plastic.cpp

Plasticity in 2d and 3d

/**
 * \file plastic.cpp
 * \example plastic.cpp
 *
 * Plasticity in 2d and 3d
 *
 */
 
#ifndef EXECUTABLE_DIMENSION
#define EXECUTABLE_DIMENSION 3
#endif
 
#include <MoFEM.hpp>
#include <MatrixFunction.hpp>
#include <IntegrationRules.hpp>
 
using namespace MoFEM;
 
template <int DIM> struct ElementsAndOps {};
 
template <> struct ElementsAndOps<2> {
  using DomainEle = PipelineManager::FaceEle;
  using BoundaryEle = PipelineManager::EdgeEle;
};
 
template <> struct ElementsAndOps<3> {
  using DomainEle = PipelineManager::VolEle;
  using BoundaryEle = PipelineManager::FaceEle;
};
 
constexpr int SPACE_DIM =
    EXECUTABLE_DIMENSION; //< Space dimension of problem, mesh
 
constexpr EntityType boundary_ent = SPACE_DIM == 3 ? MBTRI : MBEDGE;
using EntData = EntitiesFieldData::EntData;
using DomainEle = ElementsAndOps<SPACE_DIM>::DomainEle;
using DomainEleOp = DomainEle::UserDataOperator;
using BoundaryEle = ElementsAndOps<SPACE_DIM>::BoundaryEle;
using BoundaryEleOp = BoundaryEle::UserDataOperator;
using PostProcEle = PostProcBrokenMeshInMoab<DomainEle>;
 
using AssemblyDomainEleOp =
    FormsIntegrators<DomainEleOp>::Assembly<PETSC>::OpBase;
 
//! [Only used with Hooke equation (linear material model)]
using OpKCauchy = FormsIntegrators<DomainEleOp>::Assembly<PETSC>::BiLinearForm<
    GAUSS>::OpGradSymTensorGrad<1, SPACE_DIM, SPACE_DIM, 0>;
using OpInternalForceCauchy = FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpGradTimesSymTensor<1, SPACE_DIM, SPACE_DIM>;
//! [Only used with Hooke equation (linear material model)]
 
//! [Only used for dynamics]
using OpMass = FormsIntegrators<DomainEleOp>::Assembly<PETSC>::BiLinearForm<
    GAUSS>::OpMass<1, SPACE_DIM>;
using OpInertiaForce = FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpBaseTimesVector<1, SPACE_DIM, 1>;
//! [Only used for dynamics]
 
//! [Only used with Hencky/nonlinear material]
using OpKPiola = FormsIntegrators<DomainEleOp>::Assembly<PETSC>::BiLinearForm<
    GAUSS>::OpGradTensorGrad<1, SPACE_DIM, SPACE_DIM, 1>;
using OpInternalForcePiola = FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpGradTimesTensor<1, SPACE_DIM, SPACE_DIM>;
//! [Only used with Hencky/nonlinear material]
 
//! [Essential boundary conditions]
using OpBoundaryMass = FormsIntegrators<BoundaryEleOp>::Assembly<
    PETSC>::BiLinearForm<GAUSS>::OpMass<1, SPACE_DIM>;
using OpBoundaryVec = FormsIntegrators<BoundaryEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpBaseTimesVector<1, SPACE_DIM, 0>;
using OpBoundaryInternal = FormsIntegrators<BoundaryEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpBaseTimesVector<1, SPACE_DIM, 1>;
//! [Essential boundary conditions]
using OpScaleL2 = MoFEM::OpScaleBaseBySpaceInverseOfMeasure<DomainEleOp>;
 
using DomainNaturalBC =
    NaturalBC<DomainEleOp>::Assembly<PETSC>::LinearForm<GAUSS>;
using OpBodyForce =
    DomainNaturalBC::OpFlux<NaturalMeshsetType<BLOCKSET>, 1, SPACE_DIM>;
 
using BoundaryNaturalBC =
    NaturalBC<BoundaryEleOp>::Assembly<PETSC>::LinearForm<GAUSS>;
using OpForce =
    BoundaryNaturalBC::OpFlux<NaturalMeshsetType<BLOCKSET>, 1, SPACE_DIM>;
 
using OpEssentialLhs =
    EssentialBC<BoundaryEleOp>::Assembly<PETSC>::BiLinearForm<
        GAUSS>::OpEssentialLhs<DisplacementCubitBcData, 1, SPACE_DIM>;
using OpEssentialRhs = EssentialBC<BoundaryEleOp>::Assembly<PETSC>::LinearForm<
    GAUSS>::OpEssentialRhs<DisplacementCubitBcData, 1, SPACE_DIM>;
 
PetscBool is_large_strains = PETSC_TRUE;
 
double scale = 1.;
 
double young_modulus = 206913;
double poisson_ratio = 0.29;
double rho = 0;
double sigmaY = 450;
double H = 129;
double visH = 0;
double cn = 1;
double Qinf = 265;
double b_iso = 16.93;
int order = 2;
 
inline long double hardening(long double tau) {
  return H * tau + Qinf * (1. - std::exp(-b_iso * tau)) + sigmaY;
}
 
inline long double hardening_dtau(long double tau) {
  return H + Qinf * b_iso * std::exp(-b_iso * tau);
}
 
