Abstract:This paper establishes novel rigidity estimates for hyperbolic shells (surfaces with negative Gaussian curvature) and applies them to derive the \(\Gamma\)-limit of thin elastic shells. We prove a nonlinear rigidity estimate for \(H^1\) deformations on the mid-surface, and a nonlinear rigidity estimate for hyperbolic shells with clamped lateral boundary. The latter yields the optimal exponent \(h^{-4/3}\). As the main application, we characterize the \(\Gamma\)-limit of the nonlinear elastic energy for clamped hyperbolic shells across all scaling regimes \(\beta \in [0,2) \cup (8/3,\infty)\).
From: Liangbiao Chen [view email]
[v1]
Sun, 14 Jun 2026 14:05:21 UTC (111 KB)
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