Derivation of the Reissner-Mindlin model from nonlinear elasticity

TL;DR

This paper derives the Reissner-Mindlin plate model from three-dimensional nonlinear elasticity using 3-convergence, highlighting the importance of different strain scalings and technical tools like rigidity estimates.

Contribution

It provides a rigorous derivation of the Reissner-Mindlin model from 3D elasticity, incorporating transverse shear effects through novel scaling and analytical techniques.

Findings

Reissner-Mindlin model derived via -convergence.

Different strain components scaled appropriately.

Rigidity estimates combined with averaging techniques.

Abstract

We discuss how the Reissner-Mindlin plate model can be derived from three-dimensional finite elasticity in terms of $\Gamma$-convergence. The presence of transverse shear effects in the Reissner-Mindlin model requires to scale different components of the three-dimensional elastic strain differently. A main technical tool is then the combination of rigidity estimates for the deformation and suitably averaged versions.