#include <HenckyOps.hpp>
#include <PlasticOps.hpp>
 
using namespace PlasticOps;
using namespace HenckyOps;
struct Example {
 
  Example(MoFEM::Interface &m_field) : mField(m_field) {}
 
  MoFEMErrorCode runProblem();
 
private:
  MoFEM::Interface &mField;
 
  MoFEMErrorCode setupProblem();
  MoFEMErrorCode createCommonData();
  MoFEMErrorCode bC();
  MoFEMErrorCode OPs();
  MoFEMErrorCode tsSolve();
 
  boost::shared_ptr<PlasticOps::CommonData> commonPlasticDataPtr;
  boost::shared_ptr<HenckyOps::CommonData> commonHenckyDataPtr;
  boost::shared_ptr<PostProcEle> postProcFe;
  boost::shared_ptr<DomainEle> reactionFe;
  boost::shared_ptr<DomainEle> feAxiatorRhs;
  boost::shared_ptr<DomainEle> feAxiatorLhs;
 
  std::tuple<SmartPetscObj<Vec>, SmartPetscObj<VecScatter>> uXScatter;
  std::tuple<SmartPetscObj<Vec>, SmartPetscObj<VecScatter>> uYScatter;
  std::tuple<SmartPetscObj<Vec>, SmartPetscObj<VecScatter>> uZScatter;
 
  boost::shared_ptr<std::vector<unsigned char>> boundaryMarker;
  boost::shared_ptr<std::vector<unsigned char>> reactionMarker;
 
  std::vector<FTensor::Tensor1<double, 3>> bodyForces;
};
 
//! [Run problem]
MoFEMErrorCode Example::runProblem() {
  MoFEMFunctionBegin;
  CHKERR setupProblem();
  CHKERR createCommonData();
  CHKERR bC();
  CHKERR OPs();
  CHKERR tsSolve();
  MoFEMFunctionReturn(0);
}
//! [Run problem]
 
//! [Set up problem]
MoFEMErrorCode Example::setupProblem() {
  MoFEMFunctionBegin;
  Simple *simple = mField.getInterface<Simple>();
  // Add field
  constexpr FieldApproximationBase base = AINSWORTH_LEGENDRE_BASE;
  constexpr auto size_symm = (SPACE_DIM * (SPACE_DIM + 1)) / 2;
  CHKERR simple->addDomainField("U", H1, base, SPACE_DIM);
  CHKERR simple->addDomainField("TAU", L2, base, 1);
  CHKERR simple->addDomainField("EP", L2, base, size_symm);
  CHKERR simple->addBoundaryField("U", H1, base, SPACE_DIM);
  CHKERR PetscOptionsGetInt(PETSC_NULL, "", "-order", &order, PETSC_NULL);
  CHKERR simple->setFieldOrder("U", order);
  CHKERR simple->setFieldOrder("TAU", order - 1);
  CHKERR simple->setFieldOrder("EP", order - 1);
  CHKERR simple->setUp();
  CHKERR simple->addFieldToEmptyFieldBlocks("U", "TAU");
  MoFEMFunctionReturn(0);
}
//! [Set up problem]
 
//! [Create common data]
MoFEMErrorCode Example::createCommonData() {
  MoFEMFunctionBegin;
 
  auto get_command_line_parameters = [&]() {
    MoFEMFunctionBegin;
    CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-scale", &scale, PETSC_NULL);
    CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-rho", &rho, PETSC_NULL);
    CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-young_modulus",
                                 &young_modulus, PETSC_NULL);
    CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-poisson_ratio",
                                 &poisson_ratio, PETSC_NULL);
    CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-hardening", &H, PETSC_NULL);
    CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-hardening_viscous", &visH,
                                 PETSC_NULL);
    CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-yield_stress", &sigmaY,
                                 PETSC_NULL);
    CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-cn", &cn, PETSC_NULL);
    CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-Qinf", &Qinf, PETSC_NULL);
    CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-b_iso", &b_iso, PETSC_NULL);
    CHKERR PetscOptionsGetBool(PETSC_NULL, "", "-large_strains",
                               &is_large_strains, PETSC_NULL);
 
    MOFEM_LOG("EXAMPLE", Sev::inform) << "Young modulus " << young_modulus;
    MOFEM_LOG("EXAMPLE", Sev::inform) << "Poisson ratio " << poisson_ratio;
    MOFEM_LOG("EXAMPLE", Sev::inform) << "Yield stress " << sigmaY;
    MOFEM_LOG("EXAMPLE", Sev::inform) << "Hardening " << H;
    MOFEM_LOG("EXAMPLE", Sev::inform) << "Viscous hardening " << visH;
    MOFEM_LOG("EXAMPLE", Sev::inform) << "Saturation yield stress " << Qinf;
    MOFEM_LOG("EXAMPLE", Sev::inform) << "Saturation exponent " << b_iso;
    MOFEM_LOG("EXAMPLE", Sev::inform) << "cn " << cn;
 
    PetscBool is_scale = PETSC_TRUE;
    CHKERR PetscOptionsGetBool(PETSC_NULL, "", "-is_scale", &is_scale,
                               PETSC_NULL);
    if (is_scale) {
      scale = scale / young_modulus;
      young_modulus *= scale;
      rho *= scale;
      sigmaY *= scale;
      H *= scale;
      Qinf *= scale;
      visH *= scale;
 
