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.
@article{arxiv.cond-mat/0405096,
title = {Universal Breakdown of Elasticity at the Onset of Material Failure},
author = {Craig Maloney and Anaël Lemaître},
journal= {arXiv preprint arXiv:cond-mat/0405096},
year = {2016}
}