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June 2020 Relative bending energy for weakly prestrained shells
Silvia Jiménez Bolaños, Anna Zemlyanova
Rocky Mountain J. Math. 50(3): 1001-1020 (June 2020). DOI: 10.1216/rmj.2020.50.1001

Abstract

We derive a dimensionally reduced model for a thin film prestrained with a given incompatible Riemannian metric:

G h ( x , x 3 ) = I 3 + 2 h γ S ( x ) + 2 h γ 2 x 3 B ( x ) +  higher order terms , γ > 2 ,

where 0<h1 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(hγ+2) as h0.

Citation

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Silvia Jiménez Bolaños. Anna Zemlyanova. "Relative bending energy for weakly prestrained shells." Rocky Mountain J. Math. 50 (3) 1001 - 1020, June 2020. https://doi.org/10.1216/rmj.2020.50.1001

Information

Received: 24 August 2019; Revised: 8 November 2019; Accepted: 9 November 2019; Published: June 2020
First available in Project Euclid: 29 July 2020

zbMATH: 07235593
MathSciNet: MR4132623
Digital Object Identifier: 10.1216/rmj.2020.50.1001

Subjects:
Primary: 74B20, 74K25

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 3 • June 2020
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