NonlinearElasticExample.hpp

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/**
 * @file NonlinearElasticExample.hpp
 * @example mofem/tutorials/vec-2_nonlinear_elasticity/src/NonlinearElasticExample.hpp
 * @date 2025-10-5
 *
 * @copyright Anonymous authors (c) 2025 under the MIT license (see LICENSE for
 * details)
 */
 
#ifdef WITH_ADOL_C
  #include <MatOps.hpp>
  #include <MatElastic.hpp>
  #include <MatHuHu.hpp>
  #include <MatUmat.hpp>
  #include <MatGenericElastic.hpp>
  #include <MatOpsExampleGeneric.hpp>
  #ifdef WITH_ADOL_C_SIMPLE_DAMAGE
    #include <MatGenericElasticSimpleDamage.hpp>
  #endif
#endif
 
struct NonlinearElasticExample {
 
  NonlinearElasticExample(MoFEM::Interface &m_field) : mField(m_field) {}
 
  MoFEMErrorCode runProblem();
 
protected:
  MoFEM::Interface &mField;
  boost::shared_ptr<DomainEle> updateFe;
  boost::shared_ptr<PostProcEleDomain> postProcDomainFe;
  boost::shared_ptr<PostProcEleBdy> postProcBdyFe;
  PetscBool useAdolcMaterial = PETSC_FALSE;
  FieldApproximationBase approximationBase = AINSWORTH_LEGENDRE_BASE;
 
  MoFEMErrorCode readMesh();
  MoFEMErrorCode setupProblem();
  MoFEMErrorCode boundaryCondition();
  MoFEMErrorCode assembleSystemHencky();
  MoFEMErrorCode assembleSystemAdolc();
  MoFEMErrorCode opTest();
  MoFEMErrorCode TsSolve();
  MoFEMErrorCode gettingNorms();
  MoFEMErrorCode outputResults();
  MoFEMErrorCode checkPiolaStress(PetscInt test_nb);
  MoFEMErrorCode checkResults();
 
  struct TSElasticPostStep {
 
    static MoFEMErrorCode
    postStepInitialise(NonlinearElasticExample *example_ptr) {
      elasticExamplePtr = example_ptr;
      return 0;
    }
    static MoFEMErrorCode postStepDestroy() {
      elasticExamplePtr = nullptr;
      return 0;
    }
    static MoFEMErrorCode preStepFun(TS ts) { return 0; }
    static MoFEMErrorCode postStepFun(TS ts) {
      MoFEMFunctionBegin;
      (void)ts;
      auto simple = elasticExamplePtr->mField.getInterface<Simple>();
      auto dm = simple->getDM();
      if (elasticExamplePtr->updateFe) {
        CHKERR DMoFEMLoopFiniteElements(dm, simple->getDomainFEName(),
                                        elasticExamplePtr->updateFe);
      }
      MoFEMFunctionReturn(0);
    }
 
  private:
    static inline NonlinearElasticExample *elasticExamplePtr;
  };
 
  std::vector<Tag>
      listTagsToTransfer; ///< list of tags to transfer to postprocessor
 
#ifdef WITH_ADOL_C
  static inline constexpr int modelType =
      (SPACE_DIM == 3) ? MatOps::MODEL_3D : MatOps::MODEL_2D_PLANE_STRAIN;
  boost::shared_ptr<MatOps::PhysicalEquations> physicalEquationsPtr;
  boost::shared_ptr<MatOps::PhysicalEquations> physicalHuHuPtr;
#endif
 
  static auto get_skin(MoFEM::Interface &m_field, Range body_ents) {
    Skinner skin(&m_field.get_moab());
    Range skin_ents;
    CHK_MOAB_THROW(skin.find_skin(0, body_ents, false, skin_ents), "find_skin");
    return skin_ents;
  };
 
  static auto filter_true_skin(MoFEM::Interface &m_field, Range &&skin) {
    Range boundary_ents;
    ParallelComm *pcomm =
        ParallelComm::get_pcomm(&m_field.get_moab(), MYPCOMM_INDEX);
    CHK_MOAB_THROW(pcomm->filter_pstatus(skin,
                                         PSTATUS_SHARED | PSTATUS_MULTISHARED,
                                         PSTATUS_NOT, -1, &boundary_ents),
                   "filter_pstatus");
    return boundary_ents;
  };
};
 
//! [Run problem]
MoFEMErrorCode NonlinearElasticExample::runProblem() {
  MoFEMFunctionBegin;
  CHKERR readMesh();
  CHKERR setupProblem();
  CHKERR boundaryCondition();
 
  PetscBool test_op = PETSC_FALSE;
  CHKERR PetscOptionsGetBool(PETSC_NULLPTR, "", "-test_op", &test_op,
                             PETSC_NULLPTR);
 
  if (useAdolcMaterial == PETSC_TRUE) {
    CHKERR assembleSystemAdolc();
  } else {
    CHKERR assembleSystemHencky();
  }
 
  if (test_op == PETSC_TRUE) {
    CHKERR opTest();
  }
  CHKERR TsSolve();
  CHKERR gettingNorms();
  CHKERR outputResults();
  CHKERR checkResults();
  MoFEMFunctionReturn(0);
}
//! [Run problem]
 
//! [Read mesh]
MoFEMErrorCode NonlinearElasticExample::readMesh() {
  MoFEMFunctionBegin;
  auto simple = mField.getInterface<Simple>();
  CHKERR simple->getOptions();
  CHKERR simple->loadFile();
  CHKERR mField.getInterface<MeshsetsManager>()->setMeshsetFromFile();
  MoFEMFunctionReturn(0);
}
//! [Read mesh]
 
//! [Set up problem]
MoFEMErrorCode NonlinearElasticExample::setupProblem() {
  MoFEMFunctionBegin;
  Simple *simple = mField.getInterface<Simple>();
 
  enum bases { AINSWORTH, DEMKOWICZ, LASBASETOPT };
  const char *list_bases[LASBASETOPT] = {"ainsworth", "demkowicz"};
  PetscInt choice_base_value = AINSWORTH;
  CHKERR PetscOptionsGetEList(PETSC_NULLPTR, NULL, "-base", list_bases,
                              LASBASETOPT, &choice_base_value, PETSC_NULLPTR);
 
  switch (choice_base_value) {
  case AINSWORTH:
    approximationBase = AINSWORTH_LEGENDRE_BASE;
    MOFEM_LOG("WORLD", Sev::inform)
        << "Set AINSWORTH_LEGENDRE_BASE for displacements";
    break;
  case DEMKOWICZ:
    approximationBase = DEMKOWICZ_JACOBI_BASE;
    MOFEM_LOG("WORLD", Sev::inform)
        << "Set DEMKOWICZ_JACOBI_BASE for displacements";
    break;
  default:
    approximationBase = LASTBASE;
    break;
  }
 
