On the Kirchhoff-Love hypothesis (revised and vindicated)

2020/05/27 by Ozenda, Olivier, Virga, Epifanio G. · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2005.13412

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 Γ-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 Γ-convergence also appears to be removed in the cases where contact with that method and ours can be made.

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