Periodically wrinkled plate of the Föppl-von Kármán type

Abstract

In this paper we derive, by means of $\Gamma$-convergence, the periodically wrinkled plate model starting from three dimensional nonlinear elasticity. We assume that the thickness of the plate is $h^2$ and that the mid-surface of the plate is given by $(x_1,x_2) \to (x_1,x_2,h^2θ(\per))$, where $\theta$ is $[0,1{]}^2$ periodic function. We also assume that the strain energy of the plate has the order $h^8=(h^2{)}^4$, which corresponds to the Föppl-von Kármán model in the case of the ordinary plate. The obtained model mixes the bending part of the energy with the stretching part.