FiniteStrainCrystalPlasticity.C

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//* This file is part of the MOOSE framework
//* https://www.mooseframework.org
//*
//* All rights reserved, see COPYRIGHT for full restrictions
//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
//*
//* Licensed under LGPL 2.1, please see LICENSE for details
//* https://www.gnu.org/licenses/lgpl-2.1.html
 
#include "FiniteStrainCrystalPlasticity.h"
#include "petscblaslapack.h"
#include "libmesh/utility.h"
 
#include <fstream>
#include <cmath>
 
registerMooseObject("TensorMechanicsApp", FiniteStrainCrystalPlasticity);
 
defineLegacyParams(FiniteStrainCrystalPlasticity);
 
InputParameters
FiniteStrainCrystalPlasticity::validParams()
{
  InputParameters params = ComputeStressBase::validParams();
  params.addClassDescription(
      "Crystal Plasticity base class: FCC system with power law flow rule implemented");
  params.addRequiredParam<int>("nss", "Number of slip systems");
  params.addParam<std::vector<Real>>("gprops", "Initial values of slip system resistances");
  params.addParam<std::vector<Real>>("hprops", "Hardening properties");
  params.addParam<std::vector<Real>>("flowprops", "Parameters used in slip rate equations");
  params.addRequiredParam<FileName>("slip_sys_file_name",
                                    "Name of the file containing the slip system");
  params.addParam<FileName>(
      "slip_sys_res_prop_file_name",
      "",
      "Name of the file containing the initial values of slip system resistances");
  params.addParam<FileName>(
      "slip_sys_flow_prop_file_name",
      "",
      "Name of the file containing the values of slip rate equation parameters");
  params.addParam<FileName>(
      "slip_sys_hard_prop_file_name",
      "",
      "Name of the file containing the values of hardness evolution parameters");
  params.addParam<Real>("rtol", 1e-6, "Constitutive stress residue relative tolerance");
  params.addParam<Real>("abs_tol", 1e-6, "Constitutive stress residue absolute tolerance");
  params.addParam<Real>("gtol", 1e2, "Constitutive slip system resistance residual tolerance");
  params.addParam<Real>("slip_incr_tol", 2e-2, "Maximum allowable slip in an increment");
  params.addParam<unsigned int>("maxiter", 100, "Maximum number of iterations for stress update");
  params.addParam<unsigned int>(
      "maxitergss", 100, "Maximum number of iterations for slip system resistance update");
  params.addParam<unsigned int>(
      "num_slip_sys_flowrate_props",
      2,
      "Number of flow rate properties for a slip system"); // Used for reading flow rate parameters
  params.addParam<UserObjectName>("read_prop_user_object",
                                  "The ElementReadPropertyFile "
                                  "GeneralUserObject to read element "
                                  "specific property values from file");
  MooseEnum tan_mod_options("exact none", "none"); // Type of read
  params.addParam<MooseEnum>("tan_mod_type",
                             tan_mod_options,
                             "Type of tangent moduli for preconditioner: default elastic");
  MooseEnum intvar_read_options("slip_sys_file slip_sys_res_file none", "none");
  params.addParam<MooseEnum>(
      "intvar_read_type",
      intvar_read_options,
      "Read from options for initial value of internal variables: Default from .i file");
  params.addParam<unsigned int>("num_slip_sys_props",
                                0,
                                "Number of slip system specific properties provided in the file "
                                "containing slip system normals and directions");
  params.addParam<bool>(
      "gen_random_stress_flag",
      false,
      "Flag to generate random stress to perform time cutback on constitutive failure");
  params.addParam<bool>("input_random_scaling_var",
                        false,
                        "Flag to input scaling variable: _Cijkl(0,0,0,0) when false");
  params.addParam<Real>("random_scaling_var",
                        1e9,
                        "Random scaling variable: Large value can cause non-positive definiteness");
  params.addParam<unsigned int>(
      "random_seed",
      2000,
      "Random integer used to generate random stress when constitutive failure occurs");
  params.addParam<unsigned int>(
      "maximum_substep_iteration", 1, "Maximum number of substep iteration");
  params.addParam<bool>("use_line_search", false, "Use line search in constitutive update");
  params.addParam<Real>("min_line_search_step_size", 0.01, "Minimum line search step size");
  params.addParam<Real>("line_search_tol", 0.5, "Line search bisection method tolerance");
  params.addParam<unsigned int>(
      "line_search_maxiter", 20, "Line search bisection method maximum number of iteration");
  MooseEnum line_search_method("CUT_HALF BISECTION", "CUT_HALF");
  params.addParam<MooseEnum>(
      "line_search_method", line_search_method, "The method used in line search");
 
