HookeElement.cpp

Operators and data structures for linear elastic analysisSee as well header file HookeElement.hpp

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.

/** \file HookeElement.cpp
 * \example HookeElement.cpp
 * \brief Operators and data structures for linear elastic analysis
 *
 * See as well header file HookeElement.hpp
 *
 * 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.
 
 */
 
 
 
#include <MoFEM.hpp>
using namespace MoFEM;
#include <HookeElement.hpp>
 
HookeElement::OpCalculateStrainAle::OpCalculateStrainAle(
    const std::string row_field, const std::string col_field,
    boost::shared_ptr<DataAtIntegrationPts> &data_at_pts)
    : VolUserDataOperator(row_field, col_field, OPROW, false),
      dataAtPts(data_at_pts) {
  std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
}
 
MoFEMErrorCode HookeElement::OpCalculateStrainAle::doWork(int row_side,
                                                          EntityType row_type,
                                                          EntData &row_data) {
  MoFEMFunctionBegin;
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  // get number of integration points
  const int nb_integration_pts = getGaussPts().size2();
  auto t_h = getFTensor2FromMat<3, 3>(*dataAtPts->hMat);
  auto t_H = getFTensor2FromMat<3, 3>(*dataAtPts->HMat);
 
  dataAtPts->detHVec->resize(nb_integration_pts, false);
  dataAtPts->invHMat->resize(9, nb_integration_pts, false);
  dataAtPts->FMat->resize(9, nb_integration_pts, false);
  dataAtPts->smallStrainMat->resize(6, nb_integration_pts, false);
 
  auto t_detH = getFTensor0FromVec(*dataAtPts->detHVec);
  auto t_invH = getFTensor2FromMat<3, 3>(*dataAtPts->invHMat);
  auto t_F = getFTensor2FromMat<3, 3>(*dataAtPts->FMat);
  auto t_strain = getFTensor2SymmetricFromMat<3>(*dataAtPts->smallStrainMat);
 
  for (int gg = 0; gg != nb_integration_pts; ++gg) {
    CHKERR determinantTensor3by3(t_H, t_detH);
    CHKERR invertTensor3by3(t_H, t_detH, t_invH);
    t_F(i, j) = t_h(i, k) * t_invH(k, j);
    t_strain(i, j) = (t_F(i, j) || t_F(j, i)) / 2.;
 
    t_strain(0, 0) -= 1;
    t_strain(1, 1) -= 1;
    t_strain(2, 2) -= 1;
 
    ++t_strain;
    ++t_h;
    ++t_H;
    ++t_detH;
    ++t_invH;
    ++t_F;
  }
  MoFEMFunctionReturn(0);
}
 
HookeElement::OpCalculateEnergy::OpCalculateEnergy(
    const std::string row_field, const std::string col_field,
    boost::shared_ptr<DataAtIntegrationPts> data_at_pts,
    SmartPetscObj<Vec> ghost_vec)
    : VolUserDataOperator(row_field, col_field, OPROW, true),
      dataAtPts(data_at_pts), ghostVec(ghost_vec, true) {
  std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
}
 
MoFEMErrorCode HookeElement::OpCalculateEnergy::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));
  auto t_cauchy_stress =
      getFTensor2SymmetricFromMat<3>(*(dataAtPts->cauchyStressMat));
  dataAtPts->energyVec->resize(nb_integration_pts, false);
  auto t_energy = FTensor::Tensor0<FTensor::PackPtr<double *, 1>>(
      &*(dataAtPts->energyVec->data().begin()));
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
 
  for (int gg = 0; gg != nb_integration_pts; ++gg) {
    t_energy = (t_strain(i, j) * t_cauchy_stress(i, j)) / 2.;
    ++t_strain;
    ++t_cauchy_stress;
    ++t_energy;
  }
 
  if (ghostVec.get()) {
    // get element volume
    double vol = getVolume();
    // get intergrayion weights
    auto t_w = getFTensor0IntegrationWeight();
    auto &det_H = *dataAtPts->detHVec;
    auto t_energy = FTensor::Tensor0<FTensor::PackPtr<double *, 1>>(
        &*(dataAtPts->energyVec->data().begin()));
    double energy = 0;
    for (int gg = 0; gg != nb_integration_pts; ++gg) {
      // calculate scalar weight times element volume
      double a = t_w * vol;
      if (det_H.size()) {
        a *= det_H[gg];
      }
      energy += a * t_energy;
      ++t_energy;
      ++t_w;
    }
    CHKERR VecSetValue(ghostVec, 0, energy, ADD_VALUES);
  }
 
