KocksMeckingFlowViscosity.cxx

// Copyright 2023, UChicago Argonne, LLC
// All Rights Reserved
// Software Name: NEML2 -- the New Engineering material Model Library, version 2
// By: Argonne National Laboratory
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#include "neml2/models/solid_mechanics/KocksMeckingFlowViscosity.h"
 
namespace neml2
{
register_NEML2_object(KocksMeckingFlowViscosity);
 
OptionSet
KocksMeckingFlowViscosity::expected_options()
{
  OptionSet options = NonlinearParameter<Scalar>::expected_options();
  options.doc() =
      "Calculates the temperature-dependent flow viscosity for a Perzyna-type model using the "
      "Kocks-Mecking model.  The value is \\f$ \\eta = \\exp{B} \\mu "
      "\\dot{\\varepsilon}_0^\\frac{-k T A}{\\mu b^3} \\f$ with \\f$ \\mu "
      "\\f$ the shear modulus, \\f$ \\dot{\\varepsilon}_0 \\f$ a reference strain rate,  \\f$ b "
      "\\f$ the Burgers vector, "
      "\\f$  k\\f$ the Boltzmann constant, "
      "\\f$ T \\f$ absolute temperature, \\f$ A \\f$ the Kocks-Mecking slope parameter, and \\f$ B "
      "\\f$ the Kocks-Mecking intercept parameter.";
 
  options.set<CrossRef<Scalar>>("A");
  options.set("A").doc() = "The Kocks-Mecking slope parameter";
  options.set<CrossRef<Scalar>>("B");
  options.set("B").doc() = "The Kocks-Mecking intercept parameter";
  options.set<CrossRef<Scalar>>("shear_modulus");
  options.set("shear_modulus").doc() = "The shear modulus";
 
  options.set<Real>("eps0");
  options.set("eps0").doc() = "The reference strain rate";
 
  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;
}
 
KocksMeckingFlowViscosity::KocksMeckingFlowViscosity(const OptionSet & options)
  : NonlinearParameter<Scalar>(options),
    _A(declare_parameter<Scalar>("A", "A")),
    _B(declare_parameter<Scalar>("B", "B")),
    _mu(declare_parameter<Scalar>("shear_modulus", "shear_modulus")),
    _eps0(options.get<Real>("eps0")),
    _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
KocksMeckingFlowViscosity::set_value(bool out, bool dout_din, bool d2out_din2)
{
  auto post = math::pow(_eps0, _k * _T * _A / (_mu * _b3));
 
  if (out)
    _p = math::exp(_B) * _mu * post;
 
  if (dout_din)
  {
    _p.d(_T) = _A * math::exp(_B) * _k * std::log(_eps0) * post / _b3;
 
    if (const auto A = nl_param("A"))
      _p.d(*A) = math::exp(_B) * _k * _T * std::log(_eps0) * post / _b3;
 
    if (const auto B = nl_param("B"))
      _p.d(*B) = math::exp(_B) * _mu * post;
 
    if (const auto mu = nl_param("mu"))
      _p.d(*mu) = math::exp(_B) * post * (_b3 * _mu - _A * _k * _T * std::log(_eps0)) / (_b3 * _mu);
  }
 
  if (d2out_din2)
  {
    // T
    _p.d(_T, _T) = math::pow(_A * _k * std::log(_eps0) / _b3, 2.0) * math::exp(_B) * post / _mu;
 
    if (const auto A = nl_param("A"))
      _p.d(_T, *A) = math::exp(_B) * _k * std::log(_eps0) * post * (_A * _k * _T + _b3 * _mu) /
                     (_b3 * _b3 * _mu);
 
    if (const auto B = nl_param("B"))
      _p.d(_T, *B) = _A * math::exp(_B) * _k * std::log(_eps0) * post / _b3;
 
    if (const auto mu = nl_param("mu"))
      _p.d(_T, *mu) =
          -math::pow(_A * _k * std::log(_eps0) / (_b3 * _mu), 2.0) * math::exp(_B) * _T * post;
 
    // A
    if (const auto A = nl_param("A"))
    {
      _p.d(*A, _T) = math::exp(_B) * _k * std::log(_eps0) * post * (_A * _k * _T + _b3 * _mu) /
                     (_b3 * _b3 * _mu);
 
      _p.d(*A, *A) = math::exp(_B) * math::pow(_k * _T * std::log(_eps0) / _b3, 2.0) * post / _mu;
 
      if (const auto B = nl_param("B"))
        _p.d(*A, *B) = math::exp(_B) * _k * _T * std::log(_eps0) * post / _b3;
 
      if (const auto mu = nl_param("mu"))
        _p.d(*A, *mu) =
            -_A * math::exp(_B) * math::pow(_k * _T * std::log(_eps0) / (_b3 * _mu), 2.0) * post;
    }
 
    // B
    if (const auto B = nl_param("B"))
    {
      _p.d(*B, _T) = _A * math::exp(_B) * _k * std::log(_eps0) * post / _b3;
 
      if (const auto A = nl_param("A"))
        _p.d(*B, *A) = math::exp(_B) * _k * _T * std::log(_eps0) * post / _b3;
 
      _p.d(*B, *B) = math::exp(_B) * _mu * post;
 
      if (const auto mu = nl_param("mu"))
        _p.d(*B, *mu) =
            math::exp(_B) * post * (_b3 * _mu - _A * _k * _T * std::log(_eps0)) / (_b3 * _mu);
    }
 
    // mu
    if (const auto mu = nl_param("mu"))
    {
      _p.d(*mu, _T) =
          -math::exp(_B) * math::pow(_A * _k * std::log(_eps0) / (_b3 * _mu), 2.0) * _T * post;
 
      if (const auto A = nl_param("A)"))
        _p.d(*mu, *A) =
            -_A * math::exp(_B) * math::pow(_k * _T * std::log(_eps0) / (_b3 * _mu), 2.0) * post;
 
      if (const auto B = nl_param("B"))
        _p.d(*mu, *B) =
            math::exp(_B) * post * (_b3 * _mu - _A * _k * _T * std::log(_eps0)) / (_b3 * _mu);
 
      _p.d(*mu, *mu) = -math::pow(_A * _k * _T * std::log(_eps0) / (_b3 * _mu), 2.0) *
                       math::exp(_B) * post / _mu;
    }
  }
}
} // namespace neml2