title: Rayleigh-Taylor instability in soft elastic layers.
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, such 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.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'
authors.affiliation: MOX-Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
authors.forename: D
authors.identifier: http://orcid.org/0000-0001-6424-5689
authors.initials: D
authors.lastname: Riccobelli
authors.affiliation: MOX-Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy pasquale.ciarletta@polimi.it.
authors.forename: P
authors.initials: P
authors.lastname: Ciarletta
keywords: fingering; interfacial instability; mixed finite elements; nonlinear elasticity; pattern formation