VEC-3: Nonlinear dynamic elastic

Note

Prerequisites of this tutorial include MSH-1: Create a 2D mesh from Gmsh

Note

Intended learning outcome:

• general structure of a program developed using MoFEM
• idea of Simple Interface in MoFEM and how to use it
• second order equation in time
• idea of domain element in MoFEM and how to use it
• Use default forms integrals
• how to push the developed UDOs to the Pipeline
• utilisation of tools to convert outputs (MOAB) and visualise them (Paraview)

/**
 * \file dynamic_elastic.cpp
 * \example dynamic_elastic.cpp
 *
 * Plane stress elastic dynamic problem
 *
 */
 
#include <MoFEM.hpp>
#include <MatrixFunction.hpp>
using namespace MoFEM;
 
template <int DIM> struct ElementsAndOps {};
 
template <> struct ElementsAndOps<2> {
  using DomainEle = FaceElementForcesAndSourcesCore;
};
 
template <> struct ElementsAndOps<3> {
  using DomainEle = VolumeElementForcesAndSourcesCore;
};
 
constexpr int SPACE_DIM =
    EXECUTABLE_DIMENSION; //< Space dimension of problem, mesh
 
using EntData = EntitiesFieldData::EntData;
using DomainEle = ElementsAndOps<SPACE_DIM>::DomainEle;
using DomainEleOp = DomainEle::UserDataOperator;
using PostProcEle = PostProcBrokenMeshInMoab<DomainEle>;
 
using OpK = FormsIntegrators<DomainEleOp>::Assembly<PETSC>::BiLinearForm<
    GAUSS>::OpGradTensorGrad<1, SPACE_DIM, SPACE_DIM, 1>;
using OpMass = FormsIntegrators<DomainEleOp>::Assembly<PETSC>::BiLinearForm<
    GAUSS>::OpMass<1, SPACE_DIM>;
using OpInternalForce = FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpGradTimesTensor<1, SPACE_DIM, SPACE_DIM>;
using OpBodyForce = FormsIntegrators<DomainEleOp>::Assembly<PETSC>::LinearForm<
    GAUSS>::OpSource<1, SPACE_DIM>;
using OpInertiaForce = FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpBaseTimesVector<1, SPACE_DIM, 1>;
 
constexpr bool is_quasi_static = false;
constexpr double rho = 1;
constexpr double omega = 2.4;
constexpr double young_modulus = 1;
constexpr double poisson_ratio = 0.25;
constexpr double bulk_modulus_K = young_modulus / (3 * (1 - 2 * poisson_ratio));
constexpr double shear_modulus_G = young_modulus / (2 * (1 + poisson_ratio));
 
#include <HenckyOps.hpp>
using namespace HenckyOps;
 
static double *ts_time_ptr;
static double *ts_aa_ptr;
 
struct Example {
 
  Example(MoFEM::Interface &m_field) : mField(m_field) {}
 
  MoFEMErrorCode runProblem();
 
private:
  MoFEM::Interface &mField;
 
  MoFEMErrorCode readMesh();
  MoFEMErrorCode setupProblem();
  MoFEMErrorCode createCommonData();
  MoFEMErrorCode boundaryCondition();
  MoFEMErrorCode assembleSystem();
  MoFEMErrorCode solveSystem();
  MoFEMErrorCode outputResults();
  MoFEMErrorCode checkResults();
 
  boost::shared_ptr<MatrixDouble> matGradPtr;
  boost::shared_ptr<MatrixDouble> matStrainPtr;
  boost::shared_ptr<MatrixDouble> matStressPtr;
  boost::shared_ptr<MatrixDouble> matAccelerationPtr;
  boost::shared_ptr<MatrixDouble> matInertiaPtr;
  boost::shared_ptr<MatrixDouble> matDPtr;
 
  boost::shared_ptr<MatrixDouble> matTangentPtr;
};
 
//! [Create common data]
MoFEMErrorCode Example::createCommonData() {
  MoFEMFunctionBegin;
 
  auto set_matrial_stiffness = [&]() {
    FTensor::Index<'i', SPACE_DIM> i;
    FTensor::Index<'j', SPACE_DIM> j;
    FTensor::Index<'k', SPACE_DIM> k;
    FTensor::Index<'l', SPACE_DIM> l;
    constexpr auto t_kd = FTensor::Kronecker_Delta_symmetric<int>();
    MoFEMFunctionBegin;
    constexpr double A =
        (SPACE_DIM == 2) ? 2 * shear_modulus_G /
                               (bulk_modulus_K + (4. / 3.) * shear_modulus_G)
                         : 1;
    auto t_D = getFTensor4DdgFromMat<SPACE_DIM, SPACE_DIM, 0>(*matDPtr);
    t_D(i, j, k, l) = 2 * shear_modulus_G * ((t_kd(i, k) ^ t_kd(j, l)) / 4.) +
                      A * (bulk_modulus_K - (2. / 3.) * shear_modulus_G) *
                          t_kd(i, j) * t_kd(k, l);
    MoFEMFunctionReturn(0);
  };
 
  matGradPtr = boost::make_shared<MatrixDouble>();
  matStrainPtr = boost::make_shared<MatrixDouble>();
  matStressPtr = boost::make_shared<MatrixDouble>();
  matAccelerationPtr = boost::make_shared<MatrixDouble>();
  matInertiaPtr = boost::make_shared<MatrixDouble>();
  matDPtr = boost::make_shared<MatrixDouble>();
 
  matTangentPtr = boost::make_shared<MatrixDouble>();
 
  constexpr auto size_symm = (SPACE_DIM * (SPACE_DIM + 1)) / 2;
  matDPtr->resize(size_symm * size_symm, 1);
 