  return params;
}
 
FiniteStrainCrystalPlasticity::FiniteStrainCrystalPlasticity(const InputParameters & parameters)
  : ComputeStressBase(parameters),
    _nss(getParam<int>("nss")),
    _gprops(getParam<std::vector<Real>>("gprops")),
    _hprops(getParam<std::vector<Real>>("hprops")),
    _flowprops(getParam<std::vector<Real>>("flowprops")),
    _slip_sys_file_name(getParam<FileName>("slip_sys_file_name")),
    _slip_sys_res_prop_file_name(getParam<FileName>("slip_sys_res_prop_file_name")),
    _slip_sys_flow_prop_file_name(getParam<FileName>("slip_sys_flow_prop_file_name")),
    _slip_sys_hard_prop_file_name(getParam<FileName>("slip_sys_hard_prop_file_name")),
    _rtol(getParam<Real>("rtol")),
    _abs_tol(getParam<Real>("abs_tol")),
    _gtol(getParam<Real>("gtol")),
    _slip_incr_tol(getParam<Real>("slip_incr_tol")),
    _maxiter(getParam<unsigned int>("maxiter")),
    _maxiterg(getParam<unsigned int>("maxitergss")),
    _num_slip_sys_flowrate_props(getParam<unsigned int>("num_slip_sys_flowrate_props")),
    _tan_mod_type(getParam<MooseEnum>("tan_mod_type")),
    _intvar_read_type(getParam<MooseEnum>("intvar_read_type")),
    _num_slip_sys_props(getParam<unsigned int>("num_slip_sys_props")),
    _gen_rndm_stress_flag(getParam<bool>("gen_random_stress_flag")),
    _input_rndm_scale_var(getParam<bool>("input_random_scaling_var")),
    _rndm_scale_var(getParam<Real>("random_scaling_var")),
    _rndm_seed(getParam<unsigned int>("random_seed")),
    _max_substep_iter(getParam<unsigned int>("maximum_substep_iteration")),
    _use_line_search(getParam<bool>("use_line_search")),
    _min_lsrch_step(getParam<Real>("min_line_search_step_size")),
    _lsrch_tol(getParam<Real>("line_search_tol")),
    _lsrch_max_iter(getParam<unsigned int>("line_search_maxiter")),
    _lsrch_method(getParam<MooseEnum>("line_search_method")),
    _fp(declareProperty<RankTwoTensor>("fp")), // Plastic deformation gradient
    _fp_old(getMaterialPropertyOld<RankTwoTensor>(
        "fp")), // Plastic deformation gradient of previous increment
    _pk2(declareProperty<RankTwoTensor>("pk2")), // 2nd Piola-Kirchoff Stress
    _pk2_old(getMaterialPropertyOld<RankTwoTensor>(
        "pk2")), // 2nd Piola Kirchoff Stress of previous increment
    _lag_e(declareProperty<RankTwoTensor>("lage")), // Lagrangian strain
    _lag_e_old(
        getMaterialPropertyOld<RankTwoTensor>("lage")), // Lagrangian strain of previous increment
    _gss(declareProperty<std::vector<Real>>("gss")),    // Slip system resistances
    _gss_old(getMaterialPropertyOld<std::vector<Real>>(
        "gss")),                                  // Slip system resistances of previous increment
    _acc_slip(declareProperty<Real>("acc_slip")), // Accumulated slip
    _acc_slip_old(
        getMaterialPropertyOld<Real>("acc_slip")), // Accumulated slip of previous increment
    _update_rot(declareProperty<RankTwoTensor>(
        "update_rot")), // Rotation tensor considering material rotation and crystal orientation
    _deformation_gradient(getMaterialProperty<RankTwoTensor>("deformation_gradient")),
    _deformation_gradient_old(getMaterialPropertyOld<RankTwoTensor>("deformation_gradient")),
    _elasticity_tensor_name(_base_name + "elasticity_tensor"),
    _elasticity_tensor(getMaterialPropertyByName<RankFourTensor>(_elasticity_tensor_name)),
    _crysrot(getMaterialProperty<RankTwoTensor>("crysrot")),
    _mo(_nss * LIBMESH_DIM),
    _no(_nss * LIBMESH_DIM),
    _slip_incr(_nss),
    _tau(_nss),
    _dslipdtau(_nss),
    _s0(_nss),
    _gss_tmp(_nss),
    _gss_tmp_old(_nss),
    _dgss_dsliprate(_nss, _nss)
{
  _err_tol = false;
 
  if (_num_slip_sys_props > 0)
    _slip_sys_props.resize(_nss * _num_slip_sys_props);
 
  _pk2_tmp.zero();
  _delta_dfgrd.zero();
 
  _first_step_iter = false;
  _last_step_iter = false;
  // Initialize variables in the first iteration of substepping
  _first_substep = true;
 
  _read_from_slip_sys_file = false;
  if (_intvar_read_type == "slip_sys_file")
    _read_from_slip_sys_file = true;
 
  if (_read_from_slip_sys_file && !(_num_slip_sys_props > 0))
    mooseError("Crystal Plasticity Error: Specify number of internal variable's initial values to "
               "be read from slip system file");
 
  getSlipSystems();
 
  RankTwoTensor::initRandom(_rndm_seed);
}
 
void
FiniteStrainCrystalPlasticity::initQpStatefulProperties()
{
  _stress[_qp].zero();
 
  _fp[_qp].setToIdentity();
 
  _pk2[_qp].zero();
  _acc_slip[_qp] = 0.0;
  _lag_e[_qp].zero();
 
