Plateau Rayleigh instability of soft elastic solids. Effect of compressibility on pre and post bifurcation behavior

Abstract

Solid surface tension can deform soft elastic materials at macroscopic length scales. At a critical surface tension, elastocapillary instabilities in soft filaments emerge that resemble the Plateau–Rayleigh (P–R) instabilities in liquids. The experimentally observed P–R instability of soft elastic filaments has been recently investigated via numerical and theoretical approaches. However, these contributions focus on the incompressible limit and preclude the nonlinear Poisson's ratio effects in materials, for example, compressible hydrogels with Poisson's ratios that can go as low as 0.1. Moreover, most of the research on the solid P–R instability elaborate on the onset, ignoring the post-bifurcation regime. Here we show that compressibility matters and the form of the assumed compressible strain energy density has a significant effect on the onset and the post-bifurcation behavior of elastic P–R instability. For example, the P–R instability can be entirely suppressed depending on the form of the free energy density and Poisson's ratio. To this end, we employ a robust and variational elastocapillary formulation and its computer implementation using surface-enriched isogeometric finite elements at finite strains. We use an arclength solver to illustrate both stable-unstable amplitude growth and bifurcation points in the entire equilibrium path. Stability maps are drawn with distinct stable-unstable regions over various shear moduli, surface tensions, fiber radii, and applied stretches for cases ranging from quasi-compressible to fully compressible. The presented elastocapillary model proves to be useful in quantifying the surface and bulk energies in competition at finite strains and expected to help improve mechanical characterization of soft materials with at least one dimension that is on the orders of the elastocapillary lengthscale lsolid∼O(nm – mm).