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arXiv · 2605.19598

Wrinkling in the Lam\'e problem: a $\Gamma$-convergence approach

Roberta Marziani
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Abstract

We study wrinkling patterns in a thin elastic annulus subjected to radial stretching within the framework of the F\"oppl--von K\'arm\'an theory. Building on the analysis of the Lam\'e 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.

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Roberta Marziani. 2026-05-19. Wrinkling in the Lam\'e problem: a $\Gamma$-convergence approach. https://arxiv.org/abs/2605.19598

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