Calculus of Variations and Geometric Measure Theory
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L. Freddi - P. Hornung - M. G. Mora - R. Paroni

Generalised Sadowsky theories for ribbons from three-dimensional nonlinear elasticity

created by mora on 08 May 2018

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Submitted Paper

Inserted: 8 may 2018
Last Updated: 8 may 2018

Year: 2018

Abstract:

In the 1930s Sadowsky derived an asymptotic theory for narrow ribbons. Generalised Sadowsky theories were recently obtained by the authors as a Gamma-limit from two-dimensional plate models. In the present article, we provide a rigorous derivation of these generalised Sadowsky theories starting from nonlinear three-dimensional elasticity. On a technical level, this involves capturing a contribution to the asymptotic energy functional generated by a nonlinear constraint which is satisfied only approximately. It also involves the construction of fine-scale "corrugations" capable of reaching a bending energy regime which is strictly below that of the original Sadowsky functional.

Keywords: Gamma-convergence, nonlinear elasticity, Sadowsky functional, Elastic ribbons


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