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arXiv · 1402.4514

General homogenization of bending-torsion theory for inextensible rods from 3D elasticity

Maroje Marohnic·Igor Velcic
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Abstract

We derive, by means of Gamma-convergence, the equations of homogenized bending rod starting from $3D$ nonlinear elasticity equations. The main assumption is that the energy behaves like h^2 (after dividing by the order h^2 of vanishing volume) where h is the thickness of the body. We do not presuppose any kind of periodicity and work in the general framework. The result shows that, on a subsequence, we always obtain the equations of bending-torsion rod and identifies, in an abstract formulation, the limiting quadratic form connected with that model. This is a generalization from periodic to non-periodic homogenization of bending-torsion rod theory already present in the literature.

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Maroje Marohnic, Igor Velcic. 2014-02-18. General homogenization of bending-torsion theory for inextensible rods from 3D elasticity. https://arxiv.org/abs/1402.4514

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