Elastic multi-blisters induced by geometric constraints. (20th January 2021)

• Record Type: Journal Article
• Authors: De Tommasi, D.; Devillanova, G.; Maddalena, F.; Napoli, G.; Puglisi, G.
• Is Part Of: Proceedings. Volume 477:Number 2245(2021)
• Publication Date: 2021-01-20
• Subjects: constrained elastic stability -- Euler elastica -- blisters -- nonlinear pendulum -- calculus of variations; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2020.0562
• Languages: English
• ISSNs: 1364-5021

Abstract

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.