Beyond linear elasticity: Jammed solids at finite shear strain and rate

TL;DR

This study investigates how the linear elastic response of jammed soft solids breaks down under finite shear strain and rate, revealing their inherently nonlinear and rate-dependent behavior near the jamming transition.

Contribution

The paper provides a systematic simulation-based analysis of the strain and rate scales at which linear elasticity fails in jammed solids, linking macroscopic response to microscopic contact network changes.

Findings

Linear elasticity window narrows near jamming.

Mechanical response is nonlinear and rate-dependent.

Characteristic strain and time scales quantify elasticity breakdown.

Abstract

The shear response of soft solids can be modeled with linear elasticity, provided the forcing is slow and weak. Both of these approximations must break down when the material loses rigidity, such as in foams and emulsions at their (un)jamming point -- suggesting that the window of linear elastic response near jamming is exceedingly narrow. Yet precisely when and how this breakdown occurs remains unclear. To answer these questions, we perform computer simulations of stress relaxation and shear startup experiments in athermal soft sphere packings, the canonical model for jamming. By systematically varying the strain amplitude, strain rate, distance to jamming, and system size, we identify characteristic strain and time scales that quantify how and when the window of linear elasticity closes, and relate these scales to changes in the microscopic contact network. Our findings indicate that the mechanical response of jammed solids are generically nonlinear and rate-dependent on experimentally accessible strain and time scales.