  _update_rot[_qp].setToIdentity();
 
  initSlipSysProps(); // Initializes slip system related properties
  initAdditionalProps();
}
 
void
FiniteStrainCrystalPlasticity::initSlipSysProps()
{
  switch (_intvar_read_type)
  {
    case 0:
      assignSlipSysRes();
      break;
    case 1:
      readFileInitSlipSysRes();
      break;
    default:
      getInitSlipSysRes();
  }
 
  if (_slip_sys_flow_prop_file_name.length() != 0)
    readFileFlowRateParams();
  else
    getFlowRateParams();
 
  if (_slip_sys_hard_prop_file_name.length() != 0)
    readFileHardnessParams();
  else
    getHardnessParams();
}
 
void
FiniteStrainCrystalPlasticity::assignSlipSysRes()
{
  _gss[_qp].resize(_nss);
 
  for (unsigned int i = 0; i < _nss; ++i)
    _gss[_qp][i] = _slip_sys_props(i);
}
 
// Read initial slip system resistances  from .txt file. See test.
void
FiniteStrainCrystalPlasticity::readFileInitSlipSysRes()
{
  _gss[_qp].resize(_nss);
 
  MooseUtils::checkFileReadable(_slip_sys_res_prop_file_name);
 
  std::ifstream file;
  file.open(_slip_sys_res_prop_file_name.c_str());
 
  for (unsigned int i = 0; i < _nss; ++i)
    if (!(file >> _gss[_qp][i]))
      mooseError("Error FiniteStrainCrystalPlasticity: Premature end of slip_sys_res_prop file");
 
  file.close();
}
 
// Read initial slip system resistances  from .i file
void
FiniteStrainCrystalPlasticity::getInitSlipSysRes()
{
  if (_gprops.size() <= 0)
    mooseError("FiniteStrainCrystalPLasticity: Error in reading slip system resistance properties: "
               "Specify input in .i file or in slip_sys_res_prop_file or in slip_sys_file");
 
  _gss[_qp].resize(_nss, 0.0);
 
  unsigned int num_data_grp = 3; // Number of data per group e.g. start_slip_sys, end_slip_sys,
                                 // value
 
  for (unsigned int i = 0; i < _gprops.size() / num_data_grp; ++i)
  {
    Real vs, ve;
    unsigned int is, ie;
 
    vs = _gprops[i * num_data_grp];
    ve = _gprops[i * num_data_grp + 1];
 
    if (vs <= 0 || ve <= 0)
      mooseError("FiniteStrainCrystalPLasticity: Indices in gss property read must be positive "
                 "integers: is = ",
                 vs,
                 " ie = ",
                 ve);
 
    if (vs != floor(vs) || ve != floor(ve))
      mooseError("FiniteStrainCrystalPLasticity: Error in reading slip system resistances: Values "
                 "specifying start and end number of slip system groups should be integer");
 
    is = static_cast<unsigned int>(vs);
    ie = static_cast<unsigned int>(ve);
 
    if (is > ie)
      mooseError("FiniteStrainCrystalPLasticity: Start index is = ",
                 is,
                 " should be greater than end index ie = ",
                 ie,
                 " in slip system resistance property read");
 
    for (unsigned int j = is; j <= ie; ++j)
      _gss[_qp][j - 1] = _gprops[i * num_data_grp + 2];
  }
 
  for (unsigned int i = 0; i < _nss; ++i)
    if (_gss[_qp][i] <= 0.0)
      mooseError("FiniteStrainCrystalPLasticity: Value of resistance for slip system ",
                 i + 1,
                 " non positive");
}
 
// Read flow rate parameters from .txt file. See test.
void
FiniteStrainCrystalPlasticity::readFileFlowRateParams()
{
  _a0.resize(_nss);
  _xm.resize(_nss);
 
  MooseUtils::checkFileReadable(_slip_sys_flow_prop_file_name);
 
  std::ifstream file;
  file.open(_slip_sys_flow_prop_file_name.c_str());
 
  std::vector<Real> vec;
  vec.resize(_num_slip_sys_flowrate_props);
 
  for (unsigned int i = 0; i < _nss; ++i)
  {
    for (unsigned int j = 0; j < _num_slip_sys_flowrate_props; ++j)
      if (!(file >> vec[j]))
        mooseError(
            "Error FiniteStrainCrystalPlasticity: Premature end of slip_sys_flow_rate_param file");
 
    _a0(i) = vec[0];
    _xm(i) = vec[1];
  }
 
  file.close();
}
 
// Read flow rate parameters from .i file
void
FiniteStrainCrystalPlasticity::getFlowRateParams()
{
  if (_flowprops.size() <= 0)
    mooseError("FiniteStrainCrystalPLasticity: Error in reading flow rate  properties: Specify "
               "input in .i file or a slip_sys_flow_prop_file_name");
 
  _a0.resize(_nss);
  _xm.resize(_nss);
 
  unsigned int num_data_grp = 2 + _num_slip_sys_flowrate_props; // Number of data per group e.g.
                                                                // start_slip_sys, end_slip_sys,
                                                                // value1, value2, ..
 
