Optimization and plasticity in disordered media

TL;DR

This paper investigates the plastic yielding behavior of disordered media using a random fuse model, revealing that actual yield surfaces differ from energy-minimizing surfaces and exhibit multiscaling, impacting the understanding of material failure.

Contribution

It demonstrates that yield surfaces in disordered media are not energy-minimizing and introduces a theoretical explanation for their multiscaling behavior.

Findings

Yield surfaces differ from minimum energy surfaces.

Global yield stress is lower than naive expectations.

Yield surface fluctuations exhibit multiscaling.

Abstract

We study the plastic yielding of disordered media using the perfectly plastic random fuse model. The yield surfaces are shown to be different from those obtained minimizing the sum of the local yield thresholds, i.e. the so-called minimum 'energy' surfaces. As a result, the global yield stress is lower than expected from naive optimization and the difference persists as the sample size increases. At variance with minimum energy surfaces, height-height fluctuations of yield surfaces exhibit multiscaling. We provide a theoretical argument that explains how this behavior arises from the very different nature of the optimization problem in both cases.