KocksMeckingRateSensitivity.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/KocksMeckingRateSensitivity.h"
 
namespace neml2
{
register_NEML2_object(KocksMeckingRateSensitivity);
 
OptionSet
KocksMeckingRateSensitivity::expected_options()
{
  OptionSet options = NonlinearParameter<Scalar>::expected_options();
  options.doc() =
      "Calculates the temperature-dependent rate sensitivity for a Perzyna-type model using the "
      "Kocks-Mecking model.  The value is \\f$ n = \\frac{\\mu b^3}{k T A} \\f$ with \\f$ \\mu "
      "\\f$ the shear modulus, \\f$ b \\f$ the Burgers vector, \\f$  k\\f$ the Boltzmann constant, "
      "\\f$ T \\f$ absolute temperature, and \\f$ A \\f$ the Kocks-Mecking slope parameter.";
 
  options.set<CrossRef<Scalar>>("A");
  options.set("A").doc() = "The Kocks-Mecking slope parameter";
  options.set<CrossRef<Scalar>>("shear_modulus");
  options.set("shear_modulus").doc() = "The shear modulus";
 
  options.set<Real>("k");
  options.set("k").doc() = "Boltzmann constant";
  options.set<Real>("b");
  options.set("b").doc() = "The Burgers vector";
 
  options.set<VariableName>("temperature") = VariableName("forces", "T");
  options.set("temperature").doc() = "Absolute temperature";
  return options;
}
 
KocksMeckingRateSensitivity::KocksMeckingRateSensitivity(const OptionSet & options)
  : NonlinearParameter<Scalar>(options),
    _A(declare_parameter<Scalar>("A", "A")),
    _mu(declare_parameter<Scalar>("shear_modulus", "shear_modulus")),
    _k(options.get<Real>("k")),
    _b3(options.get<Real>("b") * options.get<Real>("b") * options.get<Real>("b")),
    _T(declare_input_variable<Scalar>("temperature"))
{
}
 
void
KocksMeckingRateSensitivity::set_value(bool out, bool dout_din, bool d2out_din2)
{
  if (out)
    _p = -_mu * _b3 / (_k * _T * _A);
 
  if (dout_din)
  {
    _p.d(_T) = _b3 * _mu / (_A * _k * _T * _T);
    if (const auto mu = nl_param("shear_modulus"))
      _p.d(*mu) = -_b3 / (_A * _k * _T);
    if (const auto A = nl_param("A"))
      _p.d(*A) = -_b3 * _mu / (_A * _A * _k * _T);
  }
 
  if (d2out_din2)
  {
    // T, T
    _p.d(_T, _T) = -2.0 * _b3 * _mu / (_A * _k * _T * _T * _T);
    if (const auto A = nl_param("A"))
    {
      // A, A
      _p.d(*A, *A) = -2.0 * _b3 * _mu / (_A * _A * _A * _k * _T);
      // A, T and T, A
      auto AT = -_b3 * _mu / (_A * _A * _k * _T * _T);
      _p.d(*A, _T) = AT;
      _p.d(_T, *A) = AT;
    }
    if (const auto mu = nl_param("mu"))
    {
      // mu, T and T, mu
      auto MT = _b3 / (_A * _k * _T * _T);
      _p.d(*mu, _T) = MT;
      _p.d(_T, *mu) = MT;
 
      if (const auto A = nl_param("A"))
      {
        // mu, A and A, mu
        auto MA = _b3 / (_A * _A * _k * _T);
        _p.d(*mu, *A) = MA;
        _p.d(*A, *mu) = MA;
      }
    }
  }
}
} // namespace neml2