  for (unsigned int i = 0; i < _flowprops.size() / num_data_grp; ++i)
  {
    Real vs, ve;
    unsigned int is, ie;
 
    vs = _flowprops[i * num_data_grp];
    ve = _flowprops[i * num_data_grp + 1];
 
    if (vs <= 0 || ve <= 0)
      mooseError("FiniteStrainCrystalPLasticity: Indices in flow rate parameter read must be "
                 "positive integers: is = ",
                 vs,
                 " ie = ",
                 ve);
 
    if (vs != floor(vs) || ve != floor(ve))
      mooseError("FiniteStrainCrystalPLasticity: Error in reading flow props: Values specifying "
                 "start and end number of slip system groups should be integer");
 
    is = static_cast<unsigned int>(vs);
    ie = static_cast<unsigned int>(ve);
 
    if (is > ie)
      mooseError("FiniteStrainCrystalPLasticity: Start index is = ",
                 is,
                 " should be greater than end index ie = ",
                 ie,
                 " in flow rate parameter read");
 
    for (unsigned int j = is; j <= ie; ++j)
    {
      _a0(j - 1) = _flowprops[i * num_data_grp + 2];
      _xm(j - 1) = _flowprops[i * num_data_grp + 3];
    }
  }
 
  for (unsigned int i = 0; i < _nss; ++i)
  {
    if (!(_a0(i) > 0.0 && _xm(i) > 0.0))
    {
      mooseWarning(
          "FiniteStrainCrystalPlasticity: Non-positive flow rate parameters ", _a0(i), ",", _xm(i));
      break;
    }
  }
}
 
// Read hardness parameters from .txt file
void
FiniteStrainCrystalPlasticity::readFileHardnessParams()
{
}
 
// Read hardness parameters from .i file
void
FiniteStrainCrystalPlasticity::getHardnessParams()
{
  if (_hprops.size() <= 0)
    mooseError("FiniteStrainCrystalPLasticity: Error in reading hardness properties: Specify input "
               "in .i file or a slip_sys_hard_prop_file_name");
 
  _r = _hprops[0];
  _h0 = _hprops[1];
  _tau_init = _hprops[2];
  _tau_sat = _hprops[3];
}
 
// Read slip systems from file
void
FiniteStrainCrystalPlasticity::getSlipSystems()
{
  Real vec[LIBMESH_DIM];
  std::ifstream fileslipsys;
 
  MooseUtils::checkFileReadable(_slip_sys_file_name);
 
  fileslipsys.open(_slip_sys_file_name.c_str());
 
  for (unsigned int i = 0; i < _nss; ++i)
  {
    // Read the slip normal
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      if (!(fileslipsys >> vec[j]))
        mooseError("Crystal Plasticity Error: Premature end of file reading slip system file \n");
 
    // Normalize the vectors
    Real mag;
    mag = Utility::pow<2>(vec[0]) + Utility::pow<2>(vec[1]) + Utility::pow<2>(vec[2]);
    mag = std::sqrt(mag);
 
    for (unsigned j = 0; j < LIBMESH_DIM; ++j)
      _no(i * LIBMESH_DIM + j) = vec[j] / mag;
 
    // Read the slip direction
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      if (!(fileslipsys >> vec[j]))
        mooseError("Crystal Plasticity Error: Premature end of file reading slip system file \n");
 
    // Normalize the vectors
    mag = Utility::pow<2>(vec[0]) + Utility::pow<2>(vec[1]) + Utility::pow<2>(vec[2]);
    mag = std::sqrt(mag);
 
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      _mo(i * LIBMESH_DIM + j) = vec[j] / mag;
 
    mag = 0.0;
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      mag += _mo(i * LIBMESH_DIM + j) * _no(i * LIBMESH_DIM + j);
 
    if (std::abs(mag) > 1e-8)
      mooseError(
          "Crystal Plasicity Error: Slip direction and normal not orthonormal, System number = ",
          i,
          "\n");
 
    if (_read_from_slip_sys_file)
      for (unsigned int j = 0; j < _num_slip_sys_props; ++j)
        if (!(fileslipsys >> _slip_sys_props(i * _num_slip_sys_props + j)))
          mooseError("Crystal Plasticity Error: Premature end of file reading slip system file - "
                     "check in slip system file read input options/values\n");
  }
 
  fileslipsys.close();
}
 
// Initialize addtional stateful material properties
void
FiniteStrainCrystalPlasticity::initAdditionalProps()
{
}
 
void
FiniteStrainCrystalPlasticity::computeQpStress()
{
  unsigned int substep_iter = 1; // Depth of substepping; Limited to maximum substep iteration
  unsigned int num_substep = 1;  // Calculated from substep_iter as 2^substep_iter
  Real dt_original = _dt;        // Stores original _dt; Reset at the end of solve
  _first_substep = true;         // Initialize variables at substep_iter = 1
 
  if (_max_substep_iter > 1)
  {
    _dfgrd_tmp_old = _deformation_gradient_old[_qp];
    if (_dfgrd_tmp_old.det() == 0)
      _dfgrd_tmp_old.addIa(1.0);
 
    _delta_dfgrd = _deformation_gradient[_qp] - _dfgrd_tmp_old;
    _err_tol = true; // Indicator to continue substepping
  }
 
  // Substepping loop
  while (_err_tol && _max_substep_iter > 1)
  {
    _dt = dt_original / num_substep;
 
    for (unsigned int istep = 0; istep < num_substep; ++istep)
    {
      _first_step_iter = false;
      if (istep == 0)
        _first_step_iter = true;
 
      _last_step_iter = false;
      if (istep == num_substep - 1)
        _last_step_iter = true;
 
      _dfgrd_scale_factor = (static_cast<Real>(istep) + 1) / num_substep;
 
      preSolveQp();
      solveQp();
 
      if (_err_tol)
      {
        substep_iter++;
        num_substep *= 2;
        break;
      }
    }
 