  MoFEMFunctionReturn(0);
}
 
HookeElement::OpCalculateEshelbyStress::OpCalculateEshelbyStress(
    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);
}
 
MoFEMErrorCode HookeElement::OpCalculateEshelbyStress::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_energy = FTensor::Tensor0<FTensor::PackPtr<double *, 1>>(
      &*(dataAtPts->energyVec->data().begin()));
  auto t_cauchy_stress =
      getFTensor2SymmetricFromMat<3>(*(dataAtPts->cauchyStressMat));
  auto t_F = getFTensor2FromMat<3, 3>(*(dataAtPts->FMat));
  dataAtPts->eshelbyStressMat->resize(9, nb_integration_pts, false);
  auto t_eshelby_stress =
      getFTensor2FromMat<3, 3>(*(dataAtPts->eshelbyStressMat));
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
 
  for (int gg = 0; gg != nb_integration_pts; ++gg) {
    t_eshelby_stress(i, j) = -t_F(k, i) * t_cauchy_stress(k, j);
    t_eshelby_stress(0, 0) += t_energy;
    t_eshelby_stress(1, 1) += t_energy;
    t_eshelby_stress(2, 2) += t_energy;
    ++t_cauchy_stress;
    ++t_energy;
    ++t_eshelby_stress;
    ++t_F;
  }
  MoFEMFunctionReturn(0);
}
 
HookeElement::OpAssemble::OpAssemble(
    const std::string row_field, const std::string col_field,
    boost::shared_ptr<DataAtIntegrationPts> data_at_pts, const char type,
    bool symm)
    : VolUserDataOperator(row_field, col_field, type, symm),
      dataAtPts(data_at_pts) {}
 
MoFEMErrorCode HookeElement::OpAssemble::doWork(int row_side, int col_side,
                                                EntityType row_type,
                                                EntityType col_type,
                                                EntData &row_data,
                                                EntData &col_data) {
 
  MoFEMFunctionBegin;
 
  // get number of dofs on row
  nbRows = row_data.getIndices().size();
  // if no dofs on row, exit that work, nothing to do here
  if (!nbRows)
    MoFEMFunctionReturnHot(0);
 
  // get number of dofs on column
  nbCols = col_data.getIndices().size();
  // if no dofs on Columbia, exit nothing to do here
  if (!nbCols)
    MoFEMFunctionReturnHot(0);
 
  // K_ij matrix will have 3 times the number of degrees of freedom of the
  // i-th entity set (nbRows)
  // and 3 times the number of degrees of freedom of the j-th entity set
  // (nbCols)
  K.resize(nbRows, nbCols, false);
  K.clear();
 
  // get number of integration points
  nbIntegrationPts = getGaussPts().size2();
  // check if entity block is on matrix diagonal
  if (row_side == col_side && row_type == col_type) {
    isDiag = true;
  } else {
    isDiag = false;
  }
 
  // integrate local matrix for entity block
  CHKERR iNtegrate(row_data, col_data);
 
  // assemble local matrix
  CHKERR aSsemble(row_data, col_data);
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode HookeElement::OpAssemble::doWork(int row_side,
                                                EntityType row_type,
                                                EntData &row_data) {
  MoFEMFunctionBegin;
 
  // get number of dofs on row
  nbRows = row_data.getIndices().size();
  // if no dofs on row, exit that work, nothing to do here
  if (!nbRows)
    MoFEMFunctionReturnHot(0);
 
  nF.resize(nbRows, false);
  nF.clear();
 
