Relative Bending Energy for Weakly Prestrained Shells

2019/09/27 by Silvia Jimenez Bolanos, Bolanos, Silvia Jimenez, Anna Zemlaynova +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1910.00404

arXiv admin note: text overlap with arXiv:1404.3298, arXiv:1002.2252 by other authors

arxiv created 2019/09/27 · arxiv updated 2019/10/02

Abstract

In this paper, we derive a dimensionally reduced model for a thin film prestrained with a given incompatible Riemannian metric: G^h(x',x₃)=I₃+2h^γ S(x')+2h^γ/2 x₃B(x')+h.o.t, γ>2, where 0<h≪ 1 is the thickness of the film. The problem is studied rigorously by using a variational approach and establishing the Γ-convergence of the non-Euclidean version of the nonlinear elasticity functional. It is shown that the residual nonlinear elastic energy scales as O(h^γ+2) as h→ 0.

Citations

• Variational models for prestrained plates with Monge-Ampère constraint
• The von Karman equations for plates with residual strain

Cited by

• The linearized Kirchhoff theory for plates with incompatible prestrain

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