    _first_substep = false; // Prevents reinitialization
    _dt = dt_original;      // Resets dt
 
#ifdef DEBUG
    if (substep_iter > _max_substep_iter)
      mooseWarning("FiniteStrainCrystalPlasticity: Failure with substepping");
#endif
 
    if (!_err_tol || substep_iter > _max_substep_iter)
      postSolveQp(); // Evaluate variables after successful solve or indicate failure
  }
 
  // No substepping
  if (_max_substep_iter == 1)
  {
    preSolveQp();
    solveQp();
    postSolveQp();
  }
}
 
void
FiniteStrainCrystalPlasticity::preSolveQp()
{
  // Initialize variable
  if (_first_substep)
  {
    _Jacobian_mult[_qp].zero(); // Initializes jacobian for preconditioner
    calc_schmid_tensor();
  }
 
  if (_max_substep_iter == 1)
    _dfgrd_tmp = _deformation_gradient[_qp]; // Without substepping
  else
    _dfgrd_tmp = _dfgrd_scale_factor * _delta_dfgrd + _dfgrd_tmp_old;
 
  _err_tol = false;
}
 
void
FiniteStrainCrystalPlasticity::solveQp()
{
  preSolveStatevar();
  solveStatevar();
  if (_err_tol)
    return;
  postSolveStatevar();
}
 
void
FiniteStrainCrystalPlasticity::postSolveQp()
{
  if (_err_tol)
  {
    _err_tol = false;
    if (_gen_rndm_stress_flag)
    {
      if (!_input_rndm_scale_var)
        _rndm_scale_var = _elasticity_tensor[_qp](0, 0, 0, 0);
 
      _stress[_qp] = RankTwoTensor::genRandomSymmTensor(_rndm_scale_var, 1.0);
    }
    else
      mooseError("FiniteStrainCrystalPlasticity: Constitutive failure");
  }
  else
  {
    _stress[_qp] = _fe * _pk2[_qp] * _fe.transpose() / _fe.det();
 
    _Jacobian_mult[_qp] += calcTangentModuli(); // Calculate jacobian for preconditioner
 
    RankTwoTensor iden(RankTwoTensor::initIdentity);
 
    _lag_e[_qp] = _deformation_gradient[_qp].transpose() * _deformation_gradient[_qp] - iden;
    _lag_e[_qp] = _lag_e[_qp] * 0.5;
 
    RankTwoTensor rot;
    rot = get_current_rotation(_deformation_gradient[_qp]); // Calculate material rotation
    _update_rot[_qp] = rot * _crysrot[_qp];
  }
}
 
void
FiniteStrainCrystalPlasticity::preSolveStatevar()
{
  if (_max_substep_iter == 1) // No substepping
  {
    _gss_tmp = _gss_old[_qp];
    _accslip_tmp_old = _acc_slip_old[_qp];
  }
  else
  {
    if (_first_step_iter)
    {
      _gss_tmp = _gss_tmp_old = _gss_old[_qp];
      _accslip_tmp_old = _acc_slip_old[_qp];
    }
    else
      _gss_tmp = _gss_tmp_old;
  }
}
 
void
FiniteStrainCrystalPlasticity::solveStatevar()
{
  Real gmax, gdiff;
  unsigned int iterg;
  std::vector<Real> gss_prev(_nss);
 
  gmax = 1.1 * _gtol;
  iterg = 0;
 
  while (gmax > _gtol && iterg < _maxiterg) // Check for slip system resistance update tolerance
  {
    preSolveStress();
    solveStress();
    if (_err_tol)
      return;
    postSolveStress();
 
    gss_prev = _gss_tmp;
 
    update_slip_system_resistance(); // Update slip system resistance
 
    gmax = 0.0;
    for (unsigned i = 0; i < _nss; ++i)
    {
      gdiff = std::abs(gss_prev[i] - _gss_tmp[i]); // Calculate increment size
 
      if (gdiff > gmax)
        gmax = gdiff;
    }
    iterg++;
  }
 
  if (iterg == _maxiterg)
  {
#ifdef DEBUG
    mooseWarning("FiniteStrainCrystalPLasticity: Hardness Integration error gmax", gmax, "\n");
#endif
    _err_tol = true;
  }
}
 
void
FiniteStrainCrystalPlasticity::postSolveStatevar()
{
  if (_max_substep_iter == 1) // No substepping
  {
    _gss[_qp] = _gss_tmp;
    _acc_slip[_qp] = _accslip_tmp;
  }
  else
  {
    if (_last_step_iter)
    {
      _gss[_qp] = _gss_tmp;
      _acc_slip[_qp] = _accslip_tmp;
    }
    else
    {
      _gss_tmp_old = _gss_tmp;
      _accslip_tmp_old = _accslip_tmp;
    }
  }
}
 
void
FiniteStrainCrystalPlasticity::preSolveStress()
{
  if (_max_substep_iter == 1) // No substepping
  {
    _pk2_tmp = _pk2_old[_qp];
    _fp_old_inv = _fp_old[_qp].inverse();
    _fp_inv = _fp_old_inv;
    _fp_prev_inv = _fp_inv;
  }
  else
  {
    if (_first_step_iter)
    {
      _pk2_tmp = _pk2_tmp_old = _pk2_old[_qp];
      _fp_old_inv = _fp_old[_qp].inverse();
    }
    else
      _pk2_tmp = _pk2_tmp_old;
 
