Fringe instability in constrained soft elastic layers

Rate-Dependent Pattern Evolution in Peeling Adhesive Tape Driven by Cohesive Failure

In the case of low-rate peeling, an adhesive can undergo a large tensile deformation through the viscous flow and form the fingering pattern at the peeling interface, resulting in homogeneous stripes on the peeled surface. In the case of high-rate peeling, no larger viscous deformation occurs, and no surface patterns will be generated. However, it is still unclear how the surface pattern evolves when an adhesive is peeled from a relatively low rate to a high rate. Here, by peeling an adhesive tape at 180° over a wide range of rates, we find that the adhesive tape can undergo a steady peeling. As the peeling rate increases, it is observed that the surface pattern in the peeled adhesive tape tends to evolve from the initial striped pattern to a crescent pattern, then to a spotted pattern. Even in the case of the stick-slip peeling at a small angle, the patterned region also presents the same evolutionary trend. By exploiting a high-speed camera to track the deformation process of the adhesive, it is found that this evolution is actually driven by the cohesive failure of the peeling adhesive. We describe the failure process, revealing the formation mechanism of the crescent pattern. We also discuss the effect of the peeling rate on the interface instability morphology by combining the finite element simulations, elucidating how the surface pattern evolves with the peeling rate.

Ballooning, bulging, and necking: An exact solution for longitudinal phase separation in elastic systems near a critical point

Prominent examples of longitudinal phase separation in elastic systems include elastic necking, the propagation of a bulge in a cylindrical party balloon, and the beading of a gel fiber subject to surface tension. Here we demonstrate that if the parameters of such a system are tuned near a critical point (where the difference between the two phases vanishes), then the behavior of all systems is given by the minimization of a simple and universal elastic energy familiar from Ginzburg-Landau theory in an external field. We minimize this energy analytically, which yields not only the well known interfacial tanh solution, but also the complete set of stable and unstable solutions in both finite and infinite length systems, unveiling the elastic system's full shape evolution and hysteresis. Correspondingly, we also find analytic results for the the delay of onset, changes in criticality, and ultimate suppression of instability with diminishing system length, demonstrating that our simple near-critical theory captures much of the complexity and choreography of far-from-critical systems. Finally, we find critical points for the three prominent examples of phase separation given above, and demonstrate how each system then follows the universal set of solutions.

The shape of hanging elastic cylinders

Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An equilibrium configuration results from the interplay between gravity that tends to deform the cylinders downwards under their own weight, and elasticity that resists these distortions. The corresponding steady state exhibits fascinating shapes which are measured with lab-based micro-tomography. For any given initial radius to height ratio, the deformed cylinders are no longer axially symmetric beyond a critical value of a control parameter that depends on the volume force, the height and the elastic modulus: self-similar wrinkling hierarchies develop, and dimples appear at the bottom surface of the shallowest samples. We show that these patterns are the consequences of elastic instabilities.

Peristaltic Elastic Instability in an Inflated Cylindrical Channel

A long cylindrical cavity through a soft solid forms a soft microfluidic channel, or models a vascular capillary. We observe experimentally that, when such a channel bears a pressurized fluid, it first dilates homogeneously, but then becomes unstable to a peristaltic elastic instability. We combine theory and numerics to fully characterize the instability in a channel with initial radius a through an incompressible bulk neo-Hookean solid with shear modulus μ. We show instability occurs supercritically with wavelength 12.278…a when the cavity pressure exceeds 2.052…μ. In finite solids, the wavelength for peristalsis lengthens, with peristalsis ultimately being replaced by a long-wavelength bulging instability in thin-walled cylinders. Peristalsis persists in Gent strain-stiffening materials, provided the material can sustain extension by more than a factor of 6. Although naively a pressure driven failure mode of soft channels, the instability also offers a route to fabricate periodically undulating channels, producing, e.g., waveguides with photonic or phononic stop bands.

Meniscus instabilities in thin elastic layers

We consider meniscus instabilities in thin elastic layers perfectly adhered to, and confined between, much stiffer bodies. When the free boundary associated with the meniscus of the elastic layer recedes into the layer, for example by pulling the stiffer bodies apart or injecting air between them, then the meniscus will eventually undergo a purely elastic instability in which fingers of air invade the layer. Here we show that the form of this instability is identical in a range of different loading conditions, provided only that the thickness of the meniscus, a, is small compared to the in-plane dimensions and to two emergent in-plane length scales that arise if the substrate is soft or if the layer is compressible. In all such situations, we predict that the instability will occur when the meniscus has receded by approximately 1.27a, and that the instability will have wavelength λ ≈ 2.75a. We illustrate this by also calculating the threshold for fingering in a thin wedge of elastic material bonded to two rigid plates that are pried apart, and the threshold for fingering when a flexible plate is peeled from an elastic layer that glues the plate to a rigid substrate.

Competing failure modes in finite adhesive pads

Thin adhesive pads used to attach objects to each other often fail catastrophically. Here we consider the nature of failure of such a pad under loading parallel to the adhesive substrate. To determine the modes of failure of the pad and to understand what limits its load bearing capacity, we conduct experiments with finite pads composed of a soft adhesive layer with a stiff backing and load them parallel to the surface of adhesion. We find that two different peeling mechanisms emerge as a function of the slenderness of the adhesive pad: an interfacial peeling mechanism that starts close to the pulling end for very long pads, and an unstable curling mechanism that starts at the opposite end for relatively short pads. A minimal theoretical framework allows us to explain our observations and reveals the adhesive bond stiffness as a dominant parameter in defining the peeling mode. A phase diagram that delineates the different regimes of peeling modes brings our experiments and theory together. Our results suggest that unstable peeling by curling may be more common than previously thought, and could perhaps occur naturally in such examples as the gecko foot.

Vibration of Mechanically-Assembled 3D Microstructures Formed by Compressive Buckling

Micro-electromechanical systems (MEMS) that rely on structural vibrations have many important applications, ranging from oscillators and actuators, to energy harvesters and vehicles for measurement of mechanical properties. Conventional MEMS, however, mostly utilize two-dimensional (2D) vibrational modes, thereby imposing certain limitations that are not present in 3D designs (e.g., multi-directional energy harvesting). 3D vibrational microplatforms assembled through the techniques of controlled compressive buckling are promising because of their complex 3D architectures and the ability to tune their vibrational behaviour (e.g., natural frequencies and modes) by reversibly changing their dimensions by deforming their soft, elastomeric substrates. A clear understanding of such strain-dependent vibration behaviour is essential for their practical applications. Here, we present a study on the linear and nonlinear vibration of such 3D mesostructures through analytical modeling, finite element analysis (FEA) and experiment. An analytical solution is obtained for the vibration mode and linear natural frequency of a buckled ribbon, indicating a mode change as the static deflection amplitude increases. The model also yields a scaling law for linear natural frequency that can be extended to general, complex 3D geometries, as validated by FEA and experiment. In the regime of nonlinear vibration, FEA suggests that an increase of amplitude of external loading represents an effective means to enhance the bandwidth. The results also uncover a reduced nonlinearity of vibration as the static deflection amplitude of the 3D structures increases. The developed analytical model can be used in the development of new 3D vibrational microplatforms, for example, to enable simultaneous measurement of diverse mechanical properties (density, modulus, viscosity etc.) of thin films and biomaterials.