ChabochePlasticHardening.cxx

// Copyright 2023, UChicago Argonne, LLC
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// Software Name: NEML2 -- the New Engineering material Model Library, version 2
// By: Argonne National Laboratory
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#include "neml2/models/solid_mechanics/ChabochePlasticHardening.h"
#include "neml2/tensors/SSR4.h"
 
namespace neml2
{
register_NEML2_object(ChabochePlasticHardening);
 
OptionSet
ChabochePlasticHardening::expected_options()
{
  OptionSet options = FlowRule::expected_options();
  options.doc() +=
      " This object defines the non-associative Chaboche kinematic hardening. In the Chaboche "
      "model, back stress is directly treated as an internal variable. Rate of back stress is "
      "given as \\f$ \\dot{\\boldsymbol{X}} = \\left( \\frac{2}{3} C \\frac{\\partial f}{\\partial "
      "\\boldsymbol{M}} - g \\boldsymbol{X} \\right) \\dot{\\gamma} - A \\lVert \\boldsymbol{X} "
      "\\rVert^{a - 1} \\boldsymbol{X} \\f$, including kinematic hardening, dynamic recovery, and "
      "static recovery. \\f$ \\frac{\\partial f}{\\partial \\boldsymbol{M}} \\f$ is the flow "
      "direction, \\f$ \\dot{\\gamma} \\f$ is the flow rate, and \\f$ C \\f$, \\f$ g \\f$, \\f$ A "
      "\\f$, and \\f$ a \\f$ are material parameters.";
 
  options.set<VariableName>("back_stress") = VariableName("state", "internal", "X");
  options.set("back_stress").doc() = "Back stress";
 
  options.set<VariableName>("flow_direction") = VariableName("state", "internal", "NM");
  options.set("flow_direction").doc() = "Flow direction";
 
  options.set<CrossRef<Scalar>>("C");
  options.set("C").doc() = "Kinematic hardening coefficient";
 
  options.set<CrossRef<Scalar>>("g");
  options.set("g").doc() = "Dynamic recovery coefficient";
 
  options.set<CrossRef<Scalar>>("A");
  options.set("A").doc() = "Static recovery prefactor";
 
  options.set<CrossRef<Scalar>>("a");
  options.set("a").doc() = "Static recovery exponent";
 
  return options;
}
 
ChabochePlasticHardening::ChabochePlasticHardening(const OptionSet & options)
  : FlowRule(options),
    _X(declare_input_variable<SR2>("back_stress")),
    _NM(declare_input_variable<SR2>("flow_direction")),
    _X_dot(declare_output_variable<SR2>(_X.name().with_suffix("_rate"))),
    _C(declare_parameter<Scalar>("C", "C")),
    _g(declare_parameter<Scalar>("g", "g")),
    _A(declare_parameter<Scalar>("A", "A")),
    _a(declare_parameter<Scalar>("a", "a"))
{
}
 
void
ChabochePlasticHardening::set_value(bool out, bool dout_din, bool d2out_din2)
{
  neml_assert_dbg(!d2out_din2, "Chaboche model doesn't implement second derivatives.");
 
  // The effective stress
  auto s = SR2(_X).norm(NEML2_EPS);
  // The part that's proportional to the plastic strain rate
  auto g_term = 2.0 / 3.0 * _C * _NM - _g * _X;
 
  if (out)
  {
    // The static recovery term
    auto s_term = -_A * math::pow(s, _a - 1) * _X;
    _X_dot = g_term * _gamma_dot + s_term;
  }
 
  if (dout_din)
  {
    auto I = SR2::identity_map(options());
 
    _X_dot.d(_gamma_dot) = g_term;
    _X_dot.d(_NM) = 2.0 / 3.0 * _C * _gamma_dot * I;
    _X_dot.d(_X) = -_g * _gamma_dot * I -
                   _A * math::pow(s, _a - 3) * ((_a - 1) * SR2(_X).outer(SR2(_X)) + s * s * I);
  }
}
 
} // namespace neml2