  CHKERR set_matrial_stiffness();
 
  MoFEMFunctionReturn(0);
}
//! [Create common data]
 
//! [Run problem]
MoFEMErrorCode Example::runProblem() {
  MoFEMFunctionBegin;
  CHKERR readMesh();
  CHKERR setupProblem();
  CHKERR createCommonData();
  CHKERR boundaryCondition();
  CHKERR assembleSystem();
  CHKERR solveSystem();
  CHKERR outputResults();
  CHKERR checkResults();
  MoFEMFunctionReturn(0);
}
//! [Run problem]
 
//! [Read mesh]
MoFEMErrorCode Example::readMesh() {
  MoFEMFunctionBegin;
  auto simple = mField.getInterface<Simple>();
  CHKERR simple->getOptions();
  CHKERR simple->loadFile();
  MoFEMFunctionReturn(0);
}
//! [Read mesh]
 
//! [Set up problem]
MoFEMErrorCode Example::setupProblem() {
  MoFEMFunctionBegin;
  Simple *simple = mField.getInterface<Simple>();
  // Add field
  CHKERR simple->addDomainField("U", H1, AINSWORTH_BERNSTEIN_BEZIER_BASE,
                                SPACE_DIM);
  int order = 2;
  CHKERR PetscOptionsGetInt(PETSC_NULL, "", "-order", &order, PETSC_NULL);
  CHKERR simple->setFieldOrder("U", order);
  CHKERR simple->setUp();
  MoFEMFunctionReturn(0);
}
//! [Set up problem]
 
//! [Boundary condition]
MoFEMErrorCode Example::boundaryCondition() {
  MoFEMFunctionBegin;
 
  auto simple = mField.getInterface<Simple>();
  auto bc_mng = mField.getInterface<BcManager>();
 
  CHKERR bc_mng->removeBlockDOFsOnEntities<DisplacementCubitBcData>(
      simple->getProblemName(), "U");
      
  MoFEMFunctionReturn(0);
}
//! [Boundary condition]
 
//! [Push operators to pipeline]
MoFEMErrorCode Example::assembleSystem() {
  MoFEMFunctionBegin;
  auto *simple = mField.getInterface<Simple>();
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto det_ptr = boost::make_shared<VectorDouble>();
  auto jac_ptr = boost::make_shared<MatrixDouble>();
  auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
 
  auto add_base_transform = [&](auto &pipeline) {
    pipeline.push_back(new OpCalculateHOJac<SPACE_DIM>(jac_ptr));
    pipeline.push_back(
        new OpInvertMatrix<SPACE_DIM>(jac_ptr, det_ptr, inv_jac_ptr));
    pipeline.push_back(
        new OpSetHOInvJacToScalarBases<SPACE_DIM>(H1, inv_jac_ptr));
    pipeline.push_back(new OpSetHOWeights(det_ptr));
  };
  add_base_transform(pipeline_mng->getOpDomainRhsPipeline());
  add_base_transform(pipeline_mng->getOpDomainLhsPipeline());
 
  // Get pointer to U_tt shift in domain element
  auto get_rho = [this](const double, const double, const double) {
    auto *pipeline_mng = mField.getInterface<PipelineManager>();
    auto &fe_domain_lhs = pipeline_mng->getDomainLhsFE();
    return rho * fe_domain_lhs->ts_aa;
  };
 
  auto get_body_force = [this](const double, const double, const double) {
    auto *pipeline_mng = mField.getInterface<PipelineManager>();
    auto fe_domain_rhs = pipeline_mng->getDomainRhsFE();
    FTensor::Index<'i', SPACE_DIM> i;
    FTensor::Tensor1<double, SPACE_DIM> t_source;
    t_source(i) = 0.;
    t_source(0) = 0.1;
    t_source(1) = 1.;
    const auto time = fe_domain_rhs->ts_t;
    t_source(i) *= sin(time * omega * M_PI);
    return t_source;
  };
 
  auto henky_common_data_ptr = boost::make_shared<HenckyOps::CommonData>();
  henky_common_data_ptr->matGradPtr = matGradPtr;
  henky_common_data_ptr->matDPtr = matDPtr;
 
  pipeline_mng->getOpDomainLhsPipeline().push_back(
      new OpCalculateVectorFieldGradient<SPACE_DIM, SPACE_DIM>("U",
                                                               matGradPtr));
 
  pipeline_mng->getOpDomainLhsPipeline().push_back(
      new OpCalculateEigenVals<SPACE_DIM>("U", henky_common_data_ptr));
  pipeline_mng->getOpDomainLhsPipeline().push_back(
      new OpCalculateLogC<SPACE_DIM>("U", henky_common_data_ptr));
  pipeline_mng->getOpDomainLhsPipeline().push_back(
      new OpCalculateLogC_dC<SPACE_DIM>("U", henky_common_data_ptr));
  pipeline_mng->getOpDomainLhsPipeline().push_back(
      new OpCalculateHenckyStress<SPACE_DIM>("U", henky_common_data_ptr));
  pipeline_mng->getOpDomainLhsPipeline().push_back(
      new OpCalculatePiolaStress<SPACE_DIM>("U", henky_common_data_ptr));
  pipeline_mng->getOpDomainLhsPipeline().push_back(
      new OpHenckyTangent<SPACE_DIM>("U", henky_common_data_ptr));
  pipeline_mng->getOpDomainLhsPipeline().push_back(
      new OpK("U", "U", henky_common_data_ptr->getMatTangent()));
 
  if (!is_quasi_static)
    pipeline_mng->getOpDomainLhsPipeline().push_back(
        new OpMass("U", "U", get_rho));
 