    _fp_inv = _fp_old_inv;
    _fp_prev_inv = _fp_inv;
  }
}
 
void
FiniteStrainCrystalPlasticity::solveStress()
{
  unsigned int iter = 0;
  RankTwoTensor resid, dpk2;
  RankFourTensor jac;
  Real rnorm, rnorm0, rnorm_prev;
 
  calc_resid_jacob(resid, jac); // Calculate stress residual
  if (_err_tol)
  {
#ifdef DEBUG
    mooseWarning(
        "FiniteStrainCrystalPLasticity: Slip increment exceeds tolerance - Element number ",
        _current_elem->id(),
        " Gauss point = ",
        _qp);
#endif
    return;
  }
 
  rnorm = resid.L2norm();
  rnorm0 = rnorm;
 
  while (rnorm > _rtol * rnorm0 && rnorm0 > _abs_tol &&
         iter < _maxiter) // Check for stress residual tolerance
  {
    dpk2 = -jac.invSymm() * resid; // Calculate stress increment
    _pk2_tmp = _pk2_tmp + dpk2;    // Update stress
    calc_resid_jacob(resid, jac);
    internalVariableUpdateNRiteration(); // update _fp_prev_inv
 
    if (_err_tol)
    {
#ifdef DEBUG
      mooseWarning(
          "FiniteStrainCrystalPLasticity: Slip increment exceeds tolerance - Element number ",
          _current_elem->id(),
          " Gauss point = ",
          _qp);
#endif
      return;
    }
 
    rnorm_prev = rnorm;
    rnorm = resid.L2norm();
 
    if (_use_line_search && rnorm > rnorm_prev && !line_search_update(rnorm_prev, dpk2))
    {
#ifdef DEBUG
      mooseWarning("FiniteStrainCrystalPLasticity: Failed with line search");
#endif
      _err_tol = true;
      return;
    }
 
    if (_use_line_search)
      rnorm = resid.L2norm();
 
    iter++;
  }
 
  if (iter >= _maxiter)
  {
#ifdef DEBUG
    mooseWarning("FiniteStrainCrystalPLasticity: Stress Integration error rmax = ", rnorm);
#endif
    _err_tol = true;
  }
}
 
void
FiniteStrainCrystalPlasticity::postSolveStress()
{
  if (_max_substep_iter == 1) // No substepping
  {
    _fp[_qp] = _fp_inv.inverse();
    _pk2[_qp] = _pk2_tmp;
  }
  else
  {
    if (_last_step_iter)
    {
      _fp[_qp] = _fp_inv.inverse();
      _pk2[_qp] = _pk2_tmp;
    }
    else
    {
      _fp_old_inv = _fp_inv;
      _pk2_tmp_old = _pk2_tmp;
    }
  }
}
 
// Update slip system resistance. Overide to incorporate new slip system resistance laws
void
FiniteStrainCrystalPlasticity::update_slip_system_resistance()
{
  updateGss();
}
 
void
FiniteStrainCrystalPlasticity::updateGss()
{
  DenseVector<Real> hb(_nss);
  Real qab;
 
  Real a = _hprops[4]; // Kalidindi
 
  _accslip_tmp = _accslip_tmp_old;
  for (unsigned int i = 0; i < _nss; ++i)
    _accslip_tmp += std::abs(_slip_incr(i));
 
  // Real val = std::cosh(_h0 * _accslip_tmp / (_tau_sat - _tau_init)); // Karthik
  // val = _h0 * std::pow(1.0/val,2.0); // Kalidindi
 
  for (unsigned int i = 0; i < _nss; ++i)
    // hb(i)=val;
    hb(i) = _h0 * std::pow(std::abs(1.0 - _gss_tmp[i] / _tau_sat), a) *
            std::copysign(1.0, 1.0 - _gss_tmp[i] / _tau_sat);
 
  for (unsigned int i = 0; i < _nss; ++i)
  {
    if (_max_substep_iter == 1) // No substepping
      _gss_tmp[i] = _gss_old[_qp][i];
    else
      _gss_tmp[i] = _gss_tmp_old[i];
 
    for (unsigned int j = 0; j < _nss; ++j)
    {
      unsigned int iplane, jplane;
      iplane = i / 3;
      jplane = j / 3;
 
      if (iplane == jplane) // Kalidindi
        qab = 1.0;
      else
        qab = _r;
 
      _gss_tmp[i] += qab * hb(j) * std::abs(_slip_incr(j));
      _dgss_dsliprate(i, j) = qab * hb(j) * std::copysign(1.0, _slip_incr(j)) * _dt;
    }
  }
}
 
// Calculates stress residual equation and jacobian
void
FiniteStrainCrystalPlasticity::calc_resid_jacob(RankTwoTensor & resid, RankFourTensor & jac)
{
  calcResidual(resid);
  if (_err_tol)
    return;
  calcJacobian(jac);
}
 
void
FiniteStrainCrystalPlasticity::calcResidual(RankTwoTensor & resid)
{
  RankTwoTensor iden(RankTwoTensor::initIdentity), ce, ee, ce_pk2, eqv_slip_incr, pk2_new;
 