  // get number of integration points
  nbIntegrationPts = getGaussPts().size2();
 
  // integrate local matrix for entity block
  CHKERR iNtegrate(row_data);
 
  // assemble local matrix
  CHKERR aSsemble(row_data);
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode HookeElement::OpAssemble::iNtegrate(EntData &row_data,
                                                   EntData &col_data) {
  MoFEMFunctionBegin;
  SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED, "Not implemented");
  MoFEMFunctionReturn(0);
};
 
MoFEMErrorCode HookeElement::OpAssemble::iNtegrate(EntData &row_data) {
  MoFEMFunctionBegin;
  SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED, "Not implemented");
  MoFEMFunctionReturn(0);
};
 
MoFEMErrorCode HookeElement::OpAssemble::aSsemble(EntData &row_data,
                                                  EntData &col_data) {
  MoFEMFunctionBegin;
 
  // get pointer to first global index on row
  const int *row_indices = &*row_data.getIndices().data().begin();
  // get pointer to first global index on column
  const int *col_indices = &*col_data.getIndices().data().begin();
 
  auto &data = *dataAtPts;
  if (!data.forcesOnlyOnEntitiesRow.empty()) {
    rowIndices.resize(nbRows, false);
    noalias(rowIndices) = row_data.getIndices();
    row_indices = &rowIndices[0];
    VectorDofs &dofs = row_data.getFieldDofs();
    VectorDofs::iterator dit = dofs.begin();
    for (int ii = 0; dit != dofs.end(); dit++, ii++) {
      if (data.forcesOnlyOnEntitiesRow.find((*dit)->getEnt()) ==
          data.forcesOnlyOnEntitiesRow.end()) {
        rowIndices[ii] = -1;
      }
    }
  }
 
  if (!data.forcesOnlyOnEntitiesCol.empty()) {
    colIndices.resize(nbCols, false);
    noalias(colIndices) = col_data.getIndices();
    col_indices = &colIndices[0];
    VectorDofs &dofs = col_data.getFieldDofs();
    VectorDofs::iterator dit = dofs.begin();
    for (int ii = 0; dit != dofs.end(); dit++, ii++) {
      if (data.forcesOnlyOnEntitiesCol.find((*dit)->getEnt()) ==
          data.forcesOnlyOnEntitiesCol.end()) {
        colIndices[ii] = -1;
      }
    }
  }
 
  Mat B = getFEMethod()->ksp_B != PETSC_NULL ? getFEMethod()->ksp_B
                                             : getFEMethod()->snes_B;
  // assemble local matrix
  CHKERR MatSetValues(B, nbRows, row_indices, nbCols, col_indices,
                      &*K.data().begin(), ADD_VALUES);
 
  if (!isDiag && sYmm) {
    // if not diagonal term and since global matrix is symmetric assemble
    // transpose term.
    transK.resize(K.size2(), K.size1(), false);
    noalias(transK) = trans(K);
    CHKERR MatSetValues(B, nbCols, col_indices, nbRows, row_indices,
                        &*transK.data().begin(), ADD_VALUES);
  }
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode HookeElement::OpAssemble::aSsemble(EntData &row_data) {
  MoFEMFunctionBegin;
 
  // get pointer to first global index on row
  const int *row_indices = &*row_data.getIndices().data().begin();
 
  auto &data = *dataAtPts;
  if (!data.forcesOnlyOnEntitiesRow.empty()) {
    rowIndices.resize(nbRows, false);
    noalias(rowIndices) = row_data.getIndices();
    row_indices = &rowIndices[0];
    VectorDofs &dofs = row_data.getFieldDofs();
    VectorDofs::iterator dit = dofs.begin();
    for (int ii = 0; dit != dofs.end(); dit++, ii++) {
      if (data.forcesOnlyOnEntitiesRow.find((*dit)->getEnt()) ==
          data.forcesOnlyOnEntitiesRow.end()) {
        rowIndices[ii] = -1;
      }
    }
  }
 
