Periodically wrinkled plate model of the Föppl-von Kármán type

Abstract

In this paper we derive, by means of 0-convergence, the periodically wrinkled plate model starting from three dimensional nonlinear elasticity. We assume that the thickness of the plate is h2 and that the mid-surface of the plate is given by (x1, x2) → (x1, x2, h2θ( x1 h , x2 h )), where θ is [0, 1] 2 periodic function. We also assume that the strain energy of the plate has the order h8 = (h2)4, which corresponds to the Foppl-von Karman model in the case of the ordinary plate. The obtained model mixes the bending part of the energy with the stretching part. Mathematics Subject Classification (2010): 74K20 (primary); 74B20 (secondary).