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpBodyForce("U", get_body_force));
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpCalculateVectorFieldGradient<SPACE_DIM, SPACE_DIM>("U",
                                                               matGradPtr));
 
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpCalculateEigenVals<SPACE_DIM>("U", henky_common_data_ptr));
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpCalculateLogC<SPACE_DIM>("U", henky_common_data_ptr));
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpCalculateLogC_dC<SPACE_DIM>("U", henky_common_data_ptr));
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpCalculateHenckyStress<SPACE_DIM>("U", henky_common_data_ptr));
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpCalculatePiolaStress<SPACE_DIM>("U", henky_common_data_ptr));
 
  pipeline_mng->getOpDomainRhsPipeline().push_back(new OpInternalForce(
      "U", henky_common_data_ptr->getMatFirstPiolaStress()));
  if (!is_quasi_static) {
    pipeline_mng->getOpDomainRhsPipeline().push_back(
        new OpCalculateVectorFieldValuesDotDot<SPACE_DIM>("U",
                                                          matAccelerationPtr));
    pipeline_mng->getOpDomainRhsPipeline().push_back(
        new OpScaleMatrix("U", rho, matAccelerationPtr, matInertiaPtr));
    pipeline_mng->getOpDomainRhsPipeline().push_back(new OpInertiaForce(
        "U", matInertiaPtr, [](double, double, double) { return 1.; }));
  }
 
  auto integration_rule = [](int, int, int approx_order) {
    return 2 * approx_order;
  };
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setDomainLhsIntegrationRule(integration_rule);
 
  auto get_bc_hook = [&]() {
    EssentialPreProc<DisplacementCubitBcData> hook(
        mField, pipeline_mng->getDomainRhsFE(),
        {boost::make_shared<TimeScale>()});
    return hook;
  };
 
  pipeline_mng->getDomainRhsFE()->preProcessHook = get_bc_hook();
 
  MoFEMFunctionReturn(0);
}
//! [Push operators to pipeline]
 
/**
 * @brief Monitor solution
 *
 * This functions is called by TS solver at the end of each step. It is used
 * to output results to the hard drive.
 */
struct Monitor : public FEMethod {
  Monitor(SmartPetscObj<DM> dm, boost::shared_ptr<PostProcEle> post_proc)
      : dM(dm), postProc(post_proc){};
  MoFEMErrorCode postProcess() {
    MoFEMFunctionBegin;
    constexpr int save_every_nth_step = 1;
    if (ts_step % save_every_nth_step == 0) {
      CHKERR DMoFEMLoopFiniteElements(dM, "dFE", postProc);
      CHKERR postProc->writeFile(
          "out_step_" + boost::lexical_cast<std::string>(ts_step) + ".h5m");
    }
    MoFEMFunctionReturn(0);
  }
 
private:
  SmartPetscObj<DM> dM;
  boost::shared_ptr<PostProcEle> postProc;
};
 
//! [Solve]
MoFEMErrorCode Example::solveSystem() {
  MoFEMFunctionBegin;
  auto *simple = mField.getInterface<Simple>();
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto dm = simple->getDM();
  MoFEM::SmartPetscObj<TS> ts;
  if (is_quasi_static)
    ts = pipeline_mng->createTSIM();
  else
    ts = pipeline_mng->createTSIM2();
 
  // Setup postprocessing
  auto post_proc_fe = boost::make_shared<PostProcEle>(mField);
 
  auto det_ptr = boost::make_shared<VectorDouble>();
  auto jac_ptr = boost::make_shared<MatrixDouble>();
  auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculateHOJac<SPACE_DIM>(jac_ptr));
  post_proc_fe->getOpPtrVector().push_back(
      new OpInvertMatrix<SPACE_DIM>(jac_ptr, det_ptr, inv_jac_ptr));
  post_proc_fe->getOpPtrVector().push_back(
      new OpSetHOInvJacToScalarBases<SPACE_DIM>(H1, inv_jac_ptr));
 
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculateVectorFieldGradient<SPACE_DIM, SPACE_DIM>("U",
                                                               matGradPtr));
  post_proc_fe->getOpPtrVector().push_back(
      new OpSymmetrizeTensor<SPACE_DIM>("U", matGradPtr, matStrainPtr));
  post_proc_fe->getOpPtrVector().push_back(
      new OpTensorTimesSymmetricTensor<SPACE_DIM, SPACE_DIM>(
          "U", matStrainPtr, matStressPtr, matDPtr));
 
  auto u_ptr = boost::make_shared<MatrixDouble>();
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_ptr));      
 
  using OpPPMap = OpPostProcMapInMoab<SPACE_DIM, SPACE_DIM>;
 
  post_proc_fe->getOpPtrVector().push_back(
 
      new OpPPMap(
 
          post_proc_fe->getPostProcMesh(), post_proc_fe->getMapGaussPts(),
 
          {},
 
          {{"U", u_ptr}},
 
          {},
 
          {{"STRAIN", matStrainPtr}, {"STRESS", matStressPtr}}
 
          )
 
  );
 
  // Add monitor to time solver
  boost::shared_ptr<FEMethod> null_fe;
  auto monitor_ptr = boost::make_shared<Monitor>(dm, post_proc_fe);
  CHKERR DMMoFEMTSSetMonitor(dm, ts, simple->getDomainFEName(), null_fe,
                             null_fe, monitor_ptr);
 
  double ftime = 1;
  // CHKERR TSSetMaxTime(ts, ftime);
  CHKERR TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);
 
  auto T = smartCreateDMVector(simple->getDM());
  CHKERR DMoFEMMeshToLocalVector(simple->getDM(), T, INSERT_VALUES,
                                 SCATTER_FORWARD);
  if (is_quasi_static) {
    CHKERR TSSetSolution(ts, T);
    CHKERR TSSetFromOptions(ts);
  } else {
    auto TT = smartVectorDuplicate(T);
    CHKERR TS2SetSolution(ts, T, TT);
    CHKERR TSSetFromOptions(ts);
  }
 
