Scale and Nature of Sulcification Patterns

TL;DR

This paper develops a theoretical framework to understand the formation of sulcus patterns in soft elastomers, revealing their scale-free, bifurcation behavior and energy-based pattern selection at a nonlinear critical point.

Contribution

It introduces a nonlinear critical point perspective and perturbative theory to explain sulcus pattern formation, including boundary condition effects and pattern selection mechanisms.

Findings

Sulcus formation can be supercritical or subcritical depending on boundary conditions.

An infinite number of patterns emerge at the critical point, with the lowest energy pattern being selected.

The formation process is analogous to a phase transition with finite transformation energy.

Abstract

Sulci are surface folds commonly seen in strained soft elastomers and form via a strongly subsubcriticalcritical, yet scale-free instability. Treating the threshold for nonlinear instability as a nonlinear critical point, we explain the nature of sulcus patterns in terms of the scale and translation symmetries which are broken by the formation of an isolated, small sulcus. Our perturbative theory and simulations show that sulcus formation in a thick, compressed slab can arise either as a supercritical or as a weakly subcritical bifurcation relative to this nonlinear critical point, depending on the boundary conditions. An infinite number of competing, equilibrium patterns simultaneously emerge at this critical point, but the one selected has the lowest energy. We give a simple, physical explanation for the formation of these sulcification patterns using an analogy to a solid-solid phase transition with a finite energy of transformation.