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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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An existence theorem for a class of wrinkling models for highly stretched elastic sheets
We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model is characterized by a finite-strain hyperelastic membrane energy perturbed by small bending energy. In the absence of the latter, the membrane energy density is not rank-one convex for general spatial deformations but reduces to a polyconvex function when restricted to planar deformations, i.e., two-dimensional hyperelasticity. In addition, it grows unbounded as the local area ratio approaches zero. The small bending component of the model is the same as that in the classical von K´arm´an model. The latter penalizes arbitrarily fine-scale wrinkling, resolving both the amplitude and wavelength of wrinkles. Here, we prove the existence of energy minima for a general class of such models.
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- Award ID(s):
- 2006586
- PAR ID:
- 10525568
- Editor(s):
- NA
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Zeitschrift für angewandte Mathematik und Physik
- Volume:
- 74
- Issue:
- 6
- ISSN:
- 0044-2275
- Subject(s) / Keyword(s):
- Wrinkling, polyconvexity, nonlinear elasticity, energy minimization, thin plates
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00033-023-02111-9
