nonlinear_elastic.cpp

Plane stress elastic dynamic problem

/**
 * \file nonlinear_elastic.cpp
 * \example nonlinear_elastic.cpp
 *
 * Plane stress elastic dynamic problem
 *
 */
 
/* This file is part of MoFEM.
 * MoFEM is free software: you can redistribute it and/or modify it under
 * the terms of the GNU Lesser General Public License as published by the
 * Free Software Foundation, either version 3 of the License, or (at your
 * option) any later version.
 *
 * MoFEM is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 * License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with MoFEM. If not, see <http://www.gnu.org/licenses/>. */
 
#include <MoFEM.hpp>
#include <MatrixFunction.hpp>
 
using namespace MoFEM;
 
template <int DIM> struct ElementsAndOps {};
 
template <> struct ElementsAndOps<2> {
  using DomainEle = PipelineManager::FaceEle;
  using DomainEleOp = DomainEle::UserDataOperator;
  using BoundaryEle = PipelineManager::EdgeEle;
  using BoundaryEleOp = BoundaryEle::UserDataOperator;
  using PostProcEle = PostProcFaceOnRefinedMesh;
};
 
template <> struct ElementsAndOps<3> {
  using DomainEle = VolumeElementForcesAndSourcesCore;
  using DomainEleOp = DomainEle::UserDataOperator;
  using BoundaryEle = FaceElementForcesAndSourcesCore;
  using BoundaryEleOp = BoundaryEle::UserDataOperator;
  using PostProcEle = PostProcVolumeOnRefinedMesh;
};
 
constexpr int SPACE_DIM = 3; //< Space dimension of problem, mesh
 
using EntData = EntitiesFieldData::EntData;
using DomainEle = ElementsAndOps<SPACE_DIM>::DomainEle;
using DomainEleOp = ElementsAndOps<SPACE_DIM>::DomainEleOp;
using BoundaryEle = ElementsAndOps<SPACE_DIM>::BoundaryEle;
using BoundaryEleOp = ElementsAndOps<SPACE_DIM>::BoundaryEleOp;
using PostProcEle = ElementsAndOps<SPACE_DIM>::PostProcEle;
 
using OpK = FormsIntegrators<DomainEleOp>::Assembly<PETSC>::BiLinearForm<
    GAUSS>::OpGradTensorGrad<1, SPACE_DIM, SPACE_DIM, 1>;
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 OpBoundaryVec = FormsIntegrators<BoundaryEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpBaseTimesVector<1, SPACE_DIM, 0>;
 
constexpr double young_modulus = 100;
constexpr double poisson_ratio = 0.3;
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;
 
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> matDPtr;
  boost::shared_ptr<HenckyOps::CommonData> commonHenckyDataPtr;
};
 
//! [Create common data]
MoFEMErrorCode Example::createCommonData() {
  MoFEMFunctionBegin;
 
  auto set_material_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;
    MoFEMFunctionBegin;
    constexpr auto t_kd = FTensor::Kronecker_Delta_symmetric<int>();
    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>();
  matDPtr = boost::make_shared<MatrixDouble>();
 
  commonHenckyDataPtr = boost::make_shared<HenckyOps::CommonData>();
  commonHenckyDataPtr->matGradPtr = matGradPtr;
  commonHenckyDataPtr->matDPtr = matDPtr;
 
  constexpr auto size_symm = (SPACE_DIM * (SPACE_DIM + 1)) / 2;
  matDPtr->resize(size_symm * size_symm, 1);
 
  CHKERR set_material_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_LEGENDRE_BASE, SPACE_DIM);
  CHKERR simple->addBoundaryField("U", H1, AINSWORTH_LEGENDRE_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 *pipeline_mng = mField.getInterface<PipelineManager>();
  auto simple = mField.getInterface<Simple>();
  auto bc_mng = mField.getInterface<BcManager>();
 
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(), "FIX_X",
                                           "U", 0, 0);
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(), "FIX_Y",
                                           "U", 1, 1);
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(), "FIX_Z",
                                           "U", 2, 2);
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(), "FIX_ALL",
                                           "U", 0, 3);
 
  auto get_time = [&](double, double, double) {
    auto *pipeline_mng = mField.getInterface<PipelineManager>();
    auto &fe_domain_rhs = pipeline_mng->getDomainRhsFE();
    return fe_domain_rhs->ts_t;
  };
 
  for (_IT_CUBITMESHSETS_BY_SET_TYPE_FOR_LOOP_(mField, BLOCKSET, it)) {
    if (it->getName().compare(0, 5, "FORCE") == 0) {
      Range force_edges;
      std::vector<double> attr_vec;
      CHKERR it->getMeshsetIdEntitiesByDimension(mField.get_moab(), 1,
                                                 force_edges, true);
      it->getAttributes(attr_vec);
      if (attr_vec.size() < SPACE_DIM)
        SETERRQ(PETSC_COMM_WORLD, MOFEM_DATA_INCONSISTENCY,
                "Wrong size of boundary attributes vector. Set right block "
                "size attributes.");
      auto force_vec_ptr = boost::make_shared<MatrixDouble>(SPACE_DIM, 1);
      std::copy(&attr_vec[0], &attr_vec[SPACE_DIM],
                force_vec_ptr->data().begin());
      pipeline_mng->getOpBoundaryRhsPipeline().push_back(
          new OpBoundaryVec("U", force_vec_ptr, get_time,
                            boost::make_shared<Range>(force_edges)));
    }
  }
 
