2, 2) -= 1;
 
    // symmetric tensors need improvement
    t_stress_symm(i, j) = t_D(i, j, k, l) * t_small_strain_symm(k, l);
    tensor_to_tensor(t_stress_symm, t_stress);
 
    const double psi = 0.5 * t_stress_symm(i, j) * t_small_strain_symm(i, j);
 
    CHKERR postProcMesh.tag_set_data(th_psi, &mapGaussPts[gg], 1, &psi);
    CHKERR postProcMesh.tag_set_data(th_stress, &mapGaussPts[gg], 1,
                                     &t_stress(0, 0));
 
    ++t_h;
  }
 
  MoFEMFunctionReturn(0);
}
 
template <int S>
HookeElement::OpAnalyticalInternalStrain_dx<S>::OpAnalyticalInternalStrain_dx(
    const std::string row_field,
    boost::shared_ptr<DataAtIntegrationPts> data_at_pts,
    StrainFunction strain_fun)
    : OpAssemble(row_field, row_field, data_at_pts, OPROW, true),
      strainFun(strain_fun) {}
 
template <int S>
MoFEMErrorCode
HookeElement::OpAnalyticalInternalStrain_dx<S>::iNtegrate(EntData &row_data) {
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
  MoFEMFunctionBegin;
 
  auto get_tensor1 = [](VectorDouble &v, const int r) {
    return FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3>(
        &v(r + 0), &v(r + 1), &v(r + 2));
  };
 
  const int nb_integration_pts = getGaussPts().size2();
  auto t_coords = getFTensor1CoordsAtGaussPts();
 
  // get element volume
  double vol = getVolume();
  auto t_w = getFTensor0IntegrationWeight();
 
  nF.resize(nbRows, false);
  nF.clear();
 
  // elastic stiffness tensor (4th rank tensor with minor and major
  // symmetry)
  FTensor::Ddg<FTensor::PackPtr<double *, S>, 3, 3> t_D(
      MAT_TO_DDG(dataAtPts->stiffnessMat));
 
  // get derivatives of base functions on rows
  auto t_row_diff_base = row_data.getFTensor1DiffN<3>();
  const int row_nb_base_fun = row_data.getN().size2();
 
  for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
 
    auto t_fun_strain = strainFun(t_coords);
    FTensor::Tensor2_symmetric<double, 3> t_stress;
    t_stress(i, j) = -t_D(i, j, k, l) * t_fun_strain(k, l);
 
    // calculate scalar weight times element volume
    double a = t_w * vol;
 
    auto t_nf = get_tensor1(nF, 0);
 
    int rr = 0;
    for (; rr != nbRows / 3; ++rr) {
      t_nf(i) += a * t_row_diff_base(j) * t_stress(i, j);
      ++t_row_diff_base;
      ++t_nf;
    }
 
    for (; rr != row_nb_base_fun; ++rr)
      ++t_row_diff_base;
 
    ++t_w;
    ++t_coords;
    ++t_D;
  }
 
  MoFEMFunctionReturn(0);
}
 
template <int S>
HookeElement::OpAnalyticalInternalAleStrain_dX<S>::
    OpAnalyticalInternalAleStrain_dX(
        const std::string row_field,
        boost::shared_ptr<DataAtIntegrationPts> &data_at_pts,
        StrainFunction strain_fun,
        boost::shared_ptr<MatrixDouble> mat_pos_at_pts_ptr)
    : OpAssemble(row_field, row_field, data_at_pts, OPROW, true),
      strainFun(strain_fun), matPosAtPtsPtr(mat_pos_at_pts_ptr) {}
 
template <int S>
MoFEMErrorCode HookeElement::OpAnalyticalInternalAleStrain_dX<S>::iNtegrate(
    EntData &row_data) {
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
  MoFEMFunctionBegin;
 
  auto get_tensor1 = [](VectorDouble &v, const int r) {
    return FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3>(
        &v(r + 0), &v(r + 1), &v(r + 2));
  };
 
  const int nb_integration_pts = getGaussPts().size2();
 
  auto get_coords = [&]() { return getFTensor1FromMat<3>(*matPosAtPtsPtr); };
  auto t_coords = get_coords();
 
  // get element volume
  double vol = getVolume();
  auto t_w = getFTensor0IntegrationWeight();
 
  nF.resize(nbRows, false);
  nF.clear();
 
  // elastic stiffness tensor (4th rank tensor with minor and major
  // symmetry)
  FTensor::Ddg<FTensor::PackPtr<double *, S>, 3, 3> t_D(
      MAT_TO_DDG(dataAtPts->stiffnessMat));
  auto t_F = getFTensor2FromMat<3, 3>(*(dataAtPts->FMat));
  auto &det_H = *dataAtPts->detHVec;
  auto t_invH = getFTensor2FromMat<3, 3>(*dataAtPts->invHMat);
 
