Wrinkling instabilities in soft bilayered systems

Abstract

Wrinkling phenomena control the surface morphology of many technical and biological systems. While primary wrinkling has been extensively studied, experimentally, analytically and computationally, higher-order instabilities remain insufficiently understood, especially in systems with stiffness contrasts well below 100. Here, we use the model system of an elastomeric bilayer to experimentally characterize primary and secondary wrinkling at moderate stiffness contrasts. We systematically vary the film thickness and substrate prestretch to explore which parameters modulate the emergence of secondary instabilities, including period-doubling, period-tripling and wrinkle-to-fold transitions. Our experiments suggest that period-doubling is the favourable secondary instability mode and that period-tripling can emerge under disturbed boundary conditions. High substrate prestretch can suppress period-doubling and primary wrinkles immediately transform into folds. We combine analytical models with computational simulations to predict the onset of primary wrinkling, the post-buckling behaviour, secondary bifurcations and the wrinkle-to-fold transition. Understanding the mechanisms of pattern selection and identifying the critical control parameters of wrinkling will allow us to fabricate smart surfaces with tunable properties and to control undesired surface patterns like in the asthmatic airway.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

A computational study of the mechanisms of growth-driven folding patterns on shells, with application to the developing brain

“…In order to isolate the effect of spherical/ellipsoidal geometry from the advective velocity, we return to Equation (4) and set v = 0 and D = 0, with R set to the value in Table 1. This independence from cell migration in favor of cell proliferation has been adopted by several authors previously [10,11,18,19,17,20,24,37,38].…”

“…Several cortical folding studies have examined the buckling of a thin, elastic layer on an elastic substrate [10,18,37,39,40,13]. These analytic and computational investigations have considered a variety of geometries including plates and shells to elucidate the role of the layer-to-substrate thickness ratio in forming folding patterns.…”

“…There is now a sizeable literature [10,11,18,19,17,20,21,22,23] seeking to explain aspects of brain folding by inhomogeneous growth in linearized and, more appropriately, nonlinear elasticity. Some of this literature draws from linearized buckling of beams and plates [21,22,24], but much of the computational work is based on finite strains, and operates in the postbifurcation regime.…”

“…Most previous studies have reduced the problem to one of local, inhomogeneous growth controlled by a time-or load-dependent scalar parameter [10,11,18,19,17,20,23]. Effectively, this addresses only the mechanism of local cell proliferation.…”

Patterning through instabilities in complex media: theory and applications

“…Carfagna and coworkers [10] then show that a soft solid subjected to an extreme deformation may form wrinkles in a direction other than normal to the direction of greatest compression; this wrinkled state may possibly become an initial bifurcation mode. Budday and co-workers [11] study the emergence of secondary bifurcations in a compressed elastic bilayer, providing useful guidelines for the design of smart surfaces with tunable morphology. Finally, Hazel & Mullin [12] investigate the peculiar buckling characteristics of thin elastic rings confined within containers of circular or regular polygonal cross section.…”