DiffusiveCavityGrowthRate

Source: models/solid_mechanics/traction_separation_law/DiffusiveCavityGrowthRate.py

Grain-boundary-diffusion-controlled growth of a single cavity,

\[ \dot{V} = \frac{8 \pi \mathcal{D} \langle T_n \rangle}{q(f^*)}, \qquad q(f) = 2\ln\frac{1}{f} - (3-f)(1-f), \]

with \(\mathcal{D} = D_B \delta_B \Omega / (k \theta)\) the lumped grain boundary diffusion parameter. The \(8\pi\) prefactor is tied to this form of \(q\).

This is the only cavity growth mechanism in the simplified Sham-Needleman model: creep-assisted growth and the Rice constraint are both omitted. It is a separate leaf precisely so further growth terms can be summed onto it (via a ScalarLinearCombination) without touching the damage or opening laws that consume \(\dot{V}\).

The Macaulay bracket on \(T_n\) disables sintering under compression, which also keeps \(f\) away from the \(f \to 0\) singularity in the damage law.

Inputs

normal_traction — input · Scalar · required

Normal traction across the interface

effective_cavity_fraction — input · Scalar · required

Effective cavitated area fraction driving the softening function q

Outputs

cavity_volume_rate — output · Scalar · required

Rate of change of a single cavity volume

Parameters

diffusivity — parameter · Scalar · required

Lumped grain boundary diffusion parameter D = D_B delta_B Omega / (k theta)