  CHKERR TSSolve(ts, NULL);
  CHKERR TSGetTime(ts, &ftime);
 
  PetscInt steps, snesfails, rejects, nonlinits, linits;
#if PETSC_VERSION_GE(3, 8, 0)
  CHKERR TSGetStepNumber(ts, &steps);
#else
  CHKERR TSGetTimeStepNumber(ts, &steps);
#endif
  CHKERR TSGetSNESFailures(ts, &snesfails);
  CHKERR TSGetStepRejections(ts, &rejects);
  CHKERR TSGetSNESIterations(ts, &nonlinits);
  CHKERR TSGetKSPIterations(ts, &linits);
  MOFEM_LOG_C("EXAMPLE", Sev::inform,
              "steps %D (%D rejected, %D SNES fails), ftime %g, nonlinits "
              "%D, linits %D\n",
              steps, rejects, snesfails, ftime, nonlinits, linits);
 
  MoFEMFunctionReturn(0);
}
//! [Solve]
 
//! [Postprocess results]
MoFEMErrorCode Example::outputResults() {
  MoFEMFunctionBegin;
  PetscBool test_flg = PETSC_FALSE;
  CHKERR PetscOptionsGetBool(PETSC_NULL, "", "-test", &test_flg, PETSC_NULL);
  if (test_flg) {
    auto *simple = mField.getInterface<Simple>();
    auto T = smartCreateDMVector(simple->getDM());
    CHKERR DMoFEMMeshToLocalVector(simple->getDM(), T, INSERT_VALUES,
                                   SCATTER_FORWARD);
    double nrm2;
    CHKERR VecNorm(T, NORM_2, &nrm2);
    MOFEM_LOG("EXAMPLE", Sev::inform) << "Regression norm " << nrm2;
    constexpr double regression_value = 1.09572;
    if (fabs(nrm2 - regression_value) > 1e-2)
      SETERRQ(PETSC_COMM_WORLD, MOFEM_ATOM_TEST_INVALID,
              "Regression test faileed; wrong norm value.");
  }
  MoFEMFunctionReturn(0);
}
//! [Postprocess results]
 
//! [Check]
MoFEMErrorCode Example::checkResults() {
  MoFEMFunctionBegin;
  MoFEMFunctionReturn(0);
}
//! [Check]
 
static char help[] = "...\n\n";
 
int main(int argc, char *argv[]) {
 
  // Initialisation of MoFEM/PETSc and MOAB data structures
  const char param_file[] = "param_file.petsc";
  MoFEM::Core::Initialize(&argc, &argv, param_file, help);
 
  // Add logging channel for example
  auto core_log = logging::core::get();
  core_log->add_sink(
      LogManager::createSink(LogManager::getStrmWorld(), "EXAMPLE"));
  LogManager::setLog("EXAMPLE");
  MOFEM_LOG_TAG("EXAMPLE", "example");
 
  try {
 
    //! [Register MoFEM discrete manager in PETSc]
    DMType dm_name = "DMMOFEM";
    CHKERR DMRegister_MoFEM(dm_name);
    //! [Register MoFEM discrete manager in PETSc
 
    //! [Create MoAB]
    moab::Core mb_instance;              ///< mesh database
    moab::Interface &moab = mb_instance; ///< mesh database interface
    //! [Create MoAB]
 
    //! [Create MoFEM]
    MoFEM::Core core(moab);           ///< finite element database
    MoFEM::Interface &m_field = core; ///< finite element database insterface
    //! [Create MoFEM]
 
    //! [Example]
    Example ex(m_field);
    CHKERR ex.runProblem();
    //! [Example]
  }
  CATCH_ERRORS;
 
  CHKERR MoFEM::Core::Finalize();
}

/**
 * \file HenkyOps.hpp
 * \example HenkyOps.hpp
 *
 * @copyright Copyright (c) 2023
 */
 
namespace HenckyOps {
 
constexpr double eps = std::numeric_limits<float>::epsilon();
 
auto f = [](double v) { return 0.5 * std::log(v); };
auto d_f = [](double v) { return 0.5 / v; };
auto dd_f = [](double v) { return -0.5 / (v * v); };
 
struct isEq {
  static inline auto check(const double &a, const double &b) {
    return std::abs(a - b) / absMax < eps;
  }
  static double absMax;
};
 
double isEq::absMax = 1;
 
inline auto is_eq(const double &a, const double &b) {
  return isEq::check(a, b);
};
 
template <int DIM> inline auto get_uniq_nb(double *ptr) {
  std::array<double, DIM> tmp;
  std::copy(ptr, &ptr[DIM], tmp.begin());
  std::sort(tmp.begin(), tmp.end());
  isEq::absMax = std::max(std::abs(tmp[0]), std::abs(tmp[DIM - 1]));
  return std::distance(tmp.begin(), std::unique(tmp.begin(), tmp.end(), is_eq));
};
 
template <int DIM>
inline auto sort_eigen_vals(FTensor::Tensor1<double, DIM> &eig,
                            FTensor::Tensor2<double, DIM, DIM> &eigen_vec) {
 
  isEq::absMax =
      std::max(std::max(std::abs(eig(0)), std::abs(eig(1))), std::abs(eig(2)));
 
  int i = 0, j = 1, k = 2;
 
  if (is_eq(eig(0), eig(1))) {
    i = 0;
    j = 2;
    k = 1;
  } else if (is_eq(eig(0), eig(2))) {
    i = 0;
    j = 1;
    k = 2;
  } else if (is_eq(eig(1), eig(2))) {
    i = 1;
    j = 0;
    k = 2;
  }
 