  // Add field
  CHKERR simple->addDomainField("U", H1, approximationBase, SPACE_DIM);
  CHKERR simple->addBoundaryField("U", H1, approximationBase, SPACE_DIM);
  CHKERR simple->addDataField("GEOMETRY", H1, approximationBase, SPACE_DIM);
  int order = 2;
  CHKERR PetscOptionsGetInt(PETSC_NULLPTR, "", "-order", &order, PETSC_NULLPTR);
  CHKERR simple->setFieldOrder("U", order);
  CHKERR simple->setFieldOrder("GEOMETRY", 2);
  CHKERR simple->setUp();
 
  auto project_ho_geometry = [&]() {
    Projection10NodeCoordsOnField ent_method(mField, "GEOMETRY");
    return mField.loop_dofs("GEOMETRY", ent_method);
  };
  CHKERR project_ho_geometry();
 
  CHKERR PetscOptionsGetBool(PETSC_NULLPTR, "", "-use_adolc_material",
                             &useAdolcMaterial, PETSC_NULLPTR);
#ifndef WITH_ADOL_C
  if (useAdolcMaterial == PETSC_TRUE) {
    SETERRQ(PETSC_COMM_WORLD, MOFEM_DATA_INCONSISTENCY,
            "ADOL-C support is not enabled. Please reconfigure with "
            "-DWITH_ADOL_C=ON and recompile to use AdolC material model.");
  }
#endif
  if (useAdolcMaterial == PETSC_TRUE) {
    MOFEM_LOG("WORLD", Sev::inform) << "Use ADOL-C material model";
  } else {
    MOFEM_LOG("WORLD", Sev::inform) << "Use Hencky material model";
  }
 
  auto tag_meshest = [&]() {
    MoFEMFunctionBegin;
 
    auto set_block = [&](auto name, int dim) {
      std::map<int, Range> map;
      auto set_tag_impl = [&](auto name) {
        MoFEMFunctionBegin;
        auto mesh_mng = mField.getInterface<MeshsetsManager>();
        auto bcs = mesh_mng->getCubitMeshsetPtr(
 
            std::regex((boost::format("%s(.*)") % name).str())
 
        );
        std::map<int, int> ids_map;
        int bit_id = 1;
        for (auto bc : bcs) {
          int id = bc->getMeshsetId();
          ids_map[id] = bit_id;
          bit_id <<= 1;
        }
        for (auto bc : bcs) {
          Range r;
          CHKERR bc->getMeshsetIdEntitiesByDimension(mField.get_moab(), dim, r,
                                                     true);
          map[ids_map[bc->getMeshsetId()]] = r;
          MOFEM_LOG("EXAMPLE", Sev::inform)
              << "Block " << name << " id " << bc->getMeshsetId() << " : "
              << ids_map[bc->getMeshsetId()] << " has " << r.size()
              << " entities";
        }
        MoFEMFunctionReturn(0);
      };
 
      CHKERR set_tag_impl(name);
 
      return std::make_pair(name, map);
    };
 
    auto set_skin = [&](auto &&map) {
      for (auto &m : map.second) {
        auto s = filter_true_skin(mField, get_skin(mField, m.second));
        m.second.swap(s);
        MOFEM_LOG("EXAMPLE", Sev::inform)
            << "Skin for block " << map.first << " id " << m.first << " has "
            << m.second.size() << " entities";
      }
      return map;
    };
 
    auto set_tag = [&](auto &&map) {
      Tag th;
      auto name = map.first;
      int def_val[] = {-1};
      CHK_MOAB_THROW(mField.get_moab().tag_get_handle(
                         name, 1, MB_TYPE_INTEGER, th,
                         MB_TAG_SPARSE | MB_TAG_CREAT, def_val),
                     "create tag");
      for (auto &m : map.second) {
        int id = m.first;
        for (auto ent : m.second) {
          int current_id;
          CHK_MOAB_THROW(
              mField.get_moab().tag_get_data(th, &ent, 1, &current_id),
              "get tag data");
          if (current_id != -1) {
            id |= current_id;
          }
          CHK_MOAB_THROW(mField.get_moab().tag_set_data(th, &ent, 1, &id),
                         "set tag data");
        }
      }
      return th;
    };
 
    if (SPACE_DIM == 3) {
      listTagsToTransfer.push_back(set_tag(set_block("MAT_", 3)));
      listTagsToTransfer.push_back(set_tag(set_skin(set_block("MAT_", 3))));
    } else {
      listTagsToTransfer.push_back(set_tag(set_block("MAT_", 2)));
    }
 
    MoFEMFunctionReturn(0);
  };
 
  CHKERR tag_meshest();
 
  MoFEMFunctionReturn(0);
}
//! [Set up problem]
 
//! [Boundary condition]
 
MoFEMErrorCode NonlinearElasticExample::boundaryCondition() {
  MoFEMFunctionBegin;
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
  auto simple = mField.getInterface<Simple>();
  auto bc_mng = mField.getInterface<BcManager>();
  auto time_scale = boost::make_shared<ExampleTimeScale>();
 
  CHKERR BoundaryNaturalBC::AddFluxToPipeline<OpForce>::add(
      pipeline_mng->getOpBoundaryRhsPipeline(), mField, "U", {time_scale},
      "FORCE", "PRESSURE", Sev::inform);
 
  //! [Define gravity vector]
  CHKERR DomainNaturalBC::AddFluxToPipeline<OpBodyForce>::add(
      pipeline_mng->getOpDomainRhsPipeline(), mField, "U", {time_scale},
      "BODY_FORCE", Sev::inform);
 
  // Essential BC
  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->pushMarkDOFsOnEntities<DisplacementCubitBcData>(
      simple->getProblemName(), "U");
 
  MoFEMFunctionReturn(0);
}
//! [Boundary condition]
 
//! [Push operators to pipeline]
MoFEMErrorCode NonlinearElasticExample::assembleSystemHencky() {
  MoFEMFunctionBegin;
 
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto integration_rule = [](int, int, int approx_order) {
    return 2 * (approx_order - 1) + 1;
  };
 
