Mean field theory of yielding under oscillatory shear

TL;DR

This paper introduces a mean field elastoplastic model to understand the yielding transition in amorphous solids under oscillatory shear, revealing a dynamical transition and fatigue behavior consistent with simulations.

Contribution

It presents a novel mean field framework capturing the dynamical transition and fatigue phenomena in amorphous solids under oscillatory shear, aligning with particle simulation results.

Findings

Identification of a genuine dynamical transition between elastic and yielded states.

Observation of non-monotonic approach to yielding below a threshold energy.

Divergence of timescale near the yielding point, linked to fatigue limit.

Abstract

We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behaviour of athermal amorphous solids subject to oscillatory shear. We show that the model presents a genuine dynamical transition between an elastic and a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. For initial conditions prepared below the analytically derived threshold energy, we observe a non-trivial, non-monotonic approach to the yielded state. The timescale diverges as one approaches the yielding point from above, which we identify with the fatigue limit. We finally discuss the connections to brittle yielding under uniform shear.