Calculus of Variations and Geometric Measure Theory

R. Marziani

Wrinkling in the Lamé problem: a $\Gamma$-convergence approach

created by marziani on 16 May 2026
modified on 19 May 2026

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Preprint

Inserted: 16 may 2026
Last Updated: 19 may 2026

Pages: 57
Year: 2026

Abstract:

We study wrinkling patterns in a thin elastic annulus subjected to radial stretching within the framework of the Föppl–von Kármán theory. Building on the analysis of the Lamé problem in Bella and Kohn, we investigate the asymptotic regime $h\to0$ and establish a $\Gamma$-convergence result for suitably rescaled energies after subtraction of the relaxed membrane energy. The limiting functional is a scalar convex measure-valued energy coupled with a constraint on the marginal of the limiting measure, describing the distribution of wrinkle frequencies. We also prove existence and qualitative properties of minimizers of the limiting functional.

Keywords: Wrinkling, Lamé Problem, Gamma convergence


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