Surface sulci in squeezed soft solids

TL;DR

This paper investigates the complex three-dimensional sulcification patterns that occur on the surfaces of soft elastic solids under compression, revealing how morphology depends on material compressibility and stress levels.

Contribution

It introduces a numerical model capturing the transition from simple to complex sulcus patterns in compressed soft solids, extending previous two-dimensional analyses to three dimensions.

Findings

Incompressible solids form I-shaped and Y-shaped sulci with hexagonal arrangements.

Highly compressible solids develop a uniform hexagonal sulcus network.

Morphology depends on the level of compression and material compressibility.

Abstract

The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a solid to becomes unstable when its stress exceeds a critical value. Previous analyses of the surface instability have assumed two-dimensional plane-strain conditions, but in experiments isotropic stresses often lead to complex three-dimensional sulcification patterns. Here we show how such diverse morphologies arise by numerically modeling the lateral compression of a rigidly clamped elastic layer. For incompressible solids, close to the instability threshold, sulci appear as I-shaped lines aligned orthogonally with their neighbors; at higher compressions they are Y-shaped and prefer a hexagonal arrangement. In contrast, highly compressible solids when squeezed show only one sulcified phase characterized by a hexagonal sulcus network.