Avalanches, precursors and finite size fluctuations in a mesoscopic model of amorphous plasticity

TL;DR

This paper models amorphous plasticity using a mesoscopic lattice approach, revealing scale-free avalanches, finite size effects, and precursors to plastic activity, with implications for understanding material failure.

Contribution

It introduces a lattice-based mesoscopic model capturing avalanche dynamics, yield stress fluctuations, and precursors, with a novel exponent for avalanche size distribution.

Findings

Avalanche size distribution follows a power law with exponent ~1.25.

Finite size effects characterize yield stress fluctuations.

Precursor activity shows distinct spatial distribution.

Abstract

We discuss avalanche and finite size fluctuations in a mesoscopic model to describe the shear plasticity of amorphous materials. Plastic deformation is assumed to occur through series of local reorganizations. Yield stress criteria are random while each plastic slip event induces a quadrupolar long range elastic stress redistribution. The model is discretized on a regular square lattice. Shear plasticity can be studied in this context as a depinning dynamic phase transition. We show evidence for a scale free distribution of avalanches $P(s)\propto S^{-\kappa}$ with a non trivial exponent $\kappa \approx 1.25$ significantly different from the mean field result $\kappa = 1.5$. Finite size effects allow for a characterization of the scaling invariance of the yield stress fluctuations observed in small samples. We finally identify a population of precursors of plastic activity and characterize its spatial distribution.