  Vec F = getFEMethod()->snes_f;
  // assemble local matrix
  CHKERR VecSetValues(F, nbRows, row_indices, &*nF.data().begin(), ADD_VALUES);
  MoFEMFunctionReturn(0);
}
 
HookeElement::OpRhs_dx::OpRhs_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, OPROW) {}
 
MoFEMErrorCode HookeElement::OpRhs_dx::iNtegrate(EntData &row_data) {
  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));
  };
 
  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();
  auto t_cauchy_stress =
      getFTensor2SymmetricFromMat<3>(*dataAtPts->cauchyStressMat);
 
  // iterate over integration points
  for (int gg = 0; gg != nbIntegrationPts; ++gg) {
 
    // 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_cauchy_stress(i, j);
      ++t_row_diff_base;
      ++t_nf;
    }
 
    for (; rr != row_nb_base_fun; ++rr)
      ++t_row_diff_base;
 
    ++t_w;
    ++t_cauchy_stress;
  }
 
  MoFEMFunctionReturn(0);
}
 
HookeElement::OpAleRhs_dx::OpAleRhs_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, OPROW) {}
 
MoFEMErrorCode HookeElement::OpAleRhs_dx::iNtegrate(EntData &row_data) {
  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));
  };
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
 
  // 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();
  auto t_cauchy_stress =
      getFTensor2SymmetricFromMat<3>(*dataAtPts->cauchyStressMat);
  auto &det_H = *dataAtPts->detHVec;
  auto t_invH = getFTensor2FromMat<3, 3>(*dataAtPts->invHMat);
 
  // 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];
    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_cauchy_stress(i, j);
      ++t_row_diff_base;
      ++t_nf;
    }
 
    for (; rr != row_nb_base_fun; ++rr)
      ++t_row_diff_base;
 
    ++t_w;
    ++t_cauchy_stress;
    ++t_invH;
  }
 
  MoFEMFunctionReturn(0);
}
 
HookeElement::OpAleRhs_dX::OpAleRhs_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, OPROW) {}
 
MoFEMErrorCode HookeElement::OpAleRhs_dX::iNtegrate(EntData &row_data) {
  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));
  };
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
 
  // 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();
  auto t_eshelby_stress =
      getFTensor2FromMat<3, 3>(*dataAtPts->eshelbyStressMat);
  auto &det_H = *dataAtPts->detHVec;
  auto t_invH = getFTensor2FromMat<3, 3>(*dataAtPts->invHMat);
 
  // 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];
    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_eshelby_stress;
    ++t_invH;
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode HookeElement::setBlocks(
    MoFEM::Interface &m_field,
    boost::shared_ptr<map<int, BlockData>> &block_sets_ptr) {
  MoFEMFunctionBegin;
 
  if (!block_sets_ptr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Pointer to block of sets is null");
 
  for (_IT_CUBITMESHSETS_BY_BCDATA_TYPE_FOR_LOOP_(
           m_field, BLOCKSET | MAT_ELASTICSET, it)) {
    Mat_Elastic mydata;
    CHKERR it->getAttributeDataStructure(mydata);
    int id = it->getMeshsetId();
    auto &block_data = (*block_sets_ptr)[id];
    EntityHandle meshset = it->getMeshset();
    CHKERR m_field.get_moab().get_entities_by_dimension(meshset, 3,
                                                        block_data.tEts, true);
    block_data.iD = id;
    block_data.E = mydata.data.Young;
    block_data.PoissonRatio = mydata.data.Poisson;
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode HookeElement::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) {
  MoFEMFunctionBegin;
 
  if (!block_sets_ptr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Pointer to block of sets is null");
 
