A minimal integer automaton behind crystal plasticity

TL;DR

This paper demonstrates that continuum plasticity in crystalline materials can be effectively modeled by a simple integer automaton, capturing critical phenomena and correlations observed experimentally in a minimal and analytically tractable way.

Contribution

It introduces a minimal integer automaton model for 2D crystal plasticity, linking discrete automaton dynamics to continuum behavior and experimental critical exponents.

Findings

The automaton reproduces power law fluctuations in plastic flow.

It matches experimental critical exponents.

The model reveals inherent discreteness in plastic deformation.

Abstract

Power law fluctuations and scale free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova (FK) type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer valued automaton revealing inherent discreteness of the plastic flow.