      MOFEM_LOG("EXAMPLE", Sev::inform)
          << "Scaled Young modulus " << young_modulus;
      MOFEM_LOG("EXAMPLE", Sev::inform)
          << "Scaled Poisson ratio " << poisson_ratio;
      MOFEM_LOG("EXAMPLE", Sev::inform) << "Scaled Yield stress " << sigmaY;
      MOFEM_LOG("EXAMPLE", Sev::inform) << "Scaled Hardening " << H;
      MOFEM_LOG("EXAMPLE", Sev::inform) << "Scaled Viscous hardening " << visH;
      MOFEM_LOG("EXAMPLE", Sev::inform)
          << "Scaled Saturation yield stress " << Qinf;
    }
 
    MoFEMFunctionReturn(0);
  };
 
  auto set_matrial_stiffness = [&]() {
    MoFEMFunctionBegin;
    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>();
    const double bulk_modulus_K = young_modulus / (3 * (1 - 2 * poisson_ratio));
    const double shear_modulus_G = young_modulus / (2 * (1 + poisson_ratio));
 
    // Plane stress or when 1, plane strain or 3d
    const 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>(
        *commonPlasticDataPtr->mDPtr);
    auto t_D_axiator = getFTensor4DdgFromMat<SPACE_DIM, SPACE_DIM, 0>(
        *commonPlasticDataPtr->mDPtr_Axiator);
    auto t_D_deviator = getFTensor4DdgFromMat<SPACE_DIM, SPACE_DIM, 0>(
        *commonPlasticDataPtr->mDPtr_Deviator);
 
    constexpr double third = boost::math::constants::third<double>();
    t_D_axiator(i, j, k, l) = A *
                              (bulk_modulus_K - (2. / 3.) * shear_modulus_G) *
                              t_kd(i, j) * t_kd(k, l);
    t_D_deviator(i, j, k, l) =
        2 * shear_modulus_G * ((t_kd(i, k) ^ t_kd(j, l)) / 4.);
    t_D(i, j, k, l) = t_D_axiator(i, j, k, l) + t_D_deviator(i, j, k, l);
 
    MoFEMFunctionReturn(0);
  };
 
  commonPlasticDataPtr = boost::make_shared<PlasticOps::CommonData>();
  constexpr auto size_symm = (SPACE_DIM * (SPACE_DIM + 1)) / 2;
  commonPlasticDataPtr->mDPtr = boost::make_shared<MatrixDouble>();
  commonPlasticDataPtr->mDPtr->resize(size_symm * size_symm, 1);
  commonPlasticDataPtr->mDPtr_Axiator = boost::make_shared<MatrixDouble>();
  commonPlasticDataPtr->mDPtr_Axiator->resize(size_symm * size_symm, 1);
  commonPlasticDataPtr->mDPtr_Deviator = boost::make_shared<MatrixDouble>();
  commonPlasticDataPtr->mDPtr_Deviator->resize(size_symm * size_symm, 1);
 
  commonPlasticDataPtr->mGradPtr = boost::make_shared<MatrixDouble>();
  commonPlasticDataPtr->mStrainPtr = boost::make_shared<MatrixDouble>();
  commonPlasticDataPtr->mStressPtr = boost::make_shared<MatrixDouble>();
 
  CHKERR get_command_line_parameters();
  CHKERR set_matrial_stiffness();
 
  if (is_large_strains) {
    commonHenckyDataPtr = boost::make_shared<HenckyOps::CommonData>();
    commonHenckyDataPtr->matGradPtr = commonPlasticDataPtr->mGradPtr;
    commonHenckyDataPtr->matDPtr = commonPlasticDataPtr->mDPtr;
    commonHenckyDataPtr->matLogCPlastic =
        commonPlasticDataPtr->getPlasticStrainPtr();
    commonPlasticDataPtr->mStrainPtr = commonHenckyDataPtr->getMatLogC();
    commonPlasticDataPtr->mStressPtr =
        commonHenckyDataPtr->getMatHenckyStress();
  }
 
  MoFEMFunctionReturn(0);
}
//! [Create common data]
 
//! [Boundary condition]
MoFEMErrorCode Example::bC() {
  MoFEMFunctionBegin;
 
  auto simple = mField.getInterface<Simple>();
  auto bc_mng = mField.getInterface<BcManager>();
  auto prb_mng = mField.getInterface<ProblemsManager>();
 
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(), "REMOVE_X",
                                           "U", 0, 0);
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(), "REMOVE_Y",
                                           "U", 1, 1);
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(), "REMOVE_Z",
                                           "U", 2, 2);
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(),
                                           "REMOVE_ALL", "U", 0, 3);
 
  CHKERR bc_mng->pushMarkDOFsOnEntities<DisplacementCubitBcData>(
      simple->getProblemName(), "U");
 
  auto &bc_map = bc_mng->getBcMapByBlockName();
  boundaryMarker = bc_mng->getMergedBlocksMarker(vector<string>{"FIX_"});
 
  CHKERR bc_mng->pushMarkDOFsOnEntities(simple->getProblemName(), "REACTION",
                                        "U", 0, 3);
 
  for (auto bc : bc_map)
    MOFEM_LOG("EXAMPLE", Sev::verbose) << "Marker " << bc.first;
 
