Simulation of shear strain at arbitrary angles as a probe of packing instabilities

TL;DR

This paper introduces a simulation tool to study shear-induced instabilities in disordered solids at arbitrary angles, revealing complex behaviors and interactions of these instabilities across different shear orientations.

Contribution

A novel simulation method enabling continuous variation of shear angle to analyze instability behaviors and interactions in disordered solids.

Findings

Instabilities form broad angular instability lines in phase space.

Instabilities can pass through, change continuously, or fade away as shear angle varies.

Hysterons shrink to zero separation near instability disappearance, increasing small hysterons.

Abstract

Disordered solids distort and fail as particle contacts become unstable and rearrange under sufficiently large shear strains. Such instabilities can occur at different locations and, because of their proximity, can interact with one another. We develop a tool for simulations with periodic boundary conditions that allows strains to be applied at a continuously variable angle, $\theta$. We show that instabilities can persist over a broad angular ranges of applied shear to form instability lines in phase space. By applying strain at different $\theta$, we examine the correlations between the instabilities encountered at different angles and different positions in the sample. We find instabilities that pass through one another, others that change continuously as the angle is varied, and yet others that end by smoothly decreasing their magnitudes to zero as the instability fades away. Examining hysterons, i.e., instabilities that undo themselves upon reversing the direction of shear, we find that as $\theta$ is varied towards the point where the instability disappears, the separation between the forward and backward instabilities shrinks to zero so as to produce an enhanced number of very small hysterons.