ArrheniusParameter.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/ArrheniusParameter.h"
 
namespace neml2
{
register_NEML2_object(ArrheniusParameter);
 
OptionSet
ArrheniusParameter::expected_options()
{
  OptionSet options = NonlinearParameter<Scalar>::expected_options();
  options.doc() = "Define the nonlinear parameter as a function of temperature according to the "
                  "Arrhenius law \\f$ p = p_0 \\exp \\left( -\\frac{Q}{RT} \\right) \\f$, where "
                  "\\f$ p_0 \\f$ is the reference value, \\f$ Q \\f$ is the activation energy, "
                  "\\f$ R \\f$ is the ideal gas constant, and \\f$ T \\f$ is the temperature.";
 
  options.set<CrossRef<Scalar>>("reference_value");
  options.set("reference_value").doc() = "Reference value";
 
  options.set<CrossRef<Scalar>>("activation_energy");
  options.set("activation_energy").doc() = "Activation energy";
 
  options.set<Real>("ideal_gas_constant");
  options.set("ideal_gas_constant").doc() = "The ideal gas constant";
 
  options.set<VariableName>("temperature") = VariableName("forces", "T");
  options.set("temperature").doc() = "Temperature";
 
  return options;
}
 
ArrheniusParameter::ArrheniusParameter(const OptionSet & options)
  : NonlinearParameter<Scalar>(options),
    _p0(declare_parameter<Scalar>("p0", "reference_value")),
    _Q(declare_parameter<Scalar>("Q", "activation_energy")),
    _R(options.get<Real>("ideal_gas_constant")),
    _T(declare_input_variable<Scalar>("temperature"))
{
}
 
void
ArrheniusParameter::set_value(bool out, bool dout_din, bool d2out_din2)
{
  const auto p = _p0 * math::exp(-_Q / _R / _T);
 
  if (out)
    _p = p;
 
  if (dout_din || d2out_din2)
  {
    const auto dp_dT = p * _Q / _R / _T / _T;
 
    if (dout_din)
      _p.d(_T) = dp_dT;
 
    if (d2out_din2)
      _p.d(_T, _T) = dp_dT * _Q / _R / _T / _T - 2 * p * _Q / _R / _T / _T / _T;
  }
}
} // namespace neml2