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Related papers: Wrinkling in the Lam\'e problem: a $\Gamma$-conver…

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We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the…

Analysis of PDEs · Mathematics 2021-10-14 Katharina Brazda , Gaspard Jankowiak , Christian Schmeiser , Ulisse Stefanelli

We develop an irregular lattice mass-spring-model (MSM) to simulate and study the deformation modes of a thin elastic ribbon as a function of applied end-to-end twist and tension. Our simulations reproduce all reported experimentally…

Soft Condensed Matter · Physics 2023-08-02 Madelyn Leembruggen , Jovana Andrejevic , Arshad Kudrolli , Chris H. Rycroft

Experimental observations of unexpected shear rigidity in confined liquids, on very low frequency scales on the order of 0.01-0.1 Hz, call into question our basic understanding of the elasticity of liquids and have posed a challenge to…

Soft Condensed Matter · Physics 2021-01-26 Alessio Zaccone , Kostya Trachenko

The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming…

Analysis of PDEs · Mathematics 2010-10-05 Elisa Davoli , Maria Giovanna Mora

Soft elastic sheets resting on rigid surfaces develop wrinkles, rucks, and folds due to the combined influence of elasticity, gravity, and contact interactions. Despite their ubiquity, the principles governing their morphology and…

Soft Condensed Matter · Physics 2026-05-18 Keisuke Yoshida , Hirofumi Wada

The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansion. We first consider the case of the linear diffusion…

Analysis of PDEs · Mathematics 2025-07-29 Virginie Ehrlacher , Arthur Lebée , Frédéric Legoll , Adrien Lesage

A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter h of the cross-section goes to zero. More precisely, we show that stationary points of the nonlinear elastic…

Analysis of PDEs · Mathematics 2007-05-23 Maria Giovanna Mora , Stefan Müller

In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…

Analysis of PDEs · Mathematics 2019-02-01 Elisa Davoli , Rita Ferreira , Carolin Kreisbeck

We model the formation and evolution of wrinkles in a floating elastic sheet under uniaxial compression. This is a canonical setup in the study of wrinkling, and whilst its static equilibrium configuration is well characterised, its…

Fluid Dynamics · Physics 2025-10-31 Daniel J. Netherwood , Ben S. Humphries , Connor Robbins , Doireann O'Kiely

This is the first in a series of two papers in which we derive a $\Gamma$-expansion for a two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion, also known as the Ohta-Kawasaki model in connection with diblock copolymer…

Mathematical Physics · Physics 2013-09-24 Dorian Goldman , Cyrill B. Muratov , Sylvia Serfaty

We examine a family of microscopic models of plasmas, with a parameter $\alpha$ comparing the typical distance between collisions to the strength of the grazing collisions. These microscopic models converge in distribution, in the weak…

Mathematical Physics · Physics 2009-05-06 Kay Kirkpatrick

We rigorously derive linear elasticity as a low energy limit of pure traction nonlinear elasticity. Unlike previous results, we do not impose any restrictive assumptions on the forces, and obtain a full $\Gamma$-convergence result. The…

Analysis of PDEs · Mathematics 2021-05-18 Cy Maor , Maria Giovanna Mora

We are concerned with the dimension reduction analysis for thin three-dimensional elastic films, prestrained via Riemannian metrics with weak curvatures. For the prestrain inducing the incompatible version of the F\"oppl-von K\'arm\'an…

Analysis of PDEs · Mathematics 2021-04-07 Silvia Jimenez Bolanos , Marta Lewicka

We propose an analytical framework to model the effect of single and multiple mechanical surface oscillators on the dynamics of vertically polarized elastic waves propagating in a semi-infinite medium. The formulation extends the canonical…

Applied Physics · Physics 2021-09-13 Xingbo Pu , Antonio Palermo , Alessandro Marzani

We consider a thin elastic strip of thickness h and we show that stationary points of the nonlinear elastic energy (per unit height) whose energy is of order h^2 converge to stationary points of the Euler-Bernoulli functional. The proof…

Functional Analysis · Mathematics 2007-05-23 Maria Giovanna Mora , Stefan Mueller , Maximilian G. Schultz

Energy minimizers to a MEMS model with an insulating layer are shown to converge in its reinforced limit to the minimizer of the limiting model as the thickness of the layer tends to zero. The proof relies on the identification of the…

Analysis of PDEs · Mathematics 2021-10-12 Philippe Laurençot , Katerina Nik , Christoph Walker

A \Gamma-convergence result involving the elastic energy of a narrow inextensible ribbon is established. A non-dimensional form of the elastic energy is reduced to a one-dimensional integral over the centerline of the ribbon with the aspect…

Analysis of PDEs · Mathematics 2013-07-15 Nicholas Kirby , Eliot Fried

Ab initio density functional theory has been used to analyze flexural modes, elastic constants, and atomic corrugations on single and bi-layer graphene. Frequencies of flexural modes are sensitive to compressive stress; its variation under…

Materials Science · Physics 2013-01-22 P. L. de Andres , F. Guinea , M. I. Katsnelson

We use variational convergence to derive a hierarchy of one-dimensional rod theories, starting out from three-dimensional models in nonlinear elasticity subject to local volume-preservation. The densities of the resulting $\Gamma$-limits…

Analysis of PDEs · Mathematics 2020-02-25 Dominik Engl , Carolin Kreisbeck

Elastic capsules can exhibit short wavelength wrinkling in external shear flow. We analyse this instability of the capsule shape and use the length scale separation between the capsule radius and the wrinkling wavelength to derive…

Soft Condensed Matter · Physics 2007-05-23 Reimar Finken , Udo Seifert