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setDomainLhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setBoundaryRhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setEvaluationIntegrationRule(integration_rule);
 
  auto add_domain_ops_lhs = [&](auto &pip) {
    MoFEMFunctionBegin;
    CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pip, {H1},
                                                          "GEOMETRY");
    CHKERR
    HenckyOps::opFactoryDomainLhs<SPACE_DIM, PETSC, GAUSS, DomainEleOp>(
        mField, pip, "U", "MAT_ELASTIC", Sev::inform);
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_ops_rhs = [&](auto &pip) {
    MoFEMFunctionBegin;
    CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pip, {H1},
                                                          "GEOMETRY");
    CHKERR
    HenckyOps::opFactoryDomainRhs<SPACE_DIM, PETSC, GAUSS, DomainEleOp>(
        mField, pip, "U", "MAT_ELASTIC", Sev::inform);
    MoFEMFunctionReturn(0);
  };
 
  CHKERR add_domain_ops_lhs(pipeline_mng->getOpDomainLhsPipeline());
  CHKERR add_domain_ops_rhs(pipeline_mng->getOpDomainRhsPipeline());
 
  // push operators to evaluation pipeline
  CHKERR add_domain_ops_rhs(pipeline_mng->getOpEvaluationPipeline());
  auto &domain_reaction_fe = pipeline_mng->getEvaluationFE();
  domain_reaction_fe->postProcessHook =
      EssentialPreProcReaction<DisplacementCubitBcData>(mField,
                                                        domain_reaction_fe);
 
  PetscBool post_proc_vol;
  PetscBool post_proc_skin;
 
  if constexpr (SPACE_DIM == 2) {
    post_proc_vol = PETSC_TRUE;
    post_proc_skin = PETSC_FALSE;
  } else {
    post_proc_vol = PETSC_FALSE;
    post_proc_skin = PETSC_TRUE;
  }
 
  CHKERR PetscOptionsGetBool(PETSC_NULLPTR, "", "-post_proc_vol",
                             &post_proc_vol, PETSC_NULLPTR);
  CHKERR PetscOptionsGetBool(PETSC_NULLPTR, "", "-post_proc_skin",
                             &post_proc_skin, PETSC_NULLPTR);
 
  // Setup postprocessing
  auto create_post_proc_fe = [&]() {
    auto post_proc_ele_domain = [this](auto &pip_domain) {
      CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pip_domain, {H1},
                                                            "GEOMETRY");
      auto common_ptr = commonDataFactory<SPACE_DIM, GAUSS, DomainEleOp>(
          mField, pip_domain, "U", "MAT_ELASTIC", Sev::inform);
      return common_ptr;
    };
 
    auto post_proc_map = [&](auto &pip, auto u_ptr, auto common_ptr) {
      MoFEMFunctionBegin;
 
      using OpPPMap = OpPostProcMapInMoab<SPACE_DIM, SPACE_DIM>;
 
      pip->getOpPtrVector().push_back(
 
          new OpPPMap(pip->getPostProcMesh(), pip->getMapGaussPts(), {},
                      {{"U", u_ptr}},
                      {{"GRAD", common_ptr->matGradPtr},
                       {"FIRST_PIOLA", common_ptr->getMatFirstPiolaStress()}},
                      {}));
      MoFEMFunctionReturn(0);
    };
 
    auto push_post_proc_bdy = [&](auto &pip_bdy) {
      if (post_proc_skin == PETSC_FALSE)
        return boost::shared_ptr<PostProcEleBdy>();
      auto simple = mField.getInterface<Simple>();
      auto domain_fe_name = simple->getDomainFEName();
      auto u_ptr = boost::make_shared<MatrixDouble>();
      pip_bdy->getOpPtrVector().push_back(
          new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_ptr));
      auto op_loop_side =
          new OpLoopSide<SideEle>(mField, domain_fe_name, SPACE_DIM);
      auto common_ptr = post_proc_ele_domain(op_loop_side->getOpPtrVector());
      pip_bdy->getOpPtrVector().push_back(op_loop_side);
      CHKERR post_proc_map(pip_bdy, u_ptr, common_ptr);
      return pip_bdy;
    };
 
    auto push_post_proc_domain = [&](auto &pip_domain) {
      if (post_proc_vol == PETSC_FALSE)
        return boost::shared_ptr<PostProcEleDomain>();
 
      auto u_ptr = boost::make_shared<MatrixDouble>();
      pip_domain->getOpPtrVector().push_back(
          new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_ptr));
      auto common_ptr = post_proc_ele_domain(pip_domain->getOpPtrVector());
 
      CHKERR post_proc_map(pip_domain, u_ptr, common_ptr);
 
      return pip_domain;
    };
 
    auto post_proc_fe_domain = boost::make_shared<PostProcEleDomain>(mField);
    auto post_proc_fe_bdy = boost::make_shared<PostProcEleBdy>(mField);
 
    return std::make_pair(push_post_proc_domain(post_proc_fe_domain),
                          push_post_proc_bdy(post_proc_fe_bdy));
  };
 
  auto post_proc_pair = create_post_proc_fe();
  postProcDomainFe = post_proc_pair.first;
  postProcBdyFe = post_proc_pair.second;
 
  MoFEMFunctionReturn(0);
}
//! [Push operators to pipeline]
 
MoFEMErrorCode NonlinearElasticExample::opTest() {
  MoFEMFunctionBegin;
 
  // get operators tester
  auto simple = mField.getInterface<Simple>();
  auto opt = mField.getInterface<OperatorsTester>(); // get interface to
                                                     // OperatorsTester
  auto pip = mField.getInterface<PipelineManager>(); // get interface to
                                                     // pipeline manager
 
  constexpr double eps = 1e-9;
 
  auto x = opt->setRandomFields(simple->getDM(), {
 
                                                     {"U", {-1e-6, 1e-6}}
 
                                                 });
 
  auto dot_x = opt->setRandomFields(simple->getDM(), {
 
                                                         {"U", {-1, 1}}
 
                                                     });
 
  auto diff_x = opt->setRandomFields(simple->getDM(), {
 
                                                          {"U", {-1, 1}}
 
                                                      });
 
  auto test_domain_ops = [&](auto fe_name, auto lhs_pipeline,
                             auto rhs_pipeline) {
    MoFEMFunctionBegin;
 
    auto diff_res = opt->checkCentralFiniteDifference(
        simple->getDM(), fe_name, rhs_pipeline, lhs_pipeline, x, dot_x,
        SmartPetscObj<Vec>(), diff_x, 0, 0.5, eps);
 
