HookeElement.cpp

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/** \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);
}