Elasto-plastic description of brittle failure in amorphous materials

TL;DR

This paper investigates how amorphous materials transition from continuous to brittle failure as their initial stability increases, using theoretical models and mean field approximations to predict failure behavior and avalanche statistics.

Contribution

It demonstrates that brittle failure emergence can be modeled by elasto-plastic models and mean field theory, highlighting differences between infinite and finite-dimensional behaviors.

Findings

Brittle failure corresponds to a continuous transition in mean field models.

Failure can be predicted from avalanche statistics in mean field but not in finite dimensions.

Critical shear band radius scales as $(\,\Sigma-\Sigma_b)^{-2}$ near failure.

Abstract

The response of amorphous materials to an applied strain can be continuous, or instead display a macroscopic stress drop when a shear band nucleates. Such discontinuous response can be observed if the initial configuration is very stable. We study theoretically how such brittleness emerges in athermal, quasi-statically driven, materials as their initial stability is increased. We show that this emergence is well reproduced by elasto-plastic models and is predicted by a mean field approximation, where it corresponds to a continuous transition. In mean field, failure can be forecasted from the avalanche statistics. We show that this is not the case for very brittle materials in finite dimensions due to rare weak regions where a shear band nucleates. Their critical radius is predicted to follow $a_c\sim (\Sigma-\Sigma_b)^{-2}$, where $\Sigma$ is the stress and $\Sigma_b$ the stress a shear band can carry.