  _fe = _dfgrd_tmp * _fp_prev_inv; // _fp_inv  ==> _fp_prev_inv
 
  ce = _fe.transpose() * _fe;
  ce_pk2 = ce * _pk2_tmp;
  ce_pk2 = ce_pk2 / _fe.det();
 
  // Calculate Schmid tensor and resolved shear stresses
  for (unsigned int i = 0; i < _nss; ++i)
    _tau(i) = ce_pk2.doubleContraction(_s0[i]);
 
  getSlipIncrements(); // Calculate dslip,dslipdtau
 
  if (_err_tol)
    return;
 
  eqv_slip_incr.zero();
  for (unsigned int i = 0; i < _nss; ++i)
    eqv_slip_incr += _s0[i] * _slip_incr(i);
 
  eqv_slip_incr = iden - eqv_slip_incr;
  _fp_inv = _fp_old_inv * eqv_slip_incr;
  _fe = _dfgrd_tmp * _fp_inv;
 
  ce = _fe.transpose() * _fe;
  ee = ce - iden;
  ee *= 0.5;
 
  pk2_new = _elasticity_tensor[_qp] * ee;
 
  resid = _pk2_tmp - pk2_new;
}
 
void
FiniteStrainCrystalPlasticity::calcJacobian(RankFourTensor & jac)
{
  RankFourTensor dfedfpinv, deedfe, dfpinvdpk2;
 
  std::vector<RankTwoTensor> dtaudpk2(_nss), dfpinvdslip(_nss);
 
  for (unsigned int i = 0; i < _nss; ++i)
  {
    dtaudpk2[i] = _s0[i];
    dfpinvdslip[i] = -_fp_old_inv * _s0[i];
  }
 
  for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
        dfedfpinv(i, j, k, j) = _dfgrd_tmp(i, k);
 
  for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
      {
        deedfe(i, j, k, i) = deedfe(i, j, k, i) + _fe(k, j) * 0.5;
        deedfe(i, j, k, j) = deedfe(i, j, k, j) + _fe(k, i) * 0.5;
      }
 
  for (unsigned int i = 0; i < _nss; ++i)
    dfpinvdpk2 += (dfpinvdslip[i] * _dslipdtau(i)).outerProduct(dtaudpk2[i]);
 
  jac =
      RankFourTensor::IdentityFour() - (_elasticity_tensor[_qp] * deedfe * dfedfpinv * dfpinvdpk2);
}
 
// Calculate slip increment,dslipdtau. Override to modify.
void
FiniteStrainCrystalPlasticity::getSlipIncrements()
{
  for (unsigned int i = 0; i < _nss; ++i)
  {
    _slip_incr(i) = _a0(i) * std::pow(std::abs(_tau(i) / _gss_tmp[i]), 1.0 / _xm(i)) *
                    std::copysign(1.0, _tau(i)) * _dt;
    if (std::abs(_slip_incr(i)) > _slip_incr_tol)
    {
      _err_tol = true;
#ifdef DEBUG
      mooseWarning("Maximum allowable slip increment exceeded ", std::abs(_slip_incr(i)));
#endif
      return;
    }
  }
 
  for (unsigned int i = 0; i < _nss; ++i)
    _dslipdtau(i) = _a0(i) / _xm(i) *
                    std::pow(std::abs(_tau(i) / _gss_tmp[i]), 1.0 / _xm(i) - 1.0) / _gss_tmp[i] *
                    _dt;
}
 
// Calls getMatRot to perform RU factorization of a tensor.
RankTwoTensor
FiniteStrainCrystalPlasticity::get_current_rotation(const RankTwoTensor & a)
{
  return getMatRot(a);
}
 
// Performs RU factorization of a tensor
RankTwoTensor
FiniteStrainCrystalPlasticity::getMatRot(const RankTwoTensor & a)
{
  RankTwoTensor rot;
  RankTwoTensor c, diag, evec;
  PetscScalar cmat[LIBMESH_DIM][LIBMESH_DIM], work[10];
  PetscReal w[LIBMESH_DIM];
  PetscBLASInt nd = LIBMESH_DIM, lwork = 10, info;
 
  c = a.transpose() * a;
 
  for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      cmat[i][j] = c(i, j);
 
  LAPACKsyev_("V", "U", &nd, &cmat[0][0], &nd, w, work, &lwork, &info);
 
  if (info != 0)
    mooseError("FiniteStrainCrystalPLasticity: DSYEV function call in getMatRot function failed");
 
  diag.zero();
 
  for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
    diag(i, i) = std::sqrt(w[i]);
 
  for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      evec(i, j) = cmat[i][j];
 
  rot = a * ((evec.transpose() * diag * evec).inverse());
 
  return rot;
}
 
// Calculates tangent moduli which is used for global solve
void
FiniteStrainCrystalPlasticity::computeQpElasticityTensor()
{
}
 
RankFourTensor
FiniteStrainCrystalPlasticity::calcTangentModuli()
{
  RankFourTensor tan_mod;
 
  switch (_tan_mod_type)
  {
    case 0:
      tan_mod = elastoPlasticTangentModuli();
      break;
    default:
      tan_mod = elasticTangentModuli();
  }
 
  return tan_mod;
}
 
void
FiniteStrainCrystalPlasticity::calc_schmid_tensor()
{
  DenseVector<Real> mo(LIBMESH_DIM * _nss), no(LIBMESH_DIM * _nss);
 
