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arXiv · 1912.10928

Asymptotic Behavior for Textiles in von-K{\'a}rm{\'a}n regime

Georges Griso·Julia Orlik·Stephan Wackerle
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Abstract

The paper is dedicated to the investigation of simultaneous homogenization and dimension reduction of textile structures as elasticity problem with an energy in the von-K{\'a}rm{\'a}n-regime. An extension for deformations is presented allowing to use the decomposition of plate-displacements. The limit problem in terms of displacements is derived with the help of the unfolding operator and yields in the limit the von-K{\'a}rm{\'a}n plate with linear elastic cell-problems. It is shown, that for homogeneous isotropic beams in the structure, the resulting plate is orthotropic. As application of the obtained limit plate we study the buckling behavior of orthotropic textiles.

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Georges Griso, Julia Orlik, Stephan Wackerle. 2019-12-23. Asymptotic Behavior for Textiles in von-K{\'a}rm{\'a}n regime. https://arxiv.org/abs/1912.10928

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