  // OK. We have problem with GMesh, it adding empty characters at the end of
  // block. So first block is search by regexp. popMarkDOFsOnEntities should
  // work with regexp.
  std::string reaction_block_set;
  for (auto bc : bc_map) {
    if (bc_mng->checkBlock(bc, "REACTION")) {
      reaction_block_set = bc.first;
      break;
    }
  }
 
  if (auto bc = bc_mng->popMarkDOFsOnEntities(reaction_block_set)) {
    reactionMarker = bc->getBcMarkersPtr();
 
    // Only take reaction from nodes
    Range nodes;
    CHKERR mField.get_moab().get_entities_by_type(0, MBVERTEX, nodes, true);
    CHKERR prb_mng->markDofs(simple->getProblemName(), ROW,
                             ProblemsManager::MarkOP::AND, nodes,
                             *reactionMarker);
 
  } else {
    MOFEM_LOG("EXAMPLE", Sev::warning) << "REACTION blockset does not exist";
  }
 
  if (!reactionMarker) {
    MOFEM_LOG("EXAMPLE", Sev::warning) << "REACTION blockset does not exist";
  }
 
  MoFEMFunctionReturn(0);
}
//! [Boundary condition]
 
//! [Push operators to pipeline]
MoFEMErrorCode Example::OPs() {
  MoFEMFunctionBegin;
  auto pipeline_mng = mField.getInterface<PipelineManager>();
  auto simple = mField.getInterface<Simple>();
  auto bc_mng = mField.getInterface<BcManager>();
 
  feAxiatorLhs = boost::make_shared<DomainEle>(mField);
  feAxiatorRhs = boost::make_shared<DomainEle>(mField);
  auto integration_rule_axiator = [](int, int, int approx_order) {
    return 2 * (approx_order - 1);
  };
  feAxiatorLhs->getRuleHook = integration_rule_axiator;
  feAxiatorRhs->getRuleHook = integration_rule_axiator;
 
  auto integration_rule_deviator = [](int o_row, int o_col, int approx_order) {
    return 2 * (approx_order - 1);
  };
  auto integration_rule_bc = [](int, int, int approx_order) {
    return 2 * approx_order;
  };
 
  auto add_domain_base_ops = [&](auto &pipeline) {
    MoFEMFunctionBegin;
 
    auto det_ptr = boost::make_shared<VectorDouble>();
    auto jac_ptr = boost::make_shared<MatrixDouble>();
    auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
    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));
    if (SPACE_DIM == 2)
      pipeline.push_back(new OpSetHOWeightsOnFace());
    else
      pipeline.push_back(new OpSetHOWeights(det_ptr));
 
    pipeline.push_back(new OpCalculateScalarFieldValuesDot(
        "TAU", commonPlasticDataPtr->getPlasticTauDotPtr()));
    pipeline.push_back(new OpCalculateTensor2SymmetricFieldValues<SPACE_DIM>(
        "EP", commonPlasticDataPtr->getPlasticStrainPtr()));
    pipeline.push_back(new OpCalculateTensor2SymmetricFieldValuesDot<SPACE_DIM>(
        "EP", commonPlasticDataPtr->getPlasticStrainDotPtr()));
    pipeline.push_back(new OpCalculateVectorFieldGradient<SPACE_DIM, SPACE_DIM>(
        "U", commonPlasticDataPtr->mGradPtr));
    pipeline.push_back(new OpCalculateScalarFieldValues(
        "TAU", commonPlasticDataPtr->getPlasticTauPtr()));
 
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_stress_ops = [&](auto &pipeline, auto m_D_ptr) {
    MoFEMFunctionBegin;
 
    if (is_large_strains) {
 
      if (commonPlasticDataPtr->mGradPtr != commonHenckyDataPtr->matGradPtr)
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                "Wrong pointer for grad");
 
      pipeline.push_back(
          new OpCalculateEigenVals<SPACE_DIM>("U", commonHenckyDataPtr));
      pipeline.push_back(
          new OpCalculateLogC<SPACE_DIM>("U", commonHenckyDataPtr));
      pipeline.push_back(
          new OpCalculateLogC_dC<SPACE_DIM>("U", commonHenckyDataPtr));
      pipeline.push_back(new OpCalculateHenckyPlasticStress<SPACE_DIM>(
          "U", commonHenckyDataPtr, m_D_ptr));
      pipeline.push_back(
          new OpCalculatePiolaStress<SPACE_DIM>("U", commonHenckyDataPtr));
 
    } else {
      pipeline.push_back(
          new OpSymmetrizeTensor<SPACE_DIM>("U", commonPlasticDataPtr->mGradPtr,
                                            commonPlasticDataPtr->mStrainPtr));
      pipeline.push_back(
          new OpPlasticStress("U", commonPlasticDataPtr, m_D_ptr, 1));
    }
 
    if (m_D_ptr != commonPlasticDataPtr->mDPtr_Axiator)
      pipeline.push_back(
          new OpCalculatePlasticSurface("U", commonPlasticDataPtr));
 