  // get derivatives of base functions on rows
  auto t_row_diff_base = row_data.getFTensor1DiffN<3>();
  const int row_nb_base_fun = row_data.getN().size2();
 
  for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
 
    auto t_fun_strain = strainFun(t_coords);
    FTensor::Tensor2_symmetric<double, 3> t_stress;
    t_stress(i, j) = -t_D(i, j, k, l) * t_fun_strain(k, l);
    FTensor::Tensor2<double, 3, 3> t_eshelby_stress;
    t_eshelby_stress(i, j) = -t_F(k, i) * t_stress(k, j);
 
    // calculate scalar weight times element volume
    double a = t_w * vol * det_H[gg];
 
    auto t_nf = get_tensor1(nF, 0);
 
    int rr = 0;
    for (; rr != nbRows / 3; ++rr) {
      FTensor::Tensor1<double, 3> t_row_diff_base_pulled;
      t_row_diff_base_pulled(i) = t_row_diff_base(j) * t_invH(j, i);
      t_nf(i) += a * t_row_diff_base_pulled(j) * t_eshelby_stress(i, j);
      ++t_row_diff_base;
      ++t_nf;
    }
 
    for (; rr != row_nb_base_fun; ++rr)
      ++t_row_diff_base;
 
    ++t_w;
    ++t_coords;
    ++t_F;
    ++t_invH;
    ++t_D;
  }
 
  MoFEMFunctionReturn(0);
}
 
template <int S>
HookeElement::OpAnalyticalInternalAleStrain_dx<S>::
    OpAnalyticalInternalAleStrain_dx(
        const std::string row_field,
        boost::shared_ptr<DataAtIntegrationPts> &data_at_pts,
        StrainFunction strain_fun,
        boost::shared_ptr<MatrixDouble> mat_pos_at_pts_ptr)
    : OpAssemble(row_field, row_field, data_at_pts, OPROW, true),
      strainFun(strain_fun), matPosAtPtsPtr(mat_pos_at_pts_ptr) {}
 
template <int S>
MoFEMErrorCode HookeElement::OpAnalyticalInternalAleStrain_dx<S>::iNtegrate(
    EntData &row_data) {
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
  MoFEMFunctionBegin;
 
  auto get_tensor1 = [](VectorDouble &v, const int r) {
    return FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3>(
        &v(r + 0), &v(r + 1), &v(r + 2));
  };
 
  const int nb_integration_pts = getGaussPts().size2();
 
  auto get_coords = [&]() { return getFTensor1FromMat<3>(*matPosAtPtsPtr); };
  auto t_coords = get_coords();
 
  // get element volume
  double vol = getVolume();
  auto t_w = getFTensor0IntegrationWeight();
 
  nF.resize(nbRows, false);
  nF.clear();
 
  // elastic stiffness tensor (4th rank tensor with minor and major
  // symmetry)
  FTensor::Ddg<FTensor::PackPtr<double *, S>, 3, 3> t_D(
      MAT_TO_DDG(dataAtPts->stiffnessMat));
  auto &det_H = *dataAtPts->detHVec;
  auto t_invH = getFTensor2FromMat<3, 3>(*dataAtPts->invHMat);
 
  // get derivatives of base functions on rows
  auto t_row_diff_base = row_data.getFTensor1DiffN<3>();
  const int row_nb_base_fun = row_data.getN().size2();
 
  for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
 
    auto t_fun_strain = strainFun(t_coords);
    FTensor::Tensor2_symmetric<double, 3> t_stress;
    t_stress(i, j) = -t_D(i, j, k, l) * t_fun_strain(k, l);
 
    // calculate scalar weight times element volume
    double a = t_w * vol * det_H[gg];
 
    auto t_nf = get_tensor1(nF, 0);
 
    int rr = 0;
    for (; rr != nbRows / 3; ++rr) {
      FTensor::Tensor1<double, 3> t_row_diff_base_pulled;
      t_row_diff_base_pulled(i) = t_row_diff_base(j) * t_invH(j, i);
      t_nf(i) += a * t_row_diff_base_pulled(j) * t_stress(i, j);
      ++t_row_diff_base;
      ++t_nf;
    }
 
    for (; rr != row_nb_base_fun; ++rr)
      ++t_row_diff_base;
 
    ++t_w;
    ++t_coords;
    ++t_invH;
    ++t_D;
  }
 
  MoFEMFunctionReturn(0);
}
 
#endif // __HOOKE_ELEMENT_HPP