Unfolding the Sulcus

TL;DR

This paper analyzes the nonlinear instability of sulci formation on soft materials, revealing a scale-free, continuous bifurcation process with critical strains, supported by experiments.

Contribution

It introduces a novel bifurcation diagram for sulcification, showing it as a scale-free, nonlinear, and structurally stable instability in elastic materials.

Findings

Sulci nucleate at a critical strain with an essential singularity.

Sulci shrink to a point at a lower critical strain during unloading.

Experiments confirm the existence of two critical strains.

Abstract

Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for sulcfication showing that it is a scale-free, sub-critical {\em nonlinear} instability. In contrast with classical nucleation, sulcification is {\em continuous}, occurs in purely elastic continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On unloading, it quasi-statically shrinks to a point with a lower critical strain, explained by breaking of scale symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with {\em no} energy barrier. Simple experiments confirm the existence of these two critical strains.