  FTensor::Tensor2<double, 3, 3> eigen_vec_c{
      eigen_vec(i, 0), eigen_vec(i, 1), eigen_vec(i, 2),
 
      eigen_vec(j, 0), eigen_vec(j, 1), eigen_vec(j, 2),
 
      eigen_vec(k, 0), eigen_vec(k, 1), eigen_vec(k, 2)};
 
  FTensor::Tensor1<double, 3> eig_c{eig(i), eig(j), eig(k)};
 
  {
    FTensor::Index<'i', DIM> i;
    FTensor::Index<'j', DIM> j;
    eig(i) = eig_c(i);
    eigen_vec(i, j) = eigen_vec_c(i, j);
  }
};
 
struct CommonData : public boost::enable_shared_from_this<CommonData> {
  boost::shared_ptr<MatrixDouble> matGradPtr;
  boost::shared_ptr<MatrixDouble> matDPtr;
  boost::shared_ptr<MatrixDouble> matLogCPlastic;
 
  MatrixDouble matEigVal;
  MatrixDouble matEigVec;
  MatrixDouble matLogC;
  MatrixDouble matLogCdC;
  MatrixDouble matFirstPiolaStress;
  MatrixDouble matSecondPiolaStress;
  MatrixDouble matHenckyStress;
  MatrixDouble matTangent;
 
  inline auto getMatFirstPiolaStress() {
    return boost::shared_ptr<MatrixDouble>(shared_from_this(),
                                           &matFirstPiolaStress);
  }
 
  inline auto getMatHenckyStress() {
    return boost::shared_ptr<MatrixDouble>(shared_from_this(),
                                           &matHenckyStress);
  }
 
  inline auto getMatLogC() {
    return boost::shared_ptr<MatrixDouble>(shared_from_this(), &matLogC);
  }
 
  inline auto getMatTangent() {
    return boost::shared_ptr<MatrixDouble>(shared_from_this(), &matTangent);
  }
};
 
template <int DIM> struct OpCalculateEigenVals : public DomainEleOp {
 
  OpCalculateEigenVals(const std::string field_name,
                       boost::shared_ptr<CommonData> common_data)
      : DomainEleOp(field_name, DomainEleOp::OPROW),
        commonDataPtr(common_data) {
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    FTensor::Index<'i', DIM> i;
    FTensor::Index<'j', DIM> j;
    FTensor::Index<'k', DIM> k;
 
    constexpr auto t_kd = FTensor::Kronecker_Delta<int>();
    // const size_t nb_gauss_pts = matGradPtr->size2();
    const size_t nb_gauss_pts = getGaussPts().size2();
 
    auto t_grad = getFTensor2FromMat<DIM, DIM>(*(commonDataPtr->matGradPtr));
 
    commonDataPtr->matEigVal.resize(DIM, nb_gauss_pts, false);
    commonDataPtr->matEigVec.resize(DIM * DIM, nb_gauss_pts, false);
    auto t_eig_val = getFTensor1FromMat<DIM>(commonDataPtr->matEigVal);
    auto t_eig_vec = getFTensor2FromMat<DIM, DIM>(commonDataPtr->matEigVec);
 
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
 
      FTensor::Tensor2<double, DIM, DIM> F;
      FTensor::Tensor2_symmetric<double, DIM> C;
      FTensor::Tensor1<double, DIM> eig;
      FTensor::Tensor2<double, DIM, DIM> eigen_vec;
 
      F(i, j) = t_grad(i, j) + t_kd(i, j);
      C(i, j) = F(k, i) ^ F(k, j);
 
      for (int ii = 0; ii != DIM; ii++)
        for (int jj = 0; jj != DIM; jj++)
          eigen_vec(ii, jj) = C(ii, jj);
 
      CHKERR computeEigenValuesSymmetric<DIM>(eigen_vec, eig);
      for(auto ii = 0;ii!=DIM;++ii)
        eig(ii) = std::max(std::numeric_limits<double>::epsilon(), eig(ii));
 
      // rare case when two eigen values are equal
      auto nb_uniq = get_uniq_nb<DIM>(&eig(0));
      if constexpr (DIM == 3) {
        if (nb_uniq == 2) {
          sort_eigen_vals<DIM>(eig, eigen_vec);
        }
      }
 
      t_eig_val(i) = eig(i);
      t_eig_vec(i, j) = eigen_vec(i, j);
 
      ++t_grad;
      ++t_eig_val;
      ++t_eig_vec;
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<CommonData> commonDataPtr;
};
 
template <int DIM> struct OpCalculateLogC : public DomainEleOp {
 
  OpCalculateLogC(const std::string field_name,
                  boost::shared_ptr<CommonData> common_data)
      : DomainEleOp(field_name, DomainEleOp::OPROW),
        commonDataPtr(common_data) {
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    FTensor::Index<'i', DIM> i;
    FTensor::Index<'j', DIM> j;
 
    constexpr auto t_kd = FTensor::Kronecker_Delta<int>();
    // const size_t nb_gauss_pts = matGradPtr->size2();
    const size_t nb_gauss_pts = getGaussPts().size2();
    constexpr auto size_symm = (DIM * (DIM + 1)) / 2;
    commonDataPtr->matLogC.resize(size_symm, nb_gauss_pts, false);
 
    auto t_eig_val = getFTensor1FromMat<DIM>(commonDataPtr->matEigVal);
    auto t_eig_vec = getFTensor2FromMat<DIM, DIM>(commonDataPtr->matEigVec);
 
    auto t_logC = getFTensor2SymmetricFromMat<DIM>(commonDataPtr->matLogC);
 
