Fringe instability in constrained soft elastic layers

Abstract

Soft elastic layers with top and bottom surfaces adhered to rigid bodies are abundant in biological organisms and engineering applications. As the rigid bodies are pulled apart, the stressed layer can exhibit various modes of mechanical instabilities. In cases where the layer's thickness is much smaller than its length and width, the dominant modes that have been studied are the cavitation, interfacial and fingering instabilities. Here we report a new mode of instability which emerges if the thickness of the constrained elastic layer is comparable to or smaller than its width. In this case, the middle portion along the layer's thickness elongates nearly uniformly while the constrained fringe portions of the layer deform nonuniformly. When the applied stretch reaches a critical value, the exposed free surfaces of the fringe portions begin to undulate periodically without debonding from the rigid bodies, giving the fringe instability. We use experiments, theory and numerical simulations to quantitatively explain the fringe instability and derive scaling laws for its critical stress, critical strain and wavelength. We show that in a force controlled setting the elastic fingering instability is associated with a snap-through buckling that does not exist for the fringe instability. The discovery of the fringe instability will not only advance the understanding of mechanical instabilities in soft materials but also have implications on biological and engineered adhesives and joints.

The shape of hanging elastic cylinders

“…In Fig. B.10-(c) the threshold has been reached, and one recovers the fingering instability reported in [22,23]. In Fig B.10-(d) the stretch ratio is larger and one observes the formation of new generations of wrinkles.…”

“…Since the threshold for the formation of the wrinkles is for α = α c = 4.7, one concludes that the wrinkles begin to develop for deformations so that 1/ tan θ > 4.7, i.e., θ < θ c 0.21 rad. Fringe [22,23] or fingering [3,[24][25][26] instabilities have been reported in stretched elastic cylinders or layers attached by their two ends to parallel rigid plates. The analytic model developed in [26,27] as well as the simulations of [23] predict that the interface is linearly unstable for stretch ratio such that the angle θ at the contact line is smaller than 0.195 rad.…”

Vibration of mechanically-assembled 3D microstructures formed by compressive buckling

“…Recent advances in fabrication/assembly techniques such as those that use controlled mechanical buckling (Khang et al, 2006; Sun et al, 2006; Audoly and Boudaoud, 2008a; Audoly and Boudaoud, 2008b; Audoly and Boudaoud, 2008c; Dias and Audoly, 2014; Xu et al, 2015; Zhang et al, 2015; Chen et al, 2016c; Chen et al, 2016d; Lestringant et al, 2017), self-folding induced by residual stress (Golod et al, 2001; Kong and Wang, 2003; Bell et al, 2007; Huang et al, 2012; Froeter et al, 2013; Huang et al, 2014; Chen et al, 2016e; Bauhofer et al, 2017; Tian et al, 2017), surface instabilities (Yin et al, 2008; Wang and Zhao, 2015; Lin et al, 2016; Wang and Zhao, 2016; Liao et al, 2017; Lin et al, 2017; Ma et al, 2017), capillary forces (Py et al, 2007; Guo et al, 2009; Antkowiak et al, 2011; Hure and Audoly, 2013; Brubaker and Lega, 2016) and temperature changes (Stroganov et al, 2014; Cui et al, 2017) and 3D printing/writing processes (Therriault et al, 2003; Gratson et al, 2004; Lewis et al, 2006; Schaedler et al, 2011; Soukoulis and Wegener, 2011; Fischer and Wegener, 2013; Jang et al, 2013; Farahani et al, 2014; Hong et al, 2015; Farahani et al, 2016; Matlack et al, 2016; Hirt et al, 2017), allow the construction of complex 3D structures and form the structural basis of 3D vibrations. Based on 3D polymers/silicon mesostructures assembled through the techniques of controlled compressive buckling (Xu et al, 2015; Zhang et al, 2015; Liu et al, 2016; Yan et al, 2016a; Yan et al, 2016b; Nan et al, 2017; Shi et al, 2017; Yan et al, 2017b; Zhang et al, 2017), Ning et al, (2017) realized structural vibrations with a broad set of 3D modes.…”

Meniscus instabilities in thin elastic layers

“…Three of these arise when an elastic layer adhered between rigid bodies is pulled apart whilst maintaining adhesion. This leads to one of the following: cavitation in the bulk of the elastic layer 31 , fingering at the perimeter of the elastic layer 10,12 or an undulating fringe instability localized around the contact line between the layer's perimeter and the the rigid body 32,33 . The fourth tensile instability is entirely different: when adhesion between the layer and the body fails, 2-D patterns of adhered and de-adhered regions emerge on the previously adhered interface from the trade off between adhesive energy and elasticity [34][35][36][37][38][39][40] .…”