On the Kirchhoff-Love hypothesis (revised and vindicated)
Abstract
The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its attribution has been questioned, and recent rigorous dimension-reduction tools (based on -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate's mid surface (alongside the expected measures of bending). The incompatibility with -convergence also appears to be removed in the cases where contact with that method and ours can be made.
Keywords
Cite
@article{arxiv.2005.13412,
title = {On the Kirchhoff-Love hypothesis (revised and vindicated)},
author = {Olivier Ozenda and Epifanio G. Virga},
journal= {arXiv preprint arXiv:2005.13412},
year = {2020}
}