Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 477, Issue 2245, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2020.0562
Keywords
constrained elastic stability; Euler elastica; blisters; nonlinear pendulum; calculus of variations
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Funding
- Prin Project [2017J4EAYB, 2017KL4EF3]
- Gruppo Nazionale per la Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM)
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This study investigates instability effects due to geometric constraints in nonlinear elasticity by analyzing equilibrium configurations of an elastic ring constrained inside a rigid circle. Different possible shapes are determined, with single-blister solutions having the lowest energy. The model's effectiveness is tested through a simple experiment involving a thin polymer strip in a rigid cylinder.
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.
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