Yielding in an Integer Automaton Model for Amorphous Solids under Cyclic Shear.

Abstract

We present results on an automaton model of an amorphous solid under cyclic shear. After a transient, the steady state falls into one of three cases in order of increasing strain amplitude: (i)pure elastic behavior with no plastic activity, (ii)limit cycles where the state recurs after an integer period of strain cycles, and (iii)irreversible plasticity with longtime diffusion. The number of cycles N required for the system to reach a periodic orbit diverges as the amplitude approaches the yielding transition between regimes (ii) and (iii)from below, while the effective diffusivity D of the plastic strain field vanishes on approach from above. Both of these divergences can be described by a power law. We further show that the average period T of the limit cycles increases on approach to yielding.