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_ops_lhs_mechanical = [&](auto &pipeline, auto m_D_ptr) {
    MoFEMFunctionBegin;
    pipeline.push_back(new OpSetBc("U", true, boundaryMarker));
 
    if (is_large_strains) {
      pipeline.push_back(
          new OpHenckyTangent<SPACE_DIM>("U", commonHenckyDataPtr, m_D_ptr));
      pipeline.push_back(
          new OpKPiola("U", "U", commonHenckyDataPtr->getMatTangent()));
      pipeline.push_back(new OpCalculatePlasticInternalForceLhs_LogStrain_dEP(
          "U", "EP", commonPlasticDataPtr, commonHenckyDataPtr, m_D_ptr));
    } else {
      pipeline.push_back(new OpKCauchy("U", "U", m_D_ptr));
      pipeline.push_back(new OpCalculatePlasticInternalForceLhs_dEP(
          "U", "EP", commonPlasticDataPtr, m_D_ptr));
    }
 
    pipeline.push_back(new OpUnSetBc("U"));
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_ops_rhs_mechanical = [&](auto &pipeline) {
    MoFEMFunctionBegin;
    pipeline.push_back(new OpSetBc("U", true, boundaryMarker));
 
    CHKERR DomainNaturalBC::AddFluxToPipeline<OpBodyForce>::add(
        pipeline, mField, "U", {boost::make_shared<TimeScale>()}, "BODY_FORCE",
        Sev::inform);
 
    // Calculate internal forces
    if (is_large_strains) {
      pipeline.push_back(new OpInternalForcePiola(
          "U", commonHenckyDataPtr->getMatFirstPiolaStress()));
    } else {
      pipeline.push_back(
          new OpInternalForceCauchy("U", commonPlasticDataPtr->mStressPtr));
    }
 
    pipeline.push_back(new OpUnSetBc("U"));
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_ops_lhs_constrain = [&](auto &pipeline, auto m_D_ptr) {
    MoFEMFunctionBegin;
    pipeline.push_back(new OpSetBc("U", true, boundaryMarker));
 
    if (is_large_strains) {
      pipeline.push_back(
          new OpHenckyTangent<SPACE_DIM>("U", commonHenckyDataPtr));
      pipeline.push_back(new OpCalculateContrainsLhs_LogStrain_dU(
          "TAU", "U", commonPlasticDataPtr, commonHenckyDataPtr, m_D_ptr));
      pipeline.push_back(new OpCalculatePlasticFlowLhs_LogStrain_dU(
          "EP", "U", commonPlasticDataPtr, commonHenckyDataPtr, m_D_ptr));
    } else {
      pipeline.push_back(new OpCalculatePlasticFlowLhs_dU(
          "EP", "U", commonPlasticDataPtr, m_D_ptr));
      pipeline.push_back(new OpCalculateContrainsLhs_dU(
          "TAU", "U", commonPlasticDataPtr, m_D_ptr));
    }
 
    pipeline.push_back(new OpCalculatePlasticFlowLhs_dEP(
        "EP", "EP", commonPlasticDataPtr, m_D_ptr));
    pipeline.push_back(
        new OpCalculatePlasticFlowLhs_dTAU("EP", "TAU", commonPlasticDataPtr));
    pipeline.push_back(new OpCalculateContrainsLhs_dEP(
        "TAU", "EP", commonPlasticDataPtr, m_D_ptr));
    pipeline.push_back(
        new OpCalculateContrainsLhs_dTAU("TAU", "TAU", commonPlasticDataPtr));
 
    pipeline.push_back(new OpUnSetBc("U"));
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_ops_rhs_constrain = [&](auto &pipeline) {
    MoFEMFunctionBegin;
    pipeline.push_back(new OpSetBc("U", true, boundaryMarker));
 
    pipeline.push_back(
        new OpCalculatePlasticFlowRhs("EP", commonPlasticDataPtr));
    pipeline.push_back(
        new OpCalculateContrainsRhs("TAU", commonPlasticDataPtr));
 
    pipeline.push_back(new OpUnSetBc("U"));
    MoFEMFunctionReturn(0);
  };
 
  auto add_boundary_ops_lhs_mechanical = [&](auto &pipeline) {
    MoFEMFunctionBegin;
    CHKERR EssentialBC<BoundaryEleOp>::Assembly<PETSC>::BiLinearForm<GAUSS>::
        AddEssentialToPipeline<OpEssentialLhs>::add(
            mField, pipeline, simple->getProblemName(), "U");
    MoFEMFunctionReturn(0);
  };
 
  auto add_boundary_ops_rhs_mechanical = [&](auto &pipeline) {
    MoFEMFunctionBegin;
 
    pipeline.push_back(new OpSetBc("U", true, boundaryMarker));
    CHKERR BoundaryNaturalBC::AddFluxToPipeline<OpForce>::add(
        pipeline, mField, "U", {boost::make_shared<TimeScale>()}, "FORCE",
        Sev::inform);
 
    pipeline.push_back(new OpUnSetBc("U"));
 
    auto u_mat_ptr = boost::make_shared<MatrixDouble>();
    pipeline.push_back(
        new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_mat_ptr));
 
    CHKERR EssentialBC<BoundaryEleOp>::Assembly<PETSC>::LinearForm<GAUSS>::
        AddEssentialToPipeline<OpEssentialRhs>::add(
            mField, pipeline, simple->getProblemName(), "U", u_mat_ptr,
            {boost::make_shared<TimeScale>()});
 
    MoFEMFunctionReturn(0);
  };
 
