Metastability as a mechanism for yielding in amorphous solids under cyclic shear

TL;DR

This paper models the yielding of amorphous solids under cyclic shear as a random walk with an absorbing boundary, providing insights into the underlying mechanism and robustness of yielding, and proposing a new approach to understanding fatigue failure.

Contribution

It introduces a novel mapping of yielding behavior to a random walk model, elucidating the mechanism and robustness of yielding in amorphous solids.

Findings

Mapping yielding to a random walk captures key features observed in simulations.

Adding activated escape explains fatigue failure thresholds.

Provides a unified framework for understanding yielding and failure.

Abstract

We consider the yielding behavior of amorphous solids under cyclic shear deformation and show that it can be mapped into a random walk in a confining potential with an absorbing boundary. The resulting dynamics is governed by the first passage time into the absorbing state and suffices to capture the essential qualitative features recently observed in atomistic simulations of amorphous solids. Our results provide insight into the mechanism underlying yielding and its robustness. When the possibility of activated escape from absorbing states is added, it leads to a unique determination of a threshold energy and yield strain, suggesting thereby an appealing approach to understanding fatigue failure.