A cascade of length scales in elastic rings under confinement

Spears, Kevin; Alben, Silas

doi:10.1063/1.2997338

Cited by 2 publications

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“…The ring deforms with a wide range of bending length scales and undergoes spontaneous layering, with different numbers of layers formed at different locations. An inverse relationship between the number of layers and the curvature at a given location was identified in [55]. In this experiment, the confining boundary was a strip of wood, thin enough to be flexible but much more rigid than the confined ring, which is a thin strip of paper (figure 1 a ) or mylar (figure 1 b ).…”

Section: Introductionmentioning

confidence: 89%

“…The present paper studies the role of friction in such deformations, and examines a much wider range of length scales of deformations than most of the previous work in this area. Our specific problem is an initially circular elastic ring that is compressed by a shrinking circular container, shown in an experiment [55] in figure 1. Here, a system of contact forces between different points on the ring and between the ring and the confining boundary leads to complex and heterogeneous configurations.…”

Section: Introductionmentioning

confidence: 99%

“…The outer boundary shrinks as one end of the wood strip passes through a loop, in the same way that a clothing belt is tightened. Panel ( b ) reproduced from [55], with the permission of AIP Publishing. (Online version in colour.…”

Section: Introductionmentioning

confidence: 99%

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Packing of elastic rings with friction

Alben

2022

Proc. R. Soc. A.

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We study the deformations of elastic filaments confined within slowly shrinking circular boundaries, under contact forces with friction. We perform computations with a spring-lattice model that deforms like a thin inextensible filament of uniform bending stiffness. Early in the deformation, two lobes of the filament make contact. If the friction coefficient is small enough, one lobe slides inside the other; otherwise, the lobes move together or one lobe bifurcates the other. There follows a sequence of deformations that is a mixture of spiralling and bifurcations, primarily the former with small friction and the latter with large friction. With zero friction, a simple model predicts that the maximum curvature and the total elastic energy scale as the wall radius to the − 3 / 2 and − 2 powers, respectively. With non-zero friction, the elastic energy follows a similar scaling but with a prefactor up to eight times larger, due to delayering and bending with a range of small curvatures. For friction coefficients as large as 1, the deformations are qualitatively similar with and without friction at the outer wall. Above 1, the wall friction case becomes dominated by buckling near the wall.

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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

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Packing of elastic rings with friction

Alben

2022

Proc. R. Soc. A.

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“…This paper studies a basic version of the problem in which an initially circular elastic ring is compressed by a shrinking circular container. In an experiment [55], a system of contact forces between different points on the ring, and between the ring and the confining boundary led to a complex and heterogeneous configuration with a wide range of bending length scales and the spontaneous layering of the ring, with different numbers of layers formed at different locations. An inverse relationship between the number of layers and the curvature at a given location was identified.…”

Section: Introductionmentioning

confidence: 99%

“…The outer boundary shrinks as one end of the wood strip passes through a loop, in the same way that a clothing belt is tightened. Right panel reproduced from [55], with the permission of AIP Publishing.…”

Section: Introductionmentioning

confidence: 99%

Packing of elastic rings with friction

Alben

2021

Preprint

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We study the deformations of elastic filaments confined within slowly-shrinking circular boundaries, under contact forces with friction. We perform computations with a spring-lattice model that deforms like a thin inextensible filament of uniform bending stiffness. Early in the deformation, two lobes of the filament make contact. If the friction coefficient is small enough, one lobe slides inside the other; otherwise, the lobes move together or one lobe bifurcates the other. There follows a sequence of deformations that is a mixture of spiraling and bifurcations, primarily the former with small friction and the latter with large friction. With zero friction, a simple model predicts that the maximum curvature and the total elastic energy scale as the wall radius to the -3/2 and -2 powers respectively. With nonzero friction, the elastic energy follows a similar scaling but with a prefactor up to 8 times larger, due to delayering and bending with a range of small curvatures. For friction coefficients as large as 1, the deformations are qualitatively similar with and without friction at the outer wall. Above 1, the wall friction case becomes dominated by buckling near the wall.

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A cascade of length scales in elastic rings under confinement

Cited by 2 publications

References 0 publications

Packing of elastic rings with friction

Packing of elastic rings with friction

Packing of elastic rings with friction

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