Coexistence of Scale-Invariant States in Incompressible Elastomers

TL;DR

This paper explores how certain nonlinear instabilities in incompressible elastomers, such as cavitation and sulcification, can be understood as coexistence of multiple scale-invariant states, revealing new insights into their phase behavior.

Contribution

It introduces a framework to understand thresholdless instabilities as phase coexistence of scale-invariant states in incompressible elastomers and enumerates these states in two dimensions.

Findings

Instabilities correspond to coexistence of scale-invariant states.

Homogeneous and inhomogeneous states are both relevant.

A constructive enumeration of possible states is provided.

Abstract

Cavitation and sulcification of soft elastomers are two examples of thresholdless, nonlinear instabilities that evade detection by linearization. I show that the onset of such instabilities can be understood as a kind of phase coexistence between multiple scale-invariant states, and I constructively enumerate the possible scale-invariant states of incompressible rubber in two dimensions. Whereas true phases (like the affine deformations of rubber) are homogeneous, the alternatives are inhomogeneous. In terms of the thermodynamics of solids, both classes of states must generally be given equal consideration.