General homogenization of bending-torsion theory for inextensible rods from 3D elasticity
Analysis of PDEs
2014-02-20 v1
Abstract
We derive, by means of Gamma-convergence, the equations of homogenized bending rod starting from 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.
Keywords
Cite
@article{arxiv.1402.4514,
title = {General homogenization of bending-torsion theory for inextensible rods from 3D elasticity},
author = {Maroje Marohnic and Igor Velcic},
journal= {arXiv preprint arXiv:1402.4514},
year = {2014}
}