  CHKERR m_field.add_finite_element(element_name, MF_ZERO);
  CHKERR m_field.modify_finite_element_add_field_row(element_name, x_field);
  CHKERR m_field.modify_finite_element_add_field_col(element_name, x_field);
  CHKERR m_field.modify_finite_element_add_field_data(element_name, x_field);
  if (m_field.check_field(X_field)) {
    if (ale) {
      CHKERR m_field.modify_finite_element_add_field_row(element_name, X_field);
      CHKERR m_field.modify_finite_element_add_field_col(element_name, X_field);
    }
    CHKERR m_field.modify_finite_element_add_field_data(element_name, X_field);
  }
 
  for (auto &m : (*block_sets_ptr)) {
    CHKERR m_field.add_ents_to_finite_element_by_dim(m.second.tEts, 3,
                                                     element_name);
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode HookeElement::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,
    boost::shared_ptr<DataAtIntegrationPts> data_at_pts) {
  MoFEMFunctionBegin;
 
  if (!block_sets_ptr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Pointer to block of sets is null");
 
  if (!data_at_pts)
    data_at_pts = boost::make_shared<DataAtIntegrationPts>();
 
  if (fe_lhs_ptr) {
    if (ale == PETSC_FALSE) {
      if (type == MBPRISM) {
        boost::shared_ptr<MatrixDouble> inv_jac_ptr(new MatrixDouble);
        fe_lhs_ptr->getOpPtrVector().push_back(
            new OpCalculateInvJacForFatPrism(inv_jac_ptr));
        fe_lhs_ptr->getOpPtrVector().push_back(
            new OpSetInvJacH1ForFatPrism(inv_jac_ptr));
      }
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpCalculateHomogeneousStiffness<true>(
              x_field, x_field, block_sets_ptr, data_at_pts));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpLhs_dx_dx<0>(x_field, x_field, data_at_pts));
    } else {
      if (type == MBPRISM) {
        boost::shared_ptr<MatrixDouble> inv_jac_ptr(new MatrixDouble);
        fe_lhs_ptr->getOpPtrVector().push_back(
            new OpCalculateInvJacForFatPrism(inv_jac_ptr));
        fe_lhs_ptr->getOpPtrVector().push_back(
            new OpSetInvJacH1ForFatPrism(inv_jac_ptr));
      }
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpCalculateVectorFieldGradient<3, 3>(X_field, data_at_pts->HMat));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpCalculateHomogeneousStiffness<true>(
              x_field, x_field, block_sets_ptr, data_at_pts));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpCalculateVectorFieldGradient<3, 3>(x_field, data_at_pts->hMat));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpCalculateStrainAle(x_field, x_field, data_at_pts));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpCalculateStress<0>(x_field, x_field, data_at_pts));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpAleLhs_dx_dx<0>(x_field, x_field, data_at_pts));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpAleLhs_dx_dX<0>(x_field, X_field, data_at_pts));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpCalculateEnergy(X_field, X_field, data_at_pts));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpCalculateEshelbyStress(X_field, X_field, data_at_pts));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpAleLhs_dX_dX<0>(X_field, X_field, data_at_pts));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpAleLhsPre_dX_dx<0>(X_field, x_field, data_at_pts));
      fe_lhs_ptr->getOpPtrVector().push_back(
          new OpAleLhs_dX_dx(X_field, x_field, data_at_pts));
    }
  }
 
