Universal Breakdown of Elasticity at the Onset of Material Failure

TL;DR

This paper reveals that during the initial failure of amorphous materials under deformation, elastic constants universally diverge, indicating a fundamental breakdown of elasticity linked to zero-frequency modes and crack formation.

Contribution

It introduces a normal mode analysis connecting elastic divergence at failure to zero-frequency modes and crack patterns in amorphous materials.

Findings

Elastic constants diverge at failure onset.

Zero-frequency modes are related to failure.

Crack-like patterns emerge after energy relaxation.

Abstract

We show that, in the athermal quasi-static deformation of amorphous materials, the onset of failure is accompanied by universal scalings associated with a \emph{divergence} of elastic constants. A normal mode analysis of the non-affine elastic displacement field allows us to clarify its relation to the zero-frequency mode at the onset of failure and to the crack-like pattern which results from the subsequent relaxation of energy.