Front propagation at the onset of plastic yielding

The existence of a finite threshold, the yield stress, for the onset of plastic yielding is a universal feature of plasticity. This jamming-unjamming transition is naturally accounted for by the dynamics of a bistable internal state field. We show, within the athermal shear transformation zone theory of amorphous plasticity, that the transition is accompanied by the propagation of plastic fronts. We further show that the mean-field theory cannot select the velocity of these fronts, and go beyond the mean-field description to include fluctuations and correlations effects, resulting in additional nonlocal terms in the equations. Finally, we demonstrate that these terms, with an associated intrinsic length scale, provide a velocity selection mechanism for the plastic fronts.

Figure 1

(Color online) Propagating $m$ front solution of Eq. (12) with $\alpha =0.01$ and $s=1.1$ (solid line) compared to the analytic prediction given by Eq. (11) (dashed line), shifted by a few time units for clarity. (Inset) The velocity $u$ (in units of $2\ell ∕{\tau }_0$) as a function of $s$, for both the numerics (open circles) and the prediction of Eq. (14) (solid line).