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
 
      // rare case when two eigen values are equal
      auto nb_uniq = get_uniq_nb<DIM>(&(t_eig_val(0)));
 
      FTensor::Tensor1<double, DIM> eig;
      FTensor::Tensor2<double, DIM, DIM> eigen_vec;
      eig(i) = t_eig_val(i);
      eigen_vec(i, j) = t_eig_vec(i, j);
      auto logC = EigenMatrix::getMat(eig, eigen_vec, f);
      t_logC(i, j) = logC(i, j);
 
      ++t_eig_val;
      ++t_eig_vec;
      ++t_logC;
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<CommonData> commonDataPtr;
};
 
template <int DIM> struct OpCalculateLogC_dC : public DomainEleOp {
 
  OpCalculateLogC_dC(const std::string field_name,
                     boost::shared_ptr<CommonData> common_data)
      : DomainEleOp(field_name, DomainEleOp::OPROW),
        commonDataPtr(common_data) {
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    FTensor::Index<'i', DIM> i;
    FTensor::Index<'j', DIM> j;
    FTensor::Index<'k', DIM> k;
    FTensor::Index<'l', DIM> l;
 
    // const size_t nb_gauss_pts = matGradPtr->size2();
    const size_t nb_gauss_pts = getGaussPts().size2();
    constexpr auto size_symm = (DIM * (DIM + 1)) / 2;
    commonDataPtr->matLogCdC.resize(size_symm * size_symm, nb_gauss_pts, false);
    auto t_logC_dC = getFTensor4DdgFromMat<DIM, DIM>(commonDataPtr->matLogCdC);
    auto t_eig_val = getFTensor1FromMat<DIM>(commonDataPtr->matEigVal);
    auto t_eig_vec = getFTensor2FromMat<DIM, DIM>(commonDataPtr->matEigVec);
 
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
 
      FTensor::Tensor1<double, DIM> eig;
      FTensor::Tensor2<double, DIM, DIM> eigen_vec;
      eig(i) = t_eig_val(i);
      eigen_vec(i, j) = t_eig_vec(i, j);
 
      // rare case when two eigen values are equal
      auto nb_uniq = get_uniq_nb<DIM>(&eig(0));
      auto dlogC_dC = EigenMatrix::getDiffMat(eig, eigen_vec, f, d_f, nb_uniq);
      dlogC_dC(i, j, k, l) *= 2;
 
      t_logC_dC(i, j, k, l) = dlogC_dC(i, j, k, l);
 
      ++t_logC_dC;
      ++t_eig_val;
      ++t_eig_vec;
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<CommonData> commonDataPtr;
};
 
template <int DIM> struct OpCalculateHenckyStress : public DomainEleOp {
 
  OpCalculateHenckyStress(const std::string field_name,
                          boost::shared_ptr<CommonData> common_data)
      : DomainEleOp(field_name, DomainEleOp::OPROW),
        commonDataPtr(common_data) {
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    FTensor::Index<'i', DIM> i;
    FTensor::Index<'j', DIM> j;
    FTensor::Index<'k', DIM> k;
    FTensor::Index<'l', DIM> l;
 
    constexpr auto t_kd = FTensor::Kronecker_Delta<int>();
 
    // const size_t nb_gauss_pts = matGradPtr->size2();
    const size_t nb_gauss_pts = getGaussPts().size2();
    auto t_D = getFTensor4DdgFromMat<DIM, DIM, 0>(*commonDataPtr->matDPtr);
    auto t_logC = getFTensor2SymmetricFromMat<DIM>(commonDataPtr->matLogC);
    constexpr auto size_symm = (DIM * (DIM + 1)) / 2;
    commonDataPtr->matHenckyStress.resize(size_symm, nb_gauss_pts, false);
    auto t_T = getFTensor2SymmetricFromMat<DIM>(commonDataPtr->matHenckyStress);
 
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
      t_T(i, j) = t_D(i, j, k, l) * t_logC(k, l);
      ++t_logC;
      ++t_T;
      ++t_D;
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<CommonData> commonDataPtr;
};
 
template <int DIM> struct OpCalculateHenckyPlasticStress : public DomainEleOp {
 
  OpCalculateHenckyPlasticStress(const std::string field_name,
                                 boost::shared_ptr<CommonData> common_data,
                                 boost::shared_ptr<MatrixDouble> mat_D_ptr,
                                 const double scale = 1)
      : DomainEleOp(field_name, DomainEleOp::OPROW), commonDataPtr(common_data),
        scaleStress(scale), matDPtr(mat_D_ptr) {
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
 
    matLogCPlastic = commonDataPtr->matLogCPlastic;
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    FTensor::Index<'i', DIM> i;
    FTensor::Index<'j', DIM> j;
    FTensor::Index<'k', DIM> k;
    FTensor::Index<'l', DIM> l;
 
    constexpr auto t_kd = FTensor::Kronecker_Delta<int>();
 