  // Axiator
  CHKERR add_domain_base_ops(pipeline_mng->getOpDomainLhsPipeline());
  CHKERR add_domain_stress_ops(pipeline_mng->getOpDomainLhsPipeline(),
                               commonPlasticDataPtr->mDPtr_Deviator);
  CHKERR add_domain_ops_lhs_mechanical(pipeline_mng->getOpDomainLhsPipeline(),
                                       commonPlasticDataPtr->mDPtr_Deviator);
  CHKERR add_domain_ops_lhs_constrain(pipeline_mng->getOpDomainLhsPipeline(),
                                      commonPlasticDataPtr->mDPtr_Deviator);
  CHKERR add_boundary_ops_lhs_mechanical(
      pipeline_mng->getOpBoundaryLhsPipeline());
 
  CHKERR add_domain_base_ops(feAxiatorLhs->getOpPtrVector());
  CHKERR add_domain_stress_ops(feAxiatorLhs->getOpPtrVector(),
                               commonPlasticDataPtr->mDPtr_Axiator);
  CHKERR add_domain_ops_lhs_mechanical(feAxiatorLhs->getOpPtrVector(),
                                       commonPlasticDataPtr->mDPtr_Axiator);
 
  CHKERR add_domain_base_ops(pipeline_mng->getOpDomainRhsPipeline());
  CHKERR add_domain_stress_ops(pipeline_mng->getOpDomainRhsPipeline(),
                               commonPlasticDataPtr->mDPtr_Deviator);
  CHKERR add_domain_ops_rhs_mechanical(pipeline_mng->getOpDomainRhsPipeline());
  CHKERR add_domain_ops_rhs_constrain(pipeline_mng->getOpDomainRhsPipeline());
  CHKERR add_boundary_ops_rhs_mechanical(
      pipeline_mng->getOpBoundaryRhsPipeline());
 
  CHKERR add_domain_base_ops(feAxiatorRhs->getOpPtrVector());
  CHKERR add_domain_stress_ops(feAxiatorRhs->getOpPtrVector(),
                               commonPlasticDataPtr->mDPtr_Axiator);
  CHKERR add_domain_ops_rhs_mechanical(feAxiatorRhs->getOpPtrVector());
 
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(integration_rule_deviator);
  CHKERR pipeline_mng->setDomainLhsIntegrationRule(integration_rule_deviator);
 
  CHKERR pipeline_mng->setBoundaryLhsIntegrationRule(integration_rule_bc);
  CHKERR pipeline_mng->setBoundaryRhsIntegrationRule(integration_rule_bc);
 
  auto create_reaction_pipeline = [&](auto &pipeline) {
    MoFEMFunctionBegin;
 
    if (reactionMarker) {
 
      auto det_ptr = boost::make_shared<VectorDouble>();
      auto jac_ptr = boost::make_shared<MatrixDouble>();
      auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
      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));
      if (SPACE_DIM == 2)
        pipeline.push_back(new OpSetHOWeightsOnFace());
      else
        pipeline.push_back(new OpSetHOWeights(det_ptr));
 
      pipeline.push_back(
          new OpCalculateVectorFieldGradient<SPACE_DIM, SPACE_DIM>(
              "U", commonPlasticDataPtr->mGradPtr));
      pipeline.push_back(new OpCalculateTensor2SymmetricFieldValues<SPACE_DIM>(
          "EP", commonPlasticDataPtr->getPlasticStrainPtr()));
 
      if (is_large_strains) {
 
        if (commonPlasticDataPtr->mGradPtr != commonHenckyDataPtr->matGradPtr)
          SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                  "Wrong pointer for grad");
 
        pipeline.push_back(
            new OpCalculateEigenVals<SPACE_DIM>("U", commonHenckyDataPtr));
        pipeline.push_back(
            new OpCalculateLogC<SPACE_DIM>("U", commonHenckyDataPtr));
        pipeline.push_back(
            new OpCalculateLogC_dC<SPACE_DIM>("U", commonHenckyDataPtr));
        pipeline.push_back(new OpCalculateHenckyPlasticStress<SPACE_DIM>(
            "U", commonHenckyDataPtr, commonPlasticDataPtr->mDPtr));
        pipeline.push_back(
            new OpCalculatePiolaStress<SPACE_DIM>("U", commonHenckyDataPtr));
 
      } else {
        pipeline.push_back(new OpSymmetrizeTensor<SPACE_DIM>(
            "U", commonPlasticDataPtr->mGradPtr,
            commonPlasticDataPtr->mStrainPtr));
        pipeline.push_back(new OpPlasticStress(
            "U", commonPlasticDataPtr, commonPlasticDataPtr->mDPtr, scale));
      }
 
      pipeline.push_back(new OpSetBc("U", false, reactionMarker));
      // Calculate internal forece
      if (is_large_strains) {
        pipeline.push_back(new OpInternalForcePiola(
            "U", commonHenckyDataPtr->getMatFirstPiolaStress()));
      } else {
        pipeline.push_back(
            new OpInternalForceCauchy("U", commonPlasticDataPtr->mStressPtr));
      }
      pipeline.push_back(new OpUnSetBc("U"));
    }
 
    MoFEMFunctionReturn(0);
  };
 
  reactionFe = boost::make_shared<DomainEle>(mField);
  reactionFe->getRuleHook = integration_rule_deviator;
 