  // Update slip direction and normal with crystal orientation
  for (unsigned int i = 0; i < _nss; ++i)
  {
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
    {
      mo(i * LIBMESH_DIM + j) = 0.0;
      for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
        mo(i * LIBMESH_DIM + j) =
            mo(i * LIBMESH_DIM + j) + _crysrot[_qp](j, k) * _mo(i * LIBMESH_DIM + k);
    }
 
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
    {
      no(i * LIBMESH_DIM + j) = 0.0;
      for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
        no(i * LIBMESH_DIM + j) =
            no(i * LIBMESH_DIM + j) + _crysrot[_qp](j, k) * _no(i * LIBMESH_DIM + k);
    }
  }
 
  // Calculate Schmid tensor and resolved shear stresses
  for (unsigned int i = 0; i < _nss; ++i)
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
        _s0[i](j, k) = mo(i * LIBMESH_DIM + j) * no(i * LIBMESH_DIM + k);
}
 
RankFourTensor
FiniteStrainCrystalPlasticity::elastoPlasticTangentModuli()
{
  RankFourTensor tan_mod;
  RankTwoTensor pk2fet, fepk2;
  RankFourTensor deedfe, dsigdpk2dfe;
 
  // Fill in the matrix stiffness material property
 
  for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
      {
        deedfe(i, j, k, i) = deedfe(i, j, k, i) + _fe(k, j) * 0.5;
        deedfe(i, j, k, j) = deedfe(i, j, k, j) + _fe(k, i) * 0.5;
      }
 
  dsigdpk2dfe = _fe.mixedProductIkJl(_fe) * _elasticity_tensor[_qp] * deedfe;
 
  pk2fet = _pk2_tmp * _fe.transpose();
  fepk2 = _fe * _pk2_tmp;
 
  for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
    for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
      for (unsigned int l = 0; l < LIBMESH_DIM; ++l)
      {
        tan_mod(i, j, i, l) = tan_mod(i, j, i, l) + pk2fet(l, j);
        tan_mod(i, j, j, l) = tan_mod(i, j, j, l) + fepk2(i, l);
      }
 
  tan_mod += dsigdpk2dfe;
 
  Real je = _fe.det();
  if (je > 0.0)
    tan_mod /= je;
 
  return tan_mod;
}
 
RankFourTensor
FiniteStrainCrystalPlasticity::elasticTangentModuli()
{
  return _elasticity_tensor[_qp]; // update jacobian_mult
}
 
bool
FiniteStrainCrystalPlasticity::line_search_update(const Real rnorm_prev, const RankTwoTensor dpk2)
{
  if (_lsrch_method == "CUT_HALF")
  {
    Real rnorm;
    RankTwoTensor resid;
    Real step = 1.0;
 
    do
    {
      _pk2_tmp = _pk2_tmp - step * dpk2;
      step /= 2.0;
      _pk2_tmp = _pk2_tmp + step * dpk2;
 
      calcResidual(resid);
      rnorm = resid.L2norm();
    } while (rnorm > rnorm_prev && step > _min_lsrch_step);
 
    if (rnorm > rnorm_prev && step <= _min_lsrch_step)
      return false;
 
    return true;
  }
  else if (_lsrch_method == "BISECTION")
  {
    unsigned int count = 0;
    Real step_a = 0.0;
    Real step_b = 1.0;
    Real step = 1.0;
    Real s_m = 1000.0;
    Real rnorm = 1000.0;
 
    RankTwoTensor resid;
    calcResidual(resid);
    Real s_b = resid.doubleContraction(dpk2);
    Real rnorm1 = resid.L2norm();
    _pk2_tmp = _pk2_tmp - dpk2;
    calcResidual(resid);
    Real s_a = resid.doubleContraction(dpk2);
    Real rnorm0 = resid.L2norm();
    _pk2_tmp = _pk2_tmp + dpk2;
 
    if ((rnorm1 / rnorm0) < _lsrch_tol || s_a * s_b > 0)
    {
      calcResidual(resid);
      return true;
    }
 
    while ((rnorm / rnorm0) > _lsrch_tol && count < _lsrch_max_iter)
    {
      _pk2_tmp = _pk2_tmp - step * dpk2;
      step = 0.5 * (step_b + step_a);
      _pk2_tmp = _pk2_tmp + step * dpk2;
      calcResidual(resid);
      s_m = resid.doubleContraction(dpk2);
      rnorm = resid.L2norm();
 
      if (s_m * s_a < 0.0)
      {
        step_b = step;
        s_b = s_m;
      }
      if (s_m * s_b < 0.0)
      {
        step_a = step;
        s_a = s_m;
      }
      count++;
    }
 
    if ((rnorm / rnorm0) < _lsrch_tol && count < _lsrch_max_iter)
      return true;
 
    return false;
  }
  else
  {
    mooseError("Line search meothod is not provided.");
    return false;
  }
}
 
void
FiniteStrainCrystalPlasticity::internalVariableUpdateNRiteration()
{
  _fp_prev_inv = _fp_inv; // update _fp_prev_inv
}