    // const size_t nb_gauss_pts = matGradPtr->size2();
    const size_t nb_gauss_pts = getGaussPts().size2();
    auto t_D = getFTensor4DdgFromMat<DIM, DIM, 0>(*matDPtr);
    auto t_logC = getFTensor2SymmetricFromMat<DIM>(commonDataPtr->matLogC);
    auto t_logCPlastic = getFTensor2SymmetricFromMat<DIM>(*matLogCPlastic);
    constexpr auto size_symm = (DIM * (DIM + 1)) / 2;
    commonDataPtr->matHenckyStress.resize(size_symm, nb_gauss_pts, false);
    auto t_T = getFTensor2SymmetricFromMat<DIM>(commonDataPtr->matHenckyStress);
 
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
      t_T(i, j) = t_D(i, j, k, l) * (t_logC(k, l) - t_logCPlastic(k, l));
      t_T(i, j) /= scaleStress;
      ++t_logC;
      ++t_T;
      ++t_D;
      ++t_logCPlastic;
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<CommonData> commonDataPtr;
  boost::shared_ptr<MatrixDouble> matDPtr;
  boost::shared_ptr<MatrixDouble> matLogCPlastic;
  const double scaleStress;
};
 
template <int DIM> struct OpCalculatePiolaStress : public DomainEleOp {
 
  OpCalculatePiolaStress(const std::string field_name,
                         boost::shared_ptr<CommonData> common_data)
      : DomainEleOp(field_name, DomainEleOp::OPROW),
        commonDataPtr(common_data) {
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    FTensor::Index<'i', DIM> i;
    FTensor::Index<'j', DIM> j;
    FTensor::Index<'k', DIM> k;
    FTensor::Index<'l', DIM> l;
 
    constexpr auto t_kd = FTensor::Kronecker_Delta<int>();
 
    // const size_t nb_gauss_pts = matGradPtr->size2();
    const size_t nb_gauss_pts = getGaussPts().size2();
    auto t_D = getFTensor4DdgFromMat<DIM, DIM, 0>(*commonDataPtr->matDPtr);
    auto t_logC = getFTensor2SymmetricFromMat<DIM>(commonDataPtr->matLogC);
    auto t_logC_dC = getFTensor4DdgFromMat<DIM, DIM>(commonDataPtr->matLogCdC);
    constexpr auto size_symm = (DIM * (DIM + 1)) / 2;
    commonDataPtr->matFirstPiolaStress.resize(DIM * DIM, nb_gauss_pts, false);
    commonDataPtr->matSecondPiolaStress.resize(size_symm, nb_gauss_pts, false);
    auto t_P = getFTensor2FromMat<DIM, DIM>(commonDataPtr->matFirstPiolaStress);
    auto t_T = getFTensor2SymmetricFromMat<DIM>(commonDataPtr->matHenckyStress);
    auto t_S =
        getFTensor2SymmetricFromMat<DIM>(commonDataPtr->matSecondPiolaStress);
    auto t_grad = getFTensor2FromMat<DIM, DIM>(*(commonDataPtr->matGradPtr));
 
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
      FTensor::Tensor2<double, DIM, DIM> t_F;
      t_F(i, j) = t_grad(i, j) + t_kd(i, j);
      t_S(k, l) = t_T(i, j) * t_logC_dC(i, j, k, l);
      t_P(i, l) = t_F(i, k) * t_S(k, l);
 
      ++t_grad;
      ++t_logC;
      ++t_logC_dC;
      ++t_P;
      ++t_T;
      ++t_S;
      ++t_D;
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<CommonData> commonDataPtr;
};
 
template <int DIM> struct OpHenckyTangent : public DomainEleOp {
  OpHenckyTangent(const std::string field_name,
                  boost::shared_ptr<CommonData> common_data,
                  boost::shared_ptr<MatrixDouble> mat_D_ptr = nullptr)
      : DomainEleOp(field_name, DomainEleOp::OPROW),
        commonDataPtr(common_data) {
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
    if (mat_D_ptr)
      matDPtr = mat_D_ptr;
    else
      matDPtr = commonDataPtr->matDPtr;
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    FTensor::Index<'i', DIM> i;
    FTensor::Index<'j', DIM> j;
    FTensor::Index<'k', DIM> k;
    FTensor::Index<'l', DIM> l;
    FTensor::Index<'m', DIM> m;
    FTensor::Index<'n', DIM> n;
    FTensor::Index<'o', DIM> o;
    FTensor::Index<'p', DIM> p;
 
    constexpr auto t_kd = FTensor::Kronecker_Delta<int>();
    // const size_t nb_gauss_pts = matGradPtr->size2();
    const size_t nb_gauss_pts = getGaussPts().size2();
    constexpr auto size_symm = (DIM * (DIM + 1)) / 2;
    commonDataPtr->matTangent.resize(DIM * DIM * DIM * DIM, nb_gauss_pts);
    auto dP_dF =
        getFTensor4FromMat<DIM, DIM, DIM, DIM, 1>(commonDataPtr->matTangent);
 
    auto t_D = getFTensor4DdgFromMat<DIM, DIM, 0>(*matDPtr);
    auto t_eig_val = getFTensor1FromMat<DIM>(commonDataPtr->matEigVal);
    auto t_eig_vec = getFTensor2FromMat<DIM, DIM>(commonDataPtr->matEigVec);
    auto t_T = getFTensor2SymmetricFromMat<DIM>(commonDataPtr->matHenckyStress);
    auto t_S =
        getFTensor2SymmetricFromMat<DIM>(commonDataPtr->matSecondPiolaStress);
    auto t_grad = getFTensor2FromMat<DIM, DIM>(*(commonDataPtr->matGradPtr));
    auto t_logC_dC = getFTensor4DdgFromMat<DIM, DIM>(commonDataPtr->matLogCdC);
 
    for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
 
      FTensor::Tensor2<double, DIM, DIM> t_F;
      t_F(i, j) = t_grad(i, j) + t_kd(i, j);
 
