CavityNucleationRate

Source: models/solid_mechanics/traction_separation_law/CavityNucleationRate.py

Continuous, stress-driven nucleation of grain boundary cavities,

\[ \dot{N} = F_N \left\langle \frac{T_n}{\Sigma_0} \right\rangle^{\beta} \dot{\varepsilon}, \]

with \(F_N\) the nucleation coefficient, \(\Sigma_0\) a reference stress and \(\beta\) the stress exponent. The Macaulay bracket switches nucleation off under compression.

\(\dot{\varepsilon}\) is an ordinary input, so it may be fulfilled either by SlidingDrivenStrainRate (the local surrogate) or by a true bulk strain rate supplied from the input file.

Leaving this model out of a composition and wiring the damage law without a cavity_density_rate gives the same model without nucleation, with \(N\) held at its initial value.

Inputs

normal_traction — input · Scalar · required

Normal traction across the interface

strain_rate — input · Scalar · required

Strain rate driving nucleation

Outputs

cavity_density_rate — output · Scalar · required

Rate of change of the cavity number density

Parameters

nucleation_coefficient — parameter · Scalar · required

Nucleation coefficient F_N

reference_stress — parameter · Scalar · required

Nucleation reference stress Sigma_0

exponent — parameter · Scalar · required

Nucleation stress exponent beta