    // Calculate norm of difference between directional derivative calculated
    // from finite difference, and tangent matrix.
    double fnorm;
    CHKERR VecNorm(diff_res, NORM_2, &fnorm);
    MOFEM_LOG_C("EXAMPLE", Sev::inform,
                "Test consistency of tangent matrix %3.4e", fnorm);
 
    constexpr double err = 1e-5;
    if (fnorm > err)
      SETERRQ(PETSC_COMM_WORLD, MOFEM_ATOM_TEST_INVALID,
              "Norm of directional derivative too large err = %3.4e", fnorm);
 
    MoFEMFunctionReturn(0);
  };
 
  MOFEM_LOG("EXAMPLE", Sev::inform)
      << "Test operators with finite difference of directional "
         "derivative";
  CHKERR test_domain_ops(simple->getDomainFEName(), pip->getDomainLhsFE(),
                         pip->getDomainRhsFE());
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode NonlinearElasticExample::assembleSystemAdolc() {
  MoFEMFunctionBegin;
 
  auto *simple = mField.getInterface<Simple>();
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto integration_rule = [](int, int, int approx_order) {
    return 2 * (approx_order - 1) + 1;
  };
 
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setDomainLhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setBoundaryRhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setEvaluationIntegrationRule(integration_rule);
 
#ifdef WITH_ADOL_C
  auto mat_ops_data_ptr = MatOps::createMatOpsDataPtr();
 
#ifdef WITH_ADOL_C_UMAT
  {
    constexpr int umat_model_type =
        (SPACE_DIM == 3) ? MatOps::MODEL_3D : MatOps::MODEL_2D_PLANE_STRAIN;
    auto umat_physical_equations_ptr =
        MatOps::createMatOpsPhysicalEquationsPtr<MatOps::UMAT,
                                                 umat_model_type>(
            mat_ops_data_ptr, MatOps::MatOpsTagsRegistry::setTagName("Umat"));
 
    CHKERR umat_physical_equations_ptr->getOptions(&mField);
    CHKERR umat_physical_equations_ptr->recordTape();
 
    physicalEquationsPtr = umat_physical_equations_ptr;
  }
#else
  if (!physicalEquationsPtr) {
    physicalEquationsPtr =
        MatOps::createMatOpsPhysicalEquationsPtr<MatOps::ELASTICITY::META,
                                                  modelType>(
            mat_ops_data_ptr,
            MatOps::MatOpsTagsRegistry::setTagName("MetaElastic", 0));
  }
 
  #ifdef WITH_ADOL_C_GENERIC_ELASTIC
  {
    auto generic_physical_equations_ptr =
        MatOps::createMatOpsPhysicalEquationsPtr<MatOps::GenericElastic,
                                                  modelType>(
            mat_ops_data_ptr,
            MatOps::MatOpsTagsRegistry::setTagName("GenericElastic"));
 
    MatOpsExampleGeneric();
    // In example, lets do a simple linear elastic material, so we can verify the tangent matrix
    generic_physical_equations_ptr->hookEvaluateVariable =
        MatOpsExampleGeneric::hookEvaluateVariable;
    generic_physical_equations_ptr->hookEvaluateDerivatives =
        MatOpsExampleGeneric::hookEvaluateDerivatives;
    generic_physical_equations_ptr->hookUpdateState =
        MatOpsExampleGeneric::hookUpdateState;
 
    CHKERR generic_physical_equations_ptr->getOptions(&mField);
    CHKERR generic_physical_equations_ptr->recordTape();
 
    auto &material_map = getMetaElasticMap(physicalEquationsPtr);
    material_map[generic_physical_equations_ptr->tAg] =
        generic_physical_equations_ptr;
    physicalEquationsPtr->tAg = generic_physical_equations_ptr->tAg;
  }
  #endif // WITH_ADOL_C_GENERIC_ELASTIC
 
  #ifdef WITH_ADOL_C_SIMPLE_DAMAGE
  {
    auto generic_physical_equations_ptr =
        MatOps::createMatOpsPhysicalEquationsPtr<MatOps::GenericElastic,
                                                  modelType>(
            mat_ops_data_ptr, MatOps::MatOpsTagsRegistry::setTagName(
                                "GenericElasticSimpleDamage"));
 
    CHKERR GenericElasticExamples::configureSimpleDamage(
        mField, boost::dynamic_pointer_cast<MatOps::GenericElastic>(
                    generic_physical_equations_ptr));
 
    CHKERR generic_physical_equations_ptr->getOptions(&mField);
    CHKERR generic_physical_equations_ptr->recordTape();
 
    auto &material_map = getMetaElasticMap(physicalEquationsPtr);
    material_map[generic_physical_equations_ptr->tAg] =
        generic_physical_equations_ptr;
    physicalEquationsPtr->tAg = generic_physical_equations_ptr->tAg;
  }
  #endif // WITH_ADOL_C_SIMPLE_DAMAGE
 
  if (physicalEquationsPtr) {
    CHKERR physicalEquationsPtr->getOptions(&mField);
    CHKERR physicalEquationsPtr->recordTape();
  }
 
  if (!physicalHuHuPtr) {
    const int tag_hu_hu = MatOps::MatOpsTagsRegistry::setTagName("HuHU");
    physicalHuHuPtr =
        MatOps::createMatOpsPhysicalEquationsPtr<MatOps::HUHU, modelType>(
            MatOps::createMatOpsDataPtr(), tag_hu_hu);
    CHKERR physicalHuHuPtr->getOptions(&mField);
    CHKERR physicalHuHuPtr->recordTape();
  }
#endif //  WITH_ADOL_C_UMAT
 
