SimplePrecipitateGrowth

Source: models/solid_mechanics/crystal_plasticity/SimplePrecipitateGrowth.py

Simplified, volume-conserving coarsening of a precipitate population, defined by \(\dot{R} = \dfrac{K}{3 R^2}, \qquad \dot{N} = -\dfrac{K}{R^3}\) where \(R\) is the mean precipitate radius, \(N\) is the precipitate number density and \(K\) is the coarsening coefficient.

\(K\) is a promotable parameter, so it may be supplied as a constant or driven by another model – an ArrheniusParameter for the usual thermally activated form.

Note \(\dot{N}\) does not depend on \(N\), following the issue specification; the two rates are emitted by one leaf because they share the single coefficient \(K\) and the same \(R\).

Inputs

precipitate_radius — input · Scalar · required

Mean precipitate radius

precipitate_density — input · Scalar · required

Precipitate number density

Outputs

precipitate_radius_rate — output · Scalar · default precipitate_radius_rate

Optional name for the derived output (defaults to ‘precipitate_radius_rate’, i.e. the ‘precipitate_radius’ variable name with the ‘_rate’ suffix).

precipitate_density_rate — output · Scalar · default precipitate_density_rate

Optional name for the derived output (defaults to ‘precipitate_density_rate’, i.e. the ‘precipitate_density’ variable name with the ‘_rate’ suffix).

Parameters

coarsening_coefficient — parameter · Scalar · required

Coarsening coefficient