  if (fe_rhs_ptr) {
 
    if (ale == PETSC_FALSE) {
      if (type == MBPRISM) {
        boost::shared_ptr<MatrixDouble> inv_jac_ptr(new MatrixDouble);
        fe_rhs_ptr->getOpPtrVector().push_back(
            new OpCalculateInvJacForFatPrism(inv_jac_ptr));
        fe_rhs_ptr->getOpPtrVector().push_back(
            new OpSetInvJacH1ForFatPrism(inv_jac_ptr));
      }
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpCalculateVectorFieldGradient<3, 3>(x_field, data_at_pts->hMat));
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpCalculateHomogeneousStiffness<0>(x_field, x_field,
                                                 block_sets_ptr, data_at_pts));
      if (field_disp) {
        fe_rhs_ptr->getOpPtrVector().push_back(
            new OpCalculateStrain<true>(x_field, x_field, data_at_pts));
      } else {
        fe_rhs_ptr->getOpPtrVector().push_back(
            new OpCalculateStrain<false>(x_field, x_field, data_at_pts));
      }
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpCalculateStress<0>(x_field, x_field, data_at_pts));
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpRhs_dx(x_field, x_field, data_at_pts));
    } else {
      if (type == MBPRISM) {
        boost::shared_ptr<MatrixDouble> inv_jac_ptr(new MatrixDouble);
        fe_rhs_ptr->getOpPtrVector().push_back(
            new OpCalculateInvJacForFatPrism(inv_jac_ptr));
        fe_rhs_ptr->getOpPtrVector().push_back(
            new OpSetInvJacH1ForFatPrism(inv_jac_ptr));
      }
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpCalculateVectorFieldGradient<3, 3>(X_field, data_at_pts->HMat));
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpCalculateHomogeneousStiffness<0>(x_field, x_field,
                                                 block_sets_ptr, data_at_pts));
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpCalculateVectorFieldGradient<3, 3>(x_field, data_at_pts->hMat));
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpCalculateStrainAle(x_field, x_field, data_at_pts));
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpCalculateStress<0>(x_field, x_field, data_at_pts));
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpAleRhs_dx(x_field, x_field, data_at_pts));
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpCalculateEnergy(X_field, X_field, data_at_pts));
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpCalculateEshelbyStress(X_field, X_field, data_at_pts));
      fe_rhs_ptr->getOpPtrVector().push_back(
          new OpAleRhs_dX(X_field, X_field, data_at_pts));
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode HookeElement::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) {
  MoFEMFunctionBegin;
 
  MoFEM::Interface *m_field_ptr;
  CHKERR DMoFEMGetInterfacePtr(dm, &m_field_ptr);
 
  v_energy = createVectorMPI(m_field_ptr->get_comm(), PETSC_DECIDE, 1);
 
  boost::shared_ptr<DataAtIntegrationPts> data_at_pts(
      new DataAtIntegrationPts());
 
  auto fe_ptr =
      boost::make_shared<VolumeElementForcesAndSourcesCore>(*m_field_ptr);
  fe_ptr->getRuleHook = [](const double, const double, const double o) {
    return 2 * o;
  };
 
  if (m_field_ptr->check_field("MESH_NODE_POSITIONS")) CHKERR addHOOpsVol(
      "MESH_NODE_POSITIONS", *fe_ptr, true, false, false, false);
 
  struct PrismFE : public FatPrismElementForcesAndSourcesCore {
 
    using FatPrismElementForcesAndSourcesCore::
        FatPrismElementForcesAndSourcesCore;
    int getRuleTrianglesOnly(int order) { return 2 * order; }
    int getRuleThroughThickness(int order) { return 2 * order; }
  };
 
  boost::shared_ptr<ForcesAndSourcesCore> prism_fe_ptr(
      new PrismFE(*m_field_ptr));
 
