Universal Breakdown of Elasticity at the Onset of Material Failure

Abstract

We show that, in the athermal quasistatic deformation of amorphous materials, the onset of failure is accompanied by universal scalings associated with a divergence of elastic constants. A normal mode analysis of the nonaffine elastic displacement field allows us to clarify its relation to the zero-frequency mode at the onset of failure and to the cracklike pattern which results from the subsequent relaxation of energy.