GrainBoundarySlidingRate

Source: models/solid_mechanics/traction_separation_law/GrainBoundarySlidingRate.py

Linear-viscous grain boundary sliding, softened by the cavitated area fraction,

\[ \dot{[\![u]\!]}_t^v = \frac{T_t}{(1 - f^*)\, \eta}. \]

\(\eta\) is the grain boundary sliding viscosity and \((1 - f^*)\) is the uncavitated ligament fraction, so the boundary slides ever more freely as cavities coalesce. The factor vanishes at \(f^* = 1\); keeping the effective fraction strictly below one (see EffectiveCavityFraction) is what keeps this rate finite.

This is the dashpot half of the sliding branch. The elastic half lives in ShamNeedlemanTraction, which places the two in series.

Inputs

shear_traction — input · Scalar · required

Shear traction across the interface

effective_cavity_fraction — input · Scalar · required

Effective cavitated area fraction softening the sliding viscosity

Outputs

viscous_sliding_rate — output · Scalar · required

Rate of the viscous part of the sliding jump

Parameters

sliding_viscosity — parameter · Scalar · required

Grain boundary sliding viscosity