  auto add_domain_ops_lhs = [&](auto &pip) {
    MoFEMFunctionBegin;
    CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pip, {H1},
                                                          "GEOMETRY");
    if (physicalEquationsPtr) {
      CHKERR MatOps::OpMaterialFactory<MatOps::ELASTICITY, modelType>::
          template opLhsFactory<PETSC, GAUSS, DomainEleOp>(
              mField, pip, "U", physicalEquationsPtr);
    }
    if (physicalHuHuPtr) {
      CHKERR MatOps::OpMaterialFactory<MatOps::HUHU, modelType>::
          template opLhsFactory<PETSC, GAUSS, DomainEleOp>(
              mField, pip, simple->getDomainFEName(), "U", physicalHuHuPtr);
    }
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_ops_rhs = [&](auto &pip) {
    MoFEMFunctionBegin;
    CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pip, {H1},
                                                          "GEOMETRY");
    if (physicalEquationsPtr) {
      CHKERR MatOps::OpMaterialFactory<MatOps::ELASTICITY, modelType>::
          template opRhsFactory<PETSC, GAUSS, DomainEleOp>(
              mField, pip, "U", physicalEquationsPtr);
    }
    if (physicalHuHuPtr) {
      CHKERR MatOps::OpMaterialFactory<MatOps::HUHU, modelType>::
          template opRhsFactory<PETSC, GAUSS, DomainEleOp>(
              mField, pip, simple->getDomainFEName(), "U", physicalHuHuPtr);
    }
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_ops_update = [&](auto &pip) {
    MoFEMFunctionBegin;
    CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pip, {H1},
                                                          "GEOMETRY");
    if (physicalEquationsPtr) {
      CHKERR MatOps::OpMaterialFactory<MatOps::ELASTICITY, modelType>::
          opUpdateFactory(mField, pip, "U", physicalEquationsPtr);
    }
    MoFEMFunctionReturn(0);
  };
 
  CHKERR add_domain_ops_lhs(pipeline_mng->getOpDomainLhsPipeline());
  CHKERR add_domain_ops_rhs(pipeline_mng->getOpDomainRhsPipeline());
 
  updateFe = boost::make_shared<DomainEle>(mField);
  updateFe->getRuleHook = integration_rule;
  CHKERR add_domain_ops_update(updateFe->getOpPtrVector());
 
  CHKERR add_domain_ops_rhs(pipeline_mng->getOpEvaluationPipeline());
  auto &domain_reaction_fe = pipeline_mng->getEvaluationFE();
  domain_reaction_fe->postProcessHook =
      EssentialPreProcReaction<DisplacementCubitBcData>(mField,
                                                        domain_reaction_fe);
 
  PetscBool post_proc_vol;
  PetscBool post_proc_skin;
 
  if constexpr (SPACE_DIM == 2) {
    post_proc_vol = PETSC_TRUE;
    post_proc_skin = PETSC_FALSE;
  } else {
    post_proc_vol = PETSC_FALSE;
    post_proc_skin = PETSC_TRUE;
  }
 
  CHKERR PetscOptionsGetBool(PETSC_NULLPTR, "", "-post_proc_vol",
                             &post_proc_vol, PETSC_NULLPTR);
  CHKERR PetscOptionsGetBool(PETSC_NULLPTR, "", "-post_proc_skin",
                             &post_proc_skin, PETSC_NULLPTR);
 
  // Setup postprocessing
  auto create_post_proc_fe = [&]() {
    using OpPPMap = OpPostProcMapInMoab<SPACE_DIM, SPACE_DIM>;
 
    auto post_proc_ele_domain = [&](auto &pip_domain) {
      MoFEMFunctionBegin;
      CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pip_domain, {H1},
                                                            "GEOMETRY");
      if (physicalEquationsPtr) {
        CHKERR MatOps::OpMaterialFactory<MatOps::ELASTICITY, modelType>::
            opPostProcFactory(mField, pip_domain, "U", physicalEquationsPtr);
      }
      MoFEMFunctionReturn(0);
    };
 
    auto post_proc_map = [&](auto &pip, auto u_ptr) {
      MoFEMFunctionBegin;
      if (physicalEquationsPtr) {
        auto grad_ptr =
            physicalEquationsPtr->matOpsDataPtr->getCommonDataPtr("grad");
        auto first_piola_ptr =
            physicalEquationsPtr->matOpsDataPtr->getCommonDataPtr("P");
        pip->getOpPtrVector().push_back(new OpPPMap(
            pip->getPostProcMesh(), pip->getMapGaussPts(), {}, {{"U", u_ptr}},
            {{"GRAD", grad_ptr}, {"FIRST_PIOLA", first_piola_ptr}}, {}));
      }
      MoFEMFunctionReturn(0);
    };
 
    auto push_post_proc_bdy = [&](auto &pip_bdy) {
      if (post_proc_skin == PETSC_FALSE)
        return boost::shared_ptr<PostProcEleBdy>();
      auto simple = mField.getInterface<Simple>();
      auto domain_fe_name = simple->getDomainFEName();
      auto u_ptr = boost::make_shared<MatrixDouble>();
      pip_bdy->getOpPtrVector().push_back(
          new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_ptr));
      auto op_loop_side =
          new OpLoopSide<SideEle>(mField, domain_fe_name, SPACE_DIM);
      CHKERR post_proc_ele_domain(op_loop_side->getOpPtrVector());
      pip_bdy->getOpPtrVector().push_back(op_loop_side);
      CHKERR post_proc_map(pip_bdy, u_ptr);
      return pip_bdy;
    };
 
    auto push_post_proc_domain = [&](auto &pip_domain) {
      if (post_proc_vol == PETSC_FALSE)
        return boost::shared_ptr<PostProcEleDomain>();
      auto u_ptr = boost::make_shared<MatrixDouble>();
      pip_domain->getOpPtrVector().push_back(
          new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_ptr));
      CHKERR post_proc_ele_domain(pip_domain->getOpPtrVector());
 
      if (physicalEquationsPtr) {
        auto state_tags = physicalEquationsPtr->matOpsDataPtr->getStateTags();
        if (!state_tags.empty()) {
          MatOps::StateTags selected_state_tags;
          MatOps::StateTags statev_tags;
          selected_state_tags.reserve(state_tags.size());
          statev_tags.reserve(state_tags.size());
 
          constexpr auto statev_prefix = "UMAT_STATEV_";
          constexpr auto statev_prefix_len = sizeof("UMAT_STATEV_") - 1;
          auto get_statev_index = [&](const std::string &name) {
            return std::stoi(name.substr(statev_prefix_len));
          };
 
          for (const auto &state_tag : state_tags) {
            const auto &name = state_tag.name;
 
            if (name == "UMAT_DFGRD0" || name == "UMAT_STRESS") {
              selected_state_tags.push_back(state_tag);
              continue;
            }
 
            if (name.rfind(statev_prefix, 0) == 0) {
              statev_tags.push_back(state_tag);
            }
          }
 
          std::sort(statev_tags.begin(), statev_tags.end(),
                    [&](const auto &lhs, const auto &rhs) {
                      return get_statev_index(lhs.name) <
                             get_statev_index(rhs.name);
                    });
          if (statev_tags.size() > 10)
            statev_tags.resize(10);
          selected_state_tags.insert(selected_state_tags.end(),
                                     statev_tags.begin(), statev_tags.end());
 