  CHKERR create_reaction_pipeline(reactionFe->getOpPtrVector());
 
  MoFEMFunctionReturn(0);
}
//! [Push operators to pipeline]
 
//! [Solve]
MoFEMErrorCode Example::tsSolve() {
  MoFEMFunctionBegin;
 
  Simple *simple = mField.getInterface<Simple>();
  PipelineManager *pipeline_mng = mField.getInterface<PipelineManager>();
  ISManager *is_manager = mField.getInterface<ISManager>();
 
  auto snes_ctx_ptr = smartGetDMSnesCtx(simple->getDM());
 
  auto set_section_monitor = [&](auto solver) {
    MoFEMFunctionBegin;
    SNES snes;
    CHKERR TSGetSNES(solver, &snes);
    CHKERR SNESMonitorSet(snes,
                          (MoFEMErrorCode(*)(SNES, PetscInt, PetscReal,
                                             void *))MoFEMSNESMonitorFields,
                          (void *)(snes_ctx_ptr.get()), nullptr);
    MoFEMFunctionReturn(0);
  };
 
  auto create_post_process_element = [&]() {
    MoFEMFunctionBegin;
    postProcFe = boost::make_shared<PostProcEle>(mField);
    using OpPPMap = OpPostProcMapInMoab<SPACE_DIM, SPACE_DIM>;
 
    auto u_ptr = boost::make_shared<MatrixDouble>();
 
    auto det_ptr = boost::make_shared<VectorDouble>();
    auto jac_ptr = boost::make_shared<MatrixDouble>();
    auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
    postProcFe->getOpPtrVector().push_back(
        new OpCalculateHOJac<SPACE_DIM>(jac_ptr));
    postProcFe->getOpPtrVector().push_back(
        new OpInvertMatrix<SPACE_DIM>(jac_ptr, det_ptr, inv_jac_ptr));
    postProcFe->getOpPtrVector().push_back(
        new OpSetHOInvJacToScalarBases<SPACE_DIM>(H1, inv_jac_ptr));
 
    postProcFe->getOpPtrVector().push_back(
        new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_ptr));
 
    postProcFe->getOpPtrVector().push_back(
        new OpCalculateVectorFieldGradient<SPACE_DIM, SPACE_DIM>(
            "U", commonPlasticDataPtr->mGradPtr));
    postProcFe->getOpPtrVector().push_back(new OpCalculateScalarFieldValues(
        "TAU", commonPlasticDataPtr->getPlasticTauPtr()));
    postProcFe->getOpPtrVector().push_back(
        new OpCalculateTensor2SymmetricFieldValues<SPACE_DIM>(
            "EP", commonPlasticDataPtr->getPlasticStrainPtr()));
 
    if (is_large_strains) {
 
      if (commonPlasticDataPtr->mGradPtr != commonHenckyDataPtr->matGradPtr)
        SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                "Wrong pointer for grad");
 
      postProcFe->getOpPtrVector().push_back(
          new OpCalculateEigenVals<SPACE_DIM>("U", commonHenckyDataPtr));
      postProcFe->getOpPtrVector().push_back(
          new OpCalculateLogC<SPACE_DIM>("U", commonHenckyDataPtr));
      postProcFe->getOpPtrVector().push_back(
          new OpCalculateLogC_dC<SPACE_DIM>("U", commonHenckyDataPtr));
      postProcFe->getOpPtrVector().push_back(
          new OpCalculateHenckyPlasticStress<SPACE_DIM>(
              "U", commonHenckyDataPtr, commonPlasticDataPtr->mDPtr, scale));
      postProcFe->getOpPtrVector().push_back(
          new OpCalculatePiolaStress<SPACE_DIM>("U", commonHenckyDataPtr));
 
      postProcFe->getOpPtrVector().push_back(
 
          new OpPPMap(
 
              postProcFe->getPostProcMesh(), postProcFe->getMapGaussPts(),
 
              {},
 
              {{"U", u_ptr}},
 
              {{"GRAD", commonPlasticDataPtr->mGradPtr},
               {"FIRST_PIOLA", commonHenckyDataPtr->getMatFirstPiolaStress()}},
 
              {}
 
              )
 
      );
 
    } else {
      postProcFe->getOpPtrVector().push_back(
          new OpSymmetrizeTensor<SPACE_DIM>("U", commonPlasticDataPtr->mGradPtr,
                                            commonPlasticDataPtr->mStrainPtr));
      postProcFe->getOpPtrVector().push_back(new OpPlasticStress(
          "U", commonPlasticDataPtr, commonPlasticDataPtr->mDPtr, scale));
 
      postProcFe->getOpPtrVector().push_back(
 
          new OpPPMap(
 
              postProcFe->getPostProcMesh(), postProcFe->getMapGaussPts(),
 
              {},
 
              {{"U", u_ptr}},
 
              {},
 
              {{"STRAIN", commonPlasticDataPtr->mStrainPtr},
               {"STRESS", commonPlasticDataPtr->mStressPtr}}
 
              )
 
      );
    }
 
    postProcFe->getOpPtrVector().push_back(
        new OpCalculatePlasticSurface("U", commonPlasticDataPtr));
 
    postProcFe->getOpPtrVector().push_back(
 
        new OpPPMap(
 
            postProcFe->getPostProcMesh(), postProcFe->getMapGaussPts(),
 
            {{"PLASTIC_SURFACE", commonPlasticDataPtr->getPlasticSurfacePtr()},
             {"PLASTIC_MULTIPLIER", commonPlasticDataPtr->getPlasticTauPtr()}},
 