  auto push_ops = [&](boost::shared_ptr<ForcesAndSourcesCore> fe_ptr,
                      EntityType type) {
    MoFEMFunctionBeginHot;
    boost::shared_ptr<MatrixDouble> inv_jac_ptr(new MatrixDouble);
    if (ale == PETSC_FALSE) {
      if (type == MBPRISM) {
        fe_ptr->getOpPtrVector().push_back(
            new OpCalculateInvJacForFatPrism(inv_jac_ptr));
        fe_ptr->getOpPtrVector().push_back(
            new OpSetInvJacH1ForFatPrism(inv_jac_ptr));
      }
      fe_ptr->getOpPtrVector().push_back(
          new OpCalculateVectorFieldGradient<3, 3>(x_field, data_at_pts->hMat));
      fe_ptr->getOpPtrVector().push_back(new OpCalculateHomogeneousStiffness<0>(
          x_field, x_field, block_sets_ptr, data_at_pts));
      if (field_disp) {
        fe_ptr->getOpPtrVector().push_back(
            new OpCalculateStrain<true>(x_field, x_field, data_at_pts));
      } else {
        fe_ptr->getOpPtrVector().push_back(
            new OpCalculateStrain<false>(x_field, x_field, data_at_pts));
      }
      fe_ptr->getOpPtrVector().push_back(
          new OpCalculateStress<0>(x_field, x_field, data_at_pts));
      fe_ptr->getOpPtrVector().push_back(
          new OpCalculateEnergy(X_field, X_field, data_at_pts, v_energy));
    } else {
      if (type == MBPRISM) {
        fe_ptr->getOpPtrVector().push_back(
            new OpCalculateInvJacForFatPrism(inv_jac_ptr));
        fe_ptr->getOpPtrVector().push_back(
            new OpSetInvJacH1ForFatPrism(inv_jac_ptr));
      }
      fe_ptr->getOpPtrVector().push_back(
          new OpCalculateVectorFieldGradient<3, 3>(X_field, data_at_pts->HMat));
      fe_ptr->getOpPtrVector().push_back(new OpCalculateHomogeneousStiffness<0>(
          x_field, x_field, block_sets_ptr, data_at_pts));
      fe_ptr->getOpPtrVector().push_back(
          new OpCalculateVectorFieldGradient<3, 3>(x_field, data_at_pts->hMat));
      fe_ptr->getOpPtrVector().push_back(
          new OpCalculateStrainAle(x_field, x_field, data_at_pts));
      fe_ptr->getOpPtrVector().push_back(
          new OpCalculateStress<0>(x_field, x_field, data_at_pts));
      fe_ptr->getOpPtrVector().push_back(
          new OpCalculateEnergy(X_field, X_field, data_at_pts, v_energy));
    }
    MoFEMFunctionReturnHot(0);
  };
 
  CHKERR push_ops(fe_ptr, MBTET);
  CHKERR push_ops(prism_fe_ptr, MBPRISM);
 
  CHKERR VecZeroEntries(v_energy);
 
  fe_ptr->snes_ctx = SnesMethod::CTX_SNESNONE;
  CHKERR DMoFEMLoopFiniteElements(dm, "ELASTIC", fe_ptr);
  CHKERR DMoFEMLoopFiniteElements(dm, "ELASTIC", prism_fe_ptr);
 
  CHKERR VecAssemblyBegin(v_energy);
  CHKERR VecAssemblyEnd(v_energy);
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode HookeElement::OpAleLhs_dX_dx::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();
 
  auto t_invH = getFTensor2FromMat<3, 3>(*dataAtPts->invHMat);
  auto &det_H = *dataAtPts->detHVec;
 
  auto get_eshelby_stress_dx = [this]() {
    FTensor::Tensor4<FTensor::PackPtr<double *, 1>, 3, 3, 3, 3>
        t_eshelby_stress_dx;
    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();
 
  // 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::Tensor3<double, 3, 3, 3> t_row_stress_dx;
      t_row_stress_dx(i, k, l) =
          a * t_row_diff_base_pulled(j) * t_eshelby_stress_dx(i, j, k, l);
 
      // 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_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;
 
    ++t_w;
    ++t_invH;
    ++t_eshelby_stress_dx;
  }
 
  MoFEMFunctionReturn(0);
}
 
HookeElement::OpAleLhsWithDensity_dX_dX::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)
    : OpAssemble(row_field, col_field, data_at_pts, OPROWCOL, false),
      rhoAtGaussPtsPtr(rho_at_gauss_pts),
      rhoGradAtGaussPtsPtr(rho_grad_at_gauss_pts), rhoN(rho_n), rHo0(rho_0) {}
 
MoFEMErrorCode
HookeElement::OpAleLhsWithDensity_dX_dX::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)
  auto rho = getFTensor0FromVec(*rhoAtGaussPtsPtr);
  auto t_grad_rho = getFTensor1FromMat<3>(*rhoGradAtGaussPtsPtr);
 
  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 &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];
 
    const double stress_dho_coef = (rhoN / rho);
    // (rhoN / rHo0) * pow(rho / rHo0, rhoN - 1.) * (1. / pow(rho / rHo0,
    // rhoN));
 
