Rayleigh-Taylor instability in soft elastic layers

TL;DR

This paper explores the stability and pattern formation in soft elastic layers under gravity, revealing how elastic effects influence the nonlinear evolution and stability of resulting shapes, with implications for designing tunable soft systems.

Contribution

It introduces a theoretical and computational analysis of gravity-induced shape transitions in elastic layers, highlighting the nonlinear elastic effects that stabilize certain morphologies.

Findings

Elastic effects saturate the instability, preventing unbounded shape growth.

Multiple stable and unstable patterns, including wrinkling and digitations, can form.

Guidelines for designing soft systems with controllable shapes are provided.

Abstract

This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the selection of different patterns as well as their nonlinear evolution, unveiling the interplay between elastic and geometric effects for their formation. Unlike similar gravity-induced shape transitions in fluids, as the Rayleigh-Taylor instability, we prove that the nonlinear elastic effects saturate the dynamic instability of the bifurcated solutions, displaying a rich morphological diagram where both digitations and stable wrinkling can emerge. The results of this work provide important guidelines for the design of novel soft systems with tunable shapes, with several applications in engineering sciences.