            {},
 
            {},
 
            {{"PLASTIC_STRAIN", commonPlasticDataPtr->getPlasticStrainPtr()}}
 
            )
 
    );
 
    MoFEMFunctionReturn(0);
  };
 
  auto scatter_create = [&](auto D, auto coeff) {
    SmartPetscObj<IS> is;
    CHKERR is_manager->isCreateProblemFieldAndRank(simple->getProblemName(),
                                                   ROW, "U", coeff, coeff, is);
    int loc_size;
    CHKERR ISGetLocalSize(is, &loc_size);
    Vec v;
    CHKERR VecCreateMPI(mField.get_comm(), loc_size, PETSC_DETERMINE, &v);
    VecScatter scatter;
    CHKERR VecScatterCreate(D, is, v, PETSC_NULL, &scatter);
    return std::make_tuple(SmartPetscObj<Vec>(v),
                           SmartPetscObj<VecScatter>(scatter));
  };
 
  auto set_time_monitor = [&](auto dm, auto solver) {
    MoFEMFunctionBegin;
    boost::shared_ptr<Monitor> monitor_ptr(new Monitor(
        dm, postProcFe, reactionFe, uXScatter, uYScatter, uZScatter));
    boost::shared_ptr<ForcesAndSourcesCore> null;
    CHKERR DMMoFEMTSSetMonitor(dm, solver, simple->getDomainFEName(),
                               monitor_ptr, null, null);
    MoFEMFunctionReturn(0);
  };
 
  auto set_fieldsplit_preconditioner = [&](auto solver) {
    MoFEMFunctionBeginHot;
 
    SNES snes;
    CHKERR TSGetSNES(solver, &snes);
    KSP ksp;
    CHKERR SNESGetKSP(snes, &ksp);
    PC pc;
    CHKERR KSPGetPC(ksp, &pc);
    PetscBool is_pcfs = PETSC_FALSE;
    PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &is_pcfs);
 
    // Setup fieldsplit (block) solver - optional: yes/no
    if (is_pcfs == PETSC_TRUE) {
 
      auto bc_mng = mField.getInterface<BcManager>();
      auto name_prb = simple->getProblemName();
      auto is_all_bc = bc_mng->getBlockIS(name_prb, "FIX_X", "U", 0, 0);
      is_all_bc = bc_mng->getBlockIS(name_prb, "FIX_Y", "U", 1, 1, is_all_bc);
      is_all_bc = bc_mng->getBlockIS(name_prb, "FIX_Z", "U", 2, 2, is_all_bc);
      is_all_bc = bc_mng->getBlockIS(name_prb, "FIX_ALL", "U", 0, 2, is_all_bc);
 
      int is_all_bc_size;
      CHKERR ISGetSize(is_all_bc, &is_all_bc_size);
      MOFEM_LOG("EXAMPLE", Sev::inform)
          << "Field split block size " << is_all_bc_size;
 
      CHKERR PCFieldSplitSetIS(pc, PETSC_NULL,
                               is_all_bc); // boundary block
    }
 
    MoFEMFunctionReturnHot(0);
  };
 
  auto dm = simple->getDM();
  auto D = smartCreateDMVector(dm);
 
  boost::shared_ptr<FEMethod> null;
  CHKERR DMMoFEMTSSetIJacobian(dm, simple->getDomainFEName(), feAxiatorLhs,
                               null, null);
  CHKERR DMMoFEMTSSetIFunction(dm, simple->getDomainFEName(), feAxiatorRhs,
                               null, null);
 
  CHKERR create_post_process_element();
  uXScatter = scatter_create(D, 0);
  uYScatter = scatter_create(D, 1);
  if (SPACE_DIM == 3)
    uZScatter = scatter_create(D, 2);
 
  auto solver = pipeline_mng->createTSIM();
 
  CHKERR TSSetSolution(solver, D);
  CHKERR set_section_monitor(solver);
  CHKERR set_time_monitor(dm, solver);
  CHKERR TSSetSolution(solver, D);
  CHKERR TSSetFromOptions(solver);
  CHKERR set_fieldsplit_preconditioner(solver);
  CHKERR TSSetUp(solver);
  CHKERR TSSolve(solver, NULL);
 
  CHKERR VecGhostUpdateBegin(D, INSERT_VALUES, SCATTER_FORWARD);
  CHKERR VecGhostUpdateEnd(D, INSERT_VALUES, SCATTER_FORWARD);
  CHKERR DMoFEMMeshToLocalVector(dm, D, INSERT_VALUES, SCATTER_REVERSE);
 
  MoFEMFunctionReturn(0);
}
//! [Solve]
 
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]
 
    //! [Load mesh]
    Simple *simple = m_field.getInterface<Simple>();
    CHKERR simple->getOptions();
    CHKERR simple->loadFile();
    //! [Load mesh]
 
    //! [Example]
    Example ex(m_field);
    CHKERR ex.runProblem();
    //! [Example]
  }
  CATCH_ERRORS;
 
  CHKERR MoFEM::Core::Finalize();
}