Asymmetric equilibria of two nested elastic rings

Equilibrium of Two Rods in Contact Under Pressure

“…The problem discussed in this article has a theoretical relevance as a simplest paradigm apt to study the contact of elastic bodies in the presence of large deformations. While the interaction of a single elastic ring confined by rigid external container has been extensively studied (5-7), few results are available for elastic rods confined by their mutual interaction (8)(9)(10). The present contribution can be the basis for extension of the model to more complex physical systems where interaction potentials or more complex constraints intervene.…”

“…In this case, every beam is called a velaria ('like sail in the wind') (1). The adhesion problem of a rod with a rigid surface, or confined by a rigid external container, has been extensively studied (2)(3)(4)(5)(6)(7); on the other hand, the problem of two elastic rods, confined by their mutual interaction, has received less attention (8,9). In both cases, adhesion boundary conditions arise from a variational formulation, and we will follow this approach too.…”

Growth of a flexible fibre in a deformable ring

“…When extensibility is neglected, as expected for thin bars, the system assumes a particularly clear physical interpretation because the observed deformed shapes depend on two only parameters: the ratio of lengths and the ratio of flexural stiffness. 33,34 In some growth problems, as well as in a cavity filament injection scheme, the confined body is a fibre instead of a ring. 11,[35][36][37][38][39][40][41][42][43][44][45] When the container is a ring, the equilibrium shapes and deformations have different features.…”

“…When extensibility is neglected, as expected for thin bars, the system assumes a particularly clear physical interpretation because the observed deformed shapes depend on two only parameters: the ratio of lengths and the ratio of flexural stiffness. 33,34…”

Elastic multi-blisters induced by geometric constraints

“…Another aspect of the equilibrium problem, both in the presence of a rigid and soft container, is that the further growth of the internal loop may cause the blister to come into contact with the container and/or the insurgence of self-intersections [32]. Thus, beyond a certain length the equilibrium configuration breaks its symmetry [32,33] and spiral patterns emerge as a generic feature in close-packed structures. Other recent theoretical and experimental studies concern the effect of polygonal and annular confinement [34,35] on the morphology of closed rings.…”