Mean-Field Theory of Yielding under Oscillatory Shear

We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behavior 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 nontrivial, nonmonotonic 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.

Automated summary

This paper studies a mean field elastoplastic model with a disordered landscape of local yield barriers to investigate the behavior of athermal amorphous solids under oscillatory shear. The model shows a genuine dynamical transition from an elastic to a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. A nontrivial, nonmonotonic approach to the yielded state is observed for initial conditions below the analytically derived threshold energy. The timescale diverges as one approaches the yielding point from above, which is identified as the fatigue limit. The connections to brittle yielding under uniform shear are also discussed.