Plasticity and reversibility of structural transitions in a model solid

TL;DR

This paper develops a phenomenological elasto-plastic theory to model the structural transition and shape recovery in a 2D solid, emphasizing the role of plasticity in reversibility.

Contribution

It introduces a new framework combining elastic and plastic strains to describe structural transitions and shape recovery in solids.

Findings

Shape recovery depends on plasticity in transformation strains.

Plasticity influences the reversibility of the structural transition.

The model captures the dynamics of shape change during cycling.

Abstract

We formulate a phenomenological elasto-plastic theory to describe a solid undergoing a structural transition from a square (p4mm) to an oblique (p2) lattice in two dimensions. Within our theory, the components of the strain may be decomposed additively into separate elastic and plastic contributions. The plastic strain, produced when the local stress crosses a threshold, is governed by a phenomenological equation of motion. We investigate the dynamics of shape of an initially square solid as it is cycled through a transformation protocol consisting of (1) a quench across the transition (2) deformation by an external stress and finally (3) reverse transformation back to the parent state. We show that shape recovery at the end of this cycle depends on crucially on the presence of plasticity in components of the strain responsible for the transformation.