          if (selected_state_tags.empty())
            return pip_domain;
 
          auto simple = mField.getInterface<Simple>();
          int state_order = 2;
          CHKERR PetscOptionsGetInt(PETSC_NULLPTR, "", "-order", &state_order,
                                    PETSC_NULLPTR);
          auto op_loop_this = new OpLoopThis<DomainEle>(
              mField, simple->getDomainFEName(), Sev::noisy);
          op_loop_this->getThisFEPtr()->getRuleHook = integration_rule;
          pip_domain->getOpPtrVector().push_back(op_loop_this);
          CHKERR addTagDGProjectionOps<SPACE_DIM, SPACE_DIM>(
              mField.get_moab(), pip_domain->getOpPtrVector(),
              op_loop_this->getThisFEPtr()->getOpPtrVector(),
              pip_domain->getPostProcMesh(), pip_domain->getMapGaussPts(),
              selected_state_tags, state_order, approximationBase);
        }
      }
 
      CHKERR post_proc_map(pip_domain, u_ptr);
 
      return pip_domain;
    };
 
    auto post_proc_fe_domain = boost::make_shared<PostProcEleDomain>(mField);
    auto post_proc_fe_bdy = boost::make_shared<PostProcEleBdy>(mField);
 
    return std::make_pair(push_post_proc_domain(post_proc_fe_domain),
                          push_post_proc_bdy(post_proc_fe_bdy));
  };
 
  auto post_proc_pair = create_post_proc_fe();
  postProcDomainFe = post_proc_pair.first;
  postProcBdyFe = post_proc_pair.second;
 
#else
  SETERRQ(PETSC_COMM_WORLD, MOFEM_DATA_INCONSISTENCY,
          "ADOL-C support is not enabled. Please reconfigure with "
          "-DWITH_ADOL_C=ON and recompile to use AdolC material model.");
 
#endif // WITH_ADOL
  MoFEMFunctionReturn(0);
}
 
//! [TS Solve]
MoFEMErrorCode NonlinearElasticExample::TsSolve() {
  MoFEMFunctionBegin;
  auto *simple = mField.getInterface<Simple>();
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto dm = simple->getDM();
  auto ts = pipeline_mng->createTSIM();
 
  auto add_extra_finite_elements_to_solver_pipelines = [&]() {
    MoFEMFunctionBegin;
 
    auto pre_proc_ptr = boost::make_shared<FEMethod>();
    auto post_proc_rhs_ptr = boost::make_shared<FEMethod>();
    auto post_proc_lhs_ptr = boost::make_shared<FEMethod>();
 
    auto time_scale = boost::make_shared<ExampleTimeScale>();
 
    auto get_bc_hook_rhs = [this, pre_proc_ptr, time_scale]() {
      MoFEMFunctionBeginHot;
      CHKERR EssentialPreProc<DisplacementCubitBcData>(mField, pre_proc_ptr,
                                                       {time_scale}, false)();
      MoFEMFunctionReturnHot(0);
    };
 
    pre_proc_ptr->preProcessHook = get_bc_hook_rhs;
 
    auto get_post_proc_hook_rhs = [this, post_proc_rhs_ptr]() {
      MoFEMFunctionBegin;
      CHKERR EssentialPreProcReaction<DisplacementCubitBcData>(
          mField, post_proc_rhs_ptr, nullptr, Sev::verbose)();
      CHKERR EssentialPostProcRhs<DisplacementCubitBcData>(
          mField, post_proc_rhs_ptr, 1.)();
      MoFEMFunctionReturn(0);
    };
    auto get_post_proc_hook_lhs = [this, post_proc_lhs_ptr]() {
      MoFEMFunctionBegin;
      CHKERR EssentialPostProcLhs<DisplacementCubitBcData>(
          mField, post_proc_lhs_ptr, 1.)();
      MoFEMFunctionReturn(0);
    };
    post_proc_rhs_ptr->postProcessHook = get_post_proc_hook_rhs;
    post_proc_lhs_ptr->postProcessHook = get_post_proc_hook_lhs;
 
    // This is low level pushing finite elements (pipelines) to solver
    auto ts_ctx_ptr = getDMTsCtx(simple->getDM());
    ts_ctx_ptr->getPreProcessIFunction().push_front(pre_proc_ptr);
    ts_ctx_ptr->getPreProcessIJacobian().push_front(pre_proc_ptr);
    ts_ctx_ptr->getPostProcessIFunction().push_back(post_proc_rhs_ptr);
    ts_ctx_ptr->getPostProcessIJacobian().push_back(post_proc_lhs_ptr);
    MoFEMFunctionReturn(0);
  };
 
  // Add extra finite elements to SNES solver pipelines to resolve essential
  // boundary conditions
  CHKERR add_extra_finite_elements_to_solver_pipelines();
 
  auto create_monitor_fe = [dm](auto &&post_proc_fe) {
    return boost::make_shared<Monitor>(dm.get(), post_proc_fe);
  };
 
  // Set monitor which postprocessing results and saves them to the hard drive
  boost::shared_ptr<FEMethod> null_fe;
  if (postProcDomainFe)
    CHKERR postProcDomainFe->setTagsToTransfer(
        std::vector<Tag>(listTagsToTransfer));
  if (postProcBdyFe)
    CHKERR postProcBdyFe->setTagsToTransfer(
        std::vector<Tag>(listTagsToTransfer));
  auto monitor_ptr =
      create_monitor_fe(std::make_pair(postProcDomainFe, postProcBdyFe));
  CHKERR DMMoFEMTSSetMonitor(dm, ts, simple->getDomainFEName(), null_fe,
                             null_fe, monitor_ptr);
 
  // Set time solver
  double ftime = 1;
  CHKERR TSSetMaxTime(ts, ftime);
  CHKERR TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);
 
  auto B = createDMMatrix(dm);
  CHKERR TSSetI2Jacobian(ts, B, B, PETSC_NULLPTR, PETSC_NULLPTR);
  auto D = createDMVector(simple->getDM());
  CHKERR TSSetSolution(ts, D);
  CHKERR TSSetFromOptions(ts);
 
  CHKERR TSElasticPostStep::postStepInitialise(this);
  CHKERR TSSetPreStep(ts, TSElasticPostStep::preStepFun);
  CHKERR TSSetPostStep(ts, TSElasticPostStep::postStepFun);
  CHKERR TSSolve(ts, NULL);
  CHKERR TSElasticPostStep::postStepDestroy();
 
