Shear hardening in frictionless amorphous solids near the jamming transition

TL;DR

This paper investigates shear hardening in frictionless amorphous solids near the jamming transition, revealing critical scalings and microscopic origins distinct from compression hardening, and advancing the elasticity theory of amorphous materials.

Contribution

It uncovers the microscopic mechanisms of shear hardening and introduces a theoretical framework explaining its critical behavior in amorphous solids.

Findings

Shear hardening results from increased bond number and anisotropy.

Critical scalings of shear hardening are identified.

The study distinguishes shear from compression hardening mechanisms.

Abstract

The jamming transition, generally manifested by a rapid increase of rigidity under compression (i.e., compression hardening), is ubiquitous in amorphous materials. Here we study shear hardening in deeply annealed frictionless packings generated by numerical simulations, reporting critical scalings absent in compression hardening. We demonstrate that hardening is a natural consequence of shear-induced memory destruction. Based on an elasticity theory, we reveal two independent microscopic origins of shear hardening: (i) the increase of the interaction bond number and (ii) the emergence of anisotropy and long-range correlations in the orientations of bonds, the latter highlights the essential difference between compression and shear hardening. Through the establishment of physical laws specific to anisotropy, our work completes the criticality and universality of jamming transition, and the elasticity theory of amorphous solids.