      FTensor::Tensor1<double, DIM> eig;
      FTensor::Tensor2<double, DIM, DIM> eigen_vec;
      FTensor::Tensor2_symmetric<double, DIM> T;
      eig(i) = t_eig_val(i);
      eigen_vec(i, j) = t_eig_vec(i, j);
      T(i, j) = t_T(i, j);
 
      // rare case when two eigen values are equal
      auto nb_uniq = get_uniq_nb<DIM>(&eig(0));
 
      FTensor::Tensor4<double, DIM, DIM, DIM, DIM> dC_dF;
      dC_dF(i, j, k, l) = (t_kd(i, l) * t_F(k, j)) + (t_kd(j, l) * t_F(k, i));
 
      auto TL =
          EigenMatrix::getDiffDiffMat(eig, eigen_vec, f, d_f, dd_f, T, nb_uniq);
 
      TL(i, j, k, l) *= 4;
      FTensor::Ddg<double, DIM, DIM> P_D_P_plus_TL;
      P_D_P_plus_TL(i, j, k, l) =
          TL(i, j, k, l) +
          (t_logC_dC(i, j, o, p) * t_D(o, p, m, n)) * t_logC_dC(m, n, k, l);
      P_D_P_plus_TL(i, j, k, l) *= 0.5;
      dP_dF(i, j, m, n) = t_kd(i, m) * (t_kd(k, n) * t_S(k, j));
      dP_dF(i, j, m, n) +=
          t_F(i, k) * (P_D_P_plus_TL(k, j, o, p) * dC_dF(o, p, m, n));
 
      ++dP_dF;
 
      ++t_grad;
      ++t_eig_val;
      ++t_eig_vec;
      ++t_logC_dC;
      ++t_S;
      ++t_T;
      ++t_D;
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<CommonData> commonDataPtr;
  boost::shared_ptr<MatrixDouble> matDPtr;
};
 
template <int DIM> struct OpPostProcHencky : public DomainEleOp {
  OpPostProcHencky(const std::string field_name,
                   moab::Interface &post_proc_mesh,
                   std::vector<EntityHandle> &map_gauss_pts,
                   boost::shared_ptr<CommonData> common_data_ptr);
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data);
 
private:
  moab::Interface &postProcMesh;
  std::vector<EntityHandle> &mapGaussPts;
  boost::shared_ptr<CommonData> commonDataPtr;
};
 
template <int DIM>
OpPostProcHencky<DIM>::OpPostProcHencky(
    const std::string field_name, moab::Interface &post_proc_mesh,
    std::vector<EntityHandle> &map_gauss_pts,
    boost::shared_ptr<CommonData> common_data_ptr)
    : DomainEleOp(field_name, DomainEleOp::OPROW), postProcMesh(post_proc_mesh),
      mapGaussPts(map_gauss_pts), commonDataPtr(common_data_ptr) {
  // Opetor is only executed for vertices
  std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
}
 
//! [Postprocessing]
template <int DIM>
MoFEMErrorCode OpPostProcHencky<DIM>::doWork(int side, EntityType type,
                                             EntData &data) {
  MoFEMFunctionBegin;
 
  FTensor::Index<'i', DIM> i;
  FTensor::Index<'j', DIM> j;
  FTensor::Index<'k', DIM> k;
 
  std::array<double, 9> def;
  std::fill(def.begin(), def.end(), 0);
 
  auto get_tag = [&](const std::string name, size_t size) {
    Tag th;
    CHKERR postProcMesh.tag_get_handle(name.c_str(), size, MB_TYPE_DOUBLE, th,
                                       MB_TAG_CREAT | MB_TAG_SPARSE,
                                       def.data());
    return th;
  };
 
  MatrixDouble3by3 mat(3, 3);
 
  auto set_matrix = [&](auto &t) -> MatrixDouble3by3 & {
    mat.clear();
    for (size_t r = 0; r != SPACE_DIM; ++r)
      for (size_t c = 0; c != SPACE_DIM; ++c)
        mat(r, c) = t(r, c);
    return mat;
  };
 
  auto set_tag = [&](auto th, auto gg, MatrixDouble3by3 &mat) {
    return postProcMesh.tag_set_data(th, &mapGaussPts[gg], 1,
                                     &*mat.data().begin());
  };
 
  auto th_grad = get_tag("GRAD", 9);
  auto th_stress = get_tag("STRESS", 9);
 
  auto t_piola =
      getFTensor2FromMat<DIM, DIM>(commonDataPtr->matFirstPiolaStress);
  auto t_grad = getFTensor2FromMat<DIM, DIM>(*commonDataPtr->matGradPtr);
 
  FTensor::Tensor2<double, DIM, DIM> F;
  FTensor::Tensor2_symmetric<double, DIM> cauchy_stress;
 
  for (int gg = 0; gg != commonDataPtr->matGradPtr->size2(); ++gg) {
 
    F(i, j) = t_grad(i, j) + kronecker_delta(i, j);
    double inv_t_detF;
 
    if (DIM == 2)
      determinantTensor2by2(F, inv_t_detF);
    else
      determinantTensor3by3(F, inv_t_detF);
 
    inv_t_detF = 1. / inv_t_detF;
 
    cauchy_stress(i, j) = inv_t_detF * (t_piola(i, k) ^ F(j, k));
 
    CHKERR set_tag(th_grad, gg, set_matrix(t_grad));
    CHKERR set_tag(th_stress, gg, set_matrix(cauchy_stress));
 
    ++t_piola;
    ++t_grad;
  }
 
  MoFEMFunctionReturn(0);
}
 
} // namespace HenckyOps