    // 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);
 
      // get derivatives of base functions for columns
      // auto t_col_diff_base = col_data.getFTensor1DiffN<3>(gg, 0);
      auto t_col_base = col_data.getFTensor0N(gg, 0);
 
      // iterate column base functions
      for (int cc = 0; cc != nbCols / 3; ++cc) {
 
        t_m(i, k) +=
            t_row_stress(i) * stress_dho_coef * t_grad_rho(k) * t_col_base;
        // move to next column base function
        ++t_col_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_eshelby_stress;
    ++t_invH;
    ++rho;
    ++t_grad_rho;
  }
 
  MoFEMFunctionReturn(0);
}
 
HookeElement::OpAleLhsWithDensity_dx_dX::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)
    : OpAssemble(row_field, col_field, data_at_pts, OPROWCOL, false),
      rhoAtGaussPtsPtr(rho_at_gauss_pts),
      rhoGradAtGaussPtsPtr(rho_grad_at_gauss_pts), rhoN(rho_n), rHo0(rho_0) {}
 
MoFEMErrorCode
HookeElement::OpAleLhsWithDensity_dx_dX::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 integration 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();
 
  auto rho = getFTensor0FromVec(*rhoAtGaussPtsPtr);
  auto t_grad_rho = getFTensor1FromMat<3>(*rhoGradAtGaussPtsPtr);
  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];
 
    const double stress_dho_coef = (rhoN / rho);
    // (rhoN / rHo0) * pow(rho / rHo0, rhoN - 1.) * (1. / pow(rho / rHo0,
    // rhoN)); 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);
 
      // get derivatives of base functions for columns
      auto t_col_base = col_data.getFTensor0N(gg, 0);
      // iterate column base functions
      for (int cc = 0; cc != nbCols / 3; ++cc) {
 
        t_m(i, k) +=
            t_row_stress(i) * stress_dho_coef * t_grad_rho(k) * t_col_base;
 
        ++t_col_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;
    ++rho;
    ++t_grad_rho;
  }
 
  MoFEMFunctionReturn(0);
}
 
HookeElement::OpCalculateStiffnessScaledByDensityField::
    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)
 
    : VolUserDataOperator(row_field, col_field, OPROW, true),
      blockSetsPtr(block_sets_ptr), dataAtPts(data_at_pts),
      rhoAtGaussPtsPtr(rho_at_gauss_pts), rhoN(rho_n), rHo0(rho_0) {
  std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
}
 
MoFEMErrorCode HookeElement::OpCalculateStiffnessScaledByDensityField::doWork(
    int row_side, EntityType row_type, EntData &row_data) {
  MoFEMFunctionBegin;
 
  if (!rhoAtGaussPtsPtr)
    SETERRQ(PETSC_COMM_SELF, 1, "Calculate density with MWLS first.");
 
  for (auto &m : (*blockSetsPtr)) {
 
    if (m.second.tEts.find(getNumeredEntFiniteElementPtr()->getEnt()) ==
        m.second.tEts.end()) {
      continue;
    }
 
    const int nb_integration_pts = getGaussPts().size2();
    dataAtPts->stiffnessMat->resize(36, nb_integration_pts, false);
 
    FTensor::Ddg<FTensor::PackPtr<double *, 1>, 3, 3> t_D(
        MAT_TO_DDG(dataAtPts->stiffnessMat));
    const double young = m.second.E;
    const double poisson = m.second.PoissonRatio;
 
    auto rho = getFTensor0FromVec(*rhoAtGaussPtsPtr);
 
    // 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;
 
    for (int gg = 0; gg != nb_integration_pts; ++gg) {
 
      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;
      // here the coefficient is modified to take density into account for
      // porous materials: E(p) = E * (p / p_0)^n
      t_D(i, j, k, l) *= coefficient * pow(rho / rHo0, rhoN);
 
      ++t_D;
      ++rho;
    }
  }
 
  MoFEMFunctionReturn(0);
}