  CHKERR TSGetTime(ts, &ftime);
 
  PetscInt steps, snesfails, rejects, nonlinits, linits;
  CHKERR TSGetStepNumber(ts, &steps);
  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",
              steps, rejects, snesfails, ftime, nonlinits, linits);
 
  MoFEMFunctionReturn(0);
}
//! [TS Solve]
 
//! [Getting norms]
MoFEMErrorCode NonlinearElasticExample::gettingNorms() {
  MoFEMFunctionBegin;
 
  auto simple = mField.getInterface<Simple>();
  auto dm = simple->getDM();
 
  auto T = createDMVector(simple->getDM());
  CHKERR DMoFEMMeshToLocalVector(simple->getDM(), T, INSERT_VALUES,
                                 SCATTER_FORWARD);
  double nrm2;
  CHKERR VecNorm(T, NORM_2, &nrm2);
  MOFEM_LOG("EXAMPLE", Sev::inform) << "Solution norm " << nrm2;
 
  auto post_proc_norm_fe = boost::make_shared<DomainEle>(mField);
 
  auto post_proc_norm_rule_hook = [](int, int, int p) -> int { return 2 * p; };
  post_proc_norm_fe->getRuleHook = post_proc_norm_rule_hook;
 
  CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(
      post_proc_norm_fe->getOpPtrVector(), {H1}, "GEOMETRY");
 
  enum NORMS { U_NORM_L2 = 0, PIOLA_NORM, LAST_NORM };
  auto norms_vec =
      createVectorMPI(mField.get_comm(),
                      (mField.get_comm_rank() == 0) ? LAST_NORM : 0, LAST_NORM);
  CHKERR VecZeroEntries(norms_vec);
 
  auto u_ptr = boost::make_shared<MatrixDouble>();
  post_proc_norm_fe->getOpPtrVector().push_back(
      new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_ptr));
 
  post_proc_norm_fe->getOpPtrVector().push_back(
      new OpCalcNormL2Tensor1<SPACE_DIM>(u_ptr, norms_vec, U_NORM_L2));
 
  if (useAdolcMaterial == PETSC_TRUE) {
#ifdef WITH_ADOL_C
    if (physicalEquationsPtr) {
      CHKERR MatOps::OpMaterialFactory<MatOps::ELASTICITY, modelType>::
          opPostProcFactory(mField, post_proc_norm_fe->getOpPtrVector(), "U",
                            physicalEquationsPtr);
      auto m_P = physicalEquationsPtr->matOpsDataPtr->getCommonDataPtr("P");
      post_proc_norm_fe->getOpPtrVector().push_back(
          new OpCalcNormL2Tensor2<SPACE_DIM, SPACE_DIM>(m_P, norms_vec,
                                                        PIOLA_NORM));
    }
#else
    SETERRQ(PETSC_COMM_WORLD, MOFEM_DATA_INCONSISTENCY,
            "ADOL-C support is not enabled. Please reconfigure with "
            "-DWITH_ADOL_C=ON and recompile to use AdolC material model.");
#endif
  } else {
    auto common_ptr = commonDataFactory<SPACE_DIM, GAUSS, DomainEleOp>(
        mField, post_proc_norm_fe->getOpPtrVector(), "U", "MAT_ELASTIC",
        Sev::inform);
    post_proc_norm_fe->getOpPtrVector().push_back(
        new OpCalcNormL2Tensor2<SPACE_DIM, SPACE_DIM>(
            common_ptr->getMatFirstPiolaStress(), norms_vec, PIOLA_NORM));
  }
 
  CHKERR DMoFEMLoopFiniteElements(dm, simple->getDomainFEName(),
                                  post_proc_norm_fe);
 
  CHKERR VecAssemblyBegin(norms_vec);
  CHKERR VecAssemblyEnd(norms_vec);
 
  MOFEM_LOG_CHANNEL("SELF"); // Clear channel from old tags
  if (mField.get_comm_rank() == 0) {
    const double *norms;
    CHKERR VecGetArrayRead(norms_vec, &norms);
    MOFEM_TAG_AND_LOG("SELF", Sev::inform, "example")
        << "norm_u: " << std::scientific << std::sqrt(norms[U_NORM_L2]);
    MOFEM_TAG_AND_LOG("SELF", Sev::inform, "example")
        << "norm_piola: " << std::scientific << std::sqrt(norms[PIOLA_NORM]);
    CHKERR VecRestoreArrayRead(norms_vec, &norms);
  }
 
  MoFEMFunctionReturn(0);
}
//! [Getting norms]
 
//! [Postprocessing results]
MoFEMErrorCode NonlinearElasticExample::outputResults() {
  MoFEMFunctionBegin;
  MoFEMFunctionReturn(0);
}
//! [Postprocessing results]
 
MoFEMErrorCode NonlinearElasticExample::checkPiolaStress(PetscInt test_nb) {
  MoFEMFunctionBegin;
  auto simple = mField.getInterface<Simple>();
 
  FTensor::Tensor2<double, SPACE_DIM, SPACE_DIM> t_P_expected;
  FTensor::Tensor2<double, SPACE_DIM, SPACE_DIM> t_P_diff;
  FTENSOR_INDEX(SPACE_DIM, i);
  FTENSOR_INDEX(SPACE_DIM, J);
 
  constexpr double applied_F_zz = 0.99;
 
  t_P_expected(i, J) = 0.;
  auto set_linear_elastic_piola = [&](const double strain_zz,
                                      const double d_strain_d_F_zz) {
    constexpr double E = 1.;
    constexpr double nu = 0.3;
    const double lambda = E * nu / ((1. + nu) * (1. - 2. * nu));
    const double mu = E / (2. * (1. + nu));
    for (int d = 0; d != SPACE_DIM - 1; ++d)
      t_P_expected(d, d) = lambda * strain_zz;
    t_P_expected(SPACE_DIM - 1, SPACE_DIM - 1) =
        (lambda + 2. * mu) * strain_zz * d_strain_d_F_zz;
  };
 
