The Nash-Kuiper process for curves

Borrelli, Vincent; Jabrane, Saïd; Lazarus, Francis; Thibert, Boris

doi:10.5802/tsg.288

Cited by 1 publication

(2 citation statements)

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“…The parameters of the system, h, E and µ, can be combined into one effective stiffness D = Eh 3 12(1−µ 2 ) of the plate as the main parameter defining mechanical properties of the system. It has been shown for constant compressing, that increasing stiffness suppresses buckling.…”

Section: Discussionmentioning

confidence: 99%

“…In the first group of works, tentatively denoted as "geometric" [1, 2] (see also [3]), the determination of the typical profile of 2D surface is dictated by optimal "isometric" embedding of discretized 2D surface into 3D space, and is described by an appropriate change of conformal metrics. This approach relies only on geometric constraints imposed by a "conflict" between metric of a 3D Euclidean space and intrinsic hyperbolic metric of a 2D ideal membrane, and can be treated using the conformal methods.…”

Section: Introductionmentioning

confidence: 99%

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Buckling and wrinkling from geometric and energetic viewpoints

Nechaev¹,

Polovnikov²

2015

Preprint

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We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic consideration based on the minimization of the total energy functional. In the latter case the non-uniformly pre-stressed plate, which models the inhomogeneous two-dimensional growth, is analyzed in linear regime under small stochastic perturbations. It is explicitly demonstrated that both approaches give consistent results for buckling profiles and reveal self-similar behavior. We speculate that fractal-like organization of growing squeezed structure has a far-reaching impact on understanding cell proliferation in various biological tissues.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%