  //! [Define gravity vector]
  auto get_body_force = [this](const double, const double, const double) {
    auto *pipeline_mng = mField.getInterface<PipelineManager>();
    FTensor::Index<'i', SPACE_DIM> i;
    FTensor::Tensor1<double, SPACE_DIM> t_source;
    auto fe_domain_rhs = pipeline_mng->getDomainRhsFE();
    const auto time = fe_domain_rhs->ts_t;
    // hardcoded gravity load in y direction
    t_source(i) = 0;
    t_source(1) = 1 * time;
    return t_source;
  };
  //! [Define gravity vector]
 
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpBodyForce("U", get_body_force));
 
  MoFEMFunctionReturn(0);
}
//! [Boundary condition]
 
//! [Push operators to pipeline]
MoFEMErrorCode Example::assembleSystem() {
  MoFEMFunctionBegin;
  auto *simple = mField.getInterface<Simple>();
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto add_domain_base_ops = [&](auto &pipeline) {
    MoFEMFunctionBegin;
    if (SPACE_DIM == 2) {
      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 OpCalculateHOJacForFace(jac_ptr));
      pipeline.push_back(new OpInvertMatrix<2>(jac_ptr, det_ptr, inv_jac_ptr));
      pipeline.push_back(new OpSetInvJacH1ForFace(inv_jac_ptr));
    }
 
    pipeline.push_back(new OpCalculateVectorFieldGradient<SPACE_DIM, SPACE_DIM>(
        "U", matGradPtr));
    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 OpCalculateHenckyStress<SPACE_DIM>("U", commonHenckyDataPtr));
    pipeline.push_back(
        new OpCalculatePiolaStress<SPACE_DIM>("U", commonHenckyDataPtr));
 
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_ops_lhs = [&](auto &pipeline) {
    MoFEMFunctionBegin;
 
    pipeline.push_back(
        new OpHenckyTangent<SPACE_DIM>("U", commonHenckyDataPtr));
    pipeline.push_back(new OpK("U", "U", commonHenckyDataPtr->getMatTangent()));
 
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_ops_rhs = [&](auto &pipeline) {
    MoFEMFunctionBegin;
    // Calculate internal forece
    pipeline.push_back(new OpInternalForce(
        "U", commonHenckyDataPtr->getMatFirstPiolaStress()));
 
    MoFEMFunctionReturn(0);
  };
 
  CHKERR add_domain_base_ops(pipeline_mng->getOpDomainLhsPipeline());
  CHKERR add_domain_ops_lhs(pipeline_mng->getOpDomainLhsPipeline());
  CHKERR add_domain_base_ops(pipeline_mng->getOpDomainRhsPipeline());
  CHKERR add_domain_ops_rhs(pipeline_mng->getOpDomainRhsPipeline());
 
  auto integration_rule = [](int, int, int approx_order) {
    return 2 * (approx_order - 1);
  };
 
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setDomainLhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setBoundaryRhsIntegrationRule(integration_rule);
 
  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();
  auto ts = pipeline_mng->createTSIM();
 
  // Setup postprocessing
  auto post_proc_fe = boost::make_shared<PostProcEle>(mField);
  post_proc_fe->generateReferenceElementMesh();
  if (SPACE_DIM == 2) {
    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 OpCalculateHOJacForFace(jac_ptr));
    post_proc_fe->getOpPtrVector().push_back(
        new OpInvertMatrix<2>(jac_ptr, det_ptr, inv_jac_ptr));
    post_proc_fe->getOpPtrVector().push_back(
        new OpSetInvJacH1ForFace(inv_jac_ptr));
  }
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculateVectorFieldGradient<SPACE_DIM, SPACE_DIM>(
          "U", commonHenckyDataPtr->matGradPtr));
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculateEigenVals<SPACE_DIM>("U", commonHenckyDataPtr));
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculateLogC<SPACE_DIM>("U", commonHenckyDataPtr));
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculateLogC_dC<SPACE_DIM>("U", commonHenckyDataPtr));
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculateHenckyStress<SPACE_DIM>("U", commonHenckyDataPtr));
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculatePiolaStress<SPACE_DIM>("U", commonHenckyDataPtr));
 
  post_proc_fe->getOpPtrVector().push_back(new OpPostProcHencky<SPACE_DIM>(
      "U", post_proc_fe->postProcMesh, post_proc_fe->mapGaussPts,
      commonHenckyDataPtr));
 
  post_proc_fe->addFieldValuesPostProc("U");
 
  // 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 TSSetDuration(ts, PETSC_DEFAULT, ftime);
  CHKERR TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);
 
  auto D = smartCreateDMVector(simple->getDM());
 
  CHKERR TSSetSolution(ts, D);
  CHKERR TSSetFromOptions(ts);
 
  CHKERR TSSolve(ts, NULL);
  CHKERR TSGetTime(ts, &ftime);
 
  PetscInt steps, snesfails, rejects, nonlinits, linits;
  CHKERR TSGetTimeStepNumber(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\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();
}