Modelling avalanches in martensites

TL;DR

This paper reviews mathematical models that explain the avalanche-like responses observed in martensitic transformations and other solid-state phenomena, highlighting the complex, scale-free behavior of these events.

Contribution

It provides a comprehensive overview of modeling approaches to understand avalanche dynamics in martensites, emphasizing their statistical and scale-invariant properties.

Findings

Avalanche responses in martensites exhibit scale-free, complex behavior.

Mathematical models help elucidate the origin of avalanche phenomena.

Understanding these models aids in predicting material responses under stress.

Abstract

Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation, fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling.