Elastobuoyant Heavy Spheres: A Unique Way to Study Nonlinear Elasticity

Abstract

Large deformations in soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here, we investigate this complex problem systematically with a simple experiment: by introducing a heavy bead of radius a in an incompressible soft elastic medium. We find a scaling law for the penetration depth (δ) of the bead inside the softest gels as δ∼a^{3/2}, which is vindicated by an original asymptotic analytic model developed in this article. This model demonstrates that the observed relationship is precisely at the demarcating boundary of what would be required for the field variables to either diverge or converge. This correspondence between a unique mathematical prediction and the experimental observation ushers in new insights into the behavior of the deformations of strongly nonlinear materials.