Regime switching model¶

Overview¶

This model selects a stress and history update function from a input list of NEMLModel_sd objects based on a normalized activation energy. This activation energy is a function of strain rate and temperature and the form of the normalized energy comes from the work of Kocks and Mecking [KM2003].

The input to the metamodel is a list of material models and a corresponding list of activation energy cutoffs $\left[g_1, g_2, \dots, g_n \right]$ . When the caller requests a stress and history update this metamodel first calculates the normalized activation energy

$g = \frac{k T}{\mu b^3} \ln\frac{\dot{\varepsilon}_0}{\dot{\varepsilon}}.$

Here $k$ is the Boltzmann constant, $T$ the current value of temperature, $\mu$ the current, temperature-dependent shear modulus, $b$ a Burgers vector, $\dot{\varepsilon}_0$ a reference strain rate, and $\dot{\varepsilon}$ the current equivalent strain rate, computed as

$\dot{\varepsilon} = \frac{\varepsilon_{n+1} - \varepsilon_{n}}{t_{n+1} - t_{n}}$

with

$\varepsilon_{n+1} = \sqrt{\frac{2}{3}\bm{\varepsilon}_{n+1}:\bm{\varepsilon}_{n+1}}$

and similarly for state n.

If $g<g_1$ the metamodel selects the first model in the input list, if $g \ge g_n$ the metamodel selects the last model in the input, and for values in between the model selects model i such that $g_{i-1} < g \ge g_{i}$ .

The metamodel dispatches calls for the history evolution, algorithmic tangent, and energy likewise.

The Kocks-Mecking metamodel requires each model in the input list to use compatible history variables. That is, all the possible base model options must use the same history variables. This means the metamodel maintains only one copy of the history variables, which are common for all the base models. The history evolution is therefore consistent no matter which base model is selected for a particular stress update.

Warning

The KMRegimeModel metamodel does not check for consitency of history for the base models, beyond checking to make sure that each model uses the same number of history variables.

Parameters¶

Parameter	Object type	Description	Default
`elastic`	`neml::LinearElasticModel`	Temperature dependent elastic constants	No
`models`	`std::vector<neml::NEMLModel_sd>`	Vector of base models	No
`gs`	`std::vector<double>`	Corresponding vector of energies	No
`kboltz`	`double`	Boltzmann’s constant	No
`b`	`double`	Burger’s vector length	No
`eps0`	`double`	Reference strain rate	No
`alpha`	`neml::Interpolate`	Temperature dependent instantaneous CTE	`0.0`

Class description¶

class KMRegimeModel : public neml::NEMLModel_sd ¶

Combines multiple small strain integrators based on regimes of rate-dependent behavior.

Public Functions

KMRegimeModel(ParameterSet &params)¶: Parameters are an elastic model, a vector of valid NEMLModel_sd objects, the transition activation energies, the Boltzmann constant in appropriate units, a Burgers vector for normalization, a reference strain rate, and the CTE.

virtual void update_sd_actual(const double *const e_np1, const double *const e_n, double T_np1, double T_n, double t_np1, double t_n, double *const s_np1, const double *const s_n, double *const h_np1, const double *const h_n, double *const A_np1, double &u_np1, double u_n, double &p_np1, double p_n)¶: The small strain stress update.

virtual void populate_state(History &hist) const¶: Populate internal variables.

virtual void init_state(History &hist) const¶: Initialize history at time zero.

virtual void set_elastic_model(std::shared_ptr<LinearElasticModel> emodel)¶: Set a new elastic model.

Public Static Functions

static std::string type()¶: Type for the object system.

static ParameterSet parameters()¶: Parameters for the object system.

static std::unique_ptr<NEMLObject> initialize(ParameterSet &params)¶: Setup from a ParameterSet.