Elastic multi-blisters induced by geometric constraints

Abstract

We study a prototypical system describing instability effects due to geometric constraints in the framework of nonlinear elasticity. By considering the equilibrium configurations of an elastic ring constrained inside a rigid circle with smaller radius, we analytically determine different possible shapes, reproducing well-known physical phenomena. As we show, both single- (with different complexity) and multi-blister configurations can be observed, but the lowest energy always corresponds to single-blister solutions. Important physical insight is attained through an analogy between the elastica and the dynamics of a nonlinear pendulum. A complete geometric characterization is attained, proving symmetry and other relevant properties. The effectiveness of the model is tested against a simple experiment by considering a thin polymer strip constrained in a rigid cylinder.