  auto set_neohookean_piola = [&](const double F_zz, const double J) {
    constexpr double c10 = 1.;
    constexpr double K = 1.;
    double I1 = (SPACE_DIM - 1) + F_zz * F_zz;
    if constexpr (SPACE_DIM == 2)
      I1 += 1.; // Plane strain has F33 = 1.
    const double J_to_minus_two_thirds = std::pow(J, -2. / 3.);
    for (int d = 0; d != SPACE_DIM; ++d) {
      const double F_dd = d == SPACE_DIM - 1 ? F_zz : 1.;
      const double inv_F_dd = 1. / F_dd;
      t_P_expected(d, d) =
          2. * c10 * J_to_minus_two_thirds *
              (F_dd - (I1 / 3.) * inv_F_dd) +
          K * J * (J - 1.) * inv_F_dd;
    }
  };
 
  auto eval_piola_at_point = [&](boost::shared_ptr<MatrixDouble> &mat_p) {
    MoFEMFunctionBegin;
    std::array<double, 3> field_eval_coords = {0.123, -0.087, 0.193};
    auto field_eval_ptr = mField.getInterface<FieldEvaluatorInterface>();
    auto field_eval_data = field_eval_ptr->getData<DomainEle>();
    CHKERR field_eval_ptr->buildTree<SPACE_DIM>(field_eval_data,
                                                simple->getDomainFEName());
    field_eval_data->setEvalPoints(field_eval_coords.data(), 1);
 
    auto fe = field_eval_data->feMethodPtr;
    fe->getRuleHook = [](int, int, int) { return -1; };
 
    auto &pipeline = fe->getOpPtrVector();
    CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pipeline, {H1},
                                                          "GEOMETRY");
 
    if (useAdolcMaterial == PETSC_FALSE) {
      auto common_ptr = commonDataFactory<SPACE_DIM, GAUSS, DomainEleOp>(
          mField, pipeline, "U", "MAT_ELASTIC", Sev::inform);
      mat_p = common_ptr->getMatFirstPiolaStress();
    } else {
#ifdef WITH_ADOL_C
      CHKERR MatOps::OpMaterialFactory<MatOps::ELASTICITY, modelType>::
          opPostProcFactory(mField, pipeline, "U", physicalEquationsPtr);
      mat_p = physicalEquationsPtr->matOpsDataPtr->getCommonDataPtr("P");
#else
      SETERRQ(PETSC_COMM_WORLD, MOFEM_DATA_INCONSISTENCY,
              "ADOL-C support is not enabled. Please reconfigure with "
              "-DWITH_ADOL_C=ON and recompile to use MatOps material model.");
#endif
    }
    CHKERR field_eval_ptr->evalFEAtThePoint<SPACE_DIM>(
        field_eval_coords.data(), 1e-12, simple->getProblemName(),
        simple->getDomainFEName(), field_eval_data, mField.get_comm_rank(),
        mField.get_comm_rank(), nullptr, MF_EXIST, QUIET);
    MoFEMFunctionReturn(0);
  };
 
  switch (test_nb) {
  case 100: {
    // Hencky, homogeneous strain_z on cube: E = 1, nu = 0.3.
    const double hencky_strain_zz = std::log(applied_F_zz);
    set_linear_elastic_piola(hencky_strain_zz, 1. / applied_F_zz);
    break;
  }
  case 101: {
    // Neo-Hookean, homogeneous strain_z on cube: c10 = K = 1.
    const double J = applied_F_zz;
    set_neohookean_piola(applied_F_zz, J);
    break;
  }
  case 102: {
    // UMAT small strain, homogeneous strain_z on cube: E = 1, nu = 0.3.
    const double small_strain_zz = applied_F_zz - 1.;
    set_linear_elastic_piola(small_strain_zz, 1.);
    break;
  }
  default:
    SETERRQ(PETSC_COMM_WORLD, MOFEM_ATOM_TEST_INVALID,
            "Wrong Piola stress test number.");
    break;
  }
 
  boost::shared_ptr<MatrixDouble> mat_p;
  CHKERR eval_piola_at_point(mat_p);
 
  auto t_P = getFTensor2FromMat<SPACE_DIM, SPACE_DIM>(*mat_p);
  t_P_diff(i, J) = t_P(i, J) - t_P_expected(i, J);
  const double p_err = std::sqrt(t_P_diff(i, J) * t_P_diff(i, J));
  for (int r = 0; r != SPACE_DIM; ++r)
    for (int c = 0; c != SPACE_DIM; ++c)
      MOFEM_LOG("EXAMPLE", Sev::inform)
          << "Piola stress test " << test_nb << " P(" << r << ", " << c
          << ") actual " << std::scientific << t_P(r, c) << " expected "
          << t_P_expected(r, c) << " diff " << t_P_diff(r, c);
  MOFEM_LOG("EXAMPLE", Sev::inform)
      << "Piola stress test " << test_nb << " error " << std::scientific
      << p_err;
  if (p_err > 1e-8)
    SETERRQ(PETSC_COMM_WORLD, MOFEM_ATOM_TEST_INVALID,
            "Wrong Piola stress. Error %6.4e", p_err);
 
  MoFEMFunctionReturn(0);
}
 
//! [Check]
MoFEMErrorCode NonlinearElasticExample::checkResults() {
  MoFEMFunctionBegin;
  PetscInt test_nb = 0;
  PetscBool test_flg = PETSC_FALSE;
  CHKERR PetscOptionsGetInt(PETSC_NULLPTR, "", "-test", &test_nb, &test_flg);
 
  if (test_flg) {
    if (test_nb >= 100) {
      CHKERR checkPiolaStress(test_nb);
      MoFEMFunctionReturnHot(0);
    }
 
    auto simple = mField.getInterface<Simple>();
    auto T = createDMVector(simple->getDM());
    CHKERR DMoFEMMeshToLocalVector(simple->getDM(), T, INSERT_VALUES,
                                   SCATTER_FORWARD);
    double nrm2;
    CHKERR VecNorm(T, NORM_2, &nrm2);
    MOFEM_LOG("EXAMPLE", Sev::verbose) << "Regression norm " << nrm2;
 
    double regression_value = 0;
    switch (test_nb) {
    case 1:
      regression_value = 3.5112e-01;
      break;
    case 2:
      regression_value = 1.8841e+00;
      break;
    case 3:
      regression_value = 1.8841e+00;
      break;
    default:
      SETERRQ(PETSC_COMM_WORLD, MOFEM_ATOM_TEST_INVALID, "Wrong test number.");
      break;
    }
    if (fabs(nrm2 - regression_value) > 1e-2)
      SETERRQ(PETSC_COMM_WORLD, MOFEM_ATOM_TEST_INVALID,
              "Regression test field; wrong norm value. %6.4e != %6.4e", nrm2,
              regression_value);
  }
  MoFEMFunctionReturn(0);
}
//! [Check]