Nonlinear plastic modes in disordered solids

TL;DR

This paper introduces a framework for identifying precursors to plastic instabilities in disordered solids by analyzing collective modes as minima of a barrier function, enabling early detection of imminent plastic events.

Contribution

It presents a novel approach to detect plastic instabilities in glasses by analyzing the landscape of a barrier function derived from potential energy variations.

Findings

Low-lying minima of the barrier function predict plastic transitions.

The method detects imminent instabilities at strains close to the critical strain.

The approach effectively identifies unstable modes before large non-affine displacements occur.

Abstract

We propose a framework within which a robust mechanical definition of precursors to plastic instabilities, often termed `soft-spots', naturally emerges. They are shown to be collective displacements (modes) $\hat{z}_0$ that correspond to local minima of the `barrier function' $b(\hat{z})$. The latter is derived from the cubic approximation of the variation $\delta U_{\hat{z}}(s)$ of the potential energy upon displacing particles a distance $s$ along $\hat{z}$. We show that modes $\hat{z}_0$ corresponding to low-lying minima of $b(\hat{z})$ lead to transitions over energy barriers in the glass, and are therefore associated with highly asymmetric variations $\delta U_{\hat{z}}(s)$ with $s$. We further demonstrate how a heuristic search for local minima of $b(\hat{z})$ can a-priori detect the locus and geometry of imminent plastic instabilities with remarkable accuracy, at strains as large as $\gamma_c-\gamma \sim 10^{-2}$ away from the instability strain $\gamma_c$, where the non-affine displacements under shear are still largely delocalized. Our findings suggest that the a-priori detection of plastic instabilities can be effectively carried out by the investigation of the landscape of $b(\hat{z})$.