Derivation of the Reissner-Mindlin model from nonlinear elasticity

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.