Transverse corrugation solitons in a three-layered non-linearly elastic medium

The problem of the transverse bending deformations of a heavily loaded, thin, middle layer of material in a three-layer, linearly elastic medium is considered. Special versions of the theory of perturbations are developed to analyse the two-dimensional dynamics of the layers. As a result of “joining” them, a quasi-one-dimensional model is constructed which describes the evolution of the bendings of the middle layer close to the threshold of its stability. The possibility of the formation of “transverse corrugation” solitions which precede the inelastic deformation of the middle layer, is established. The condition for the existence of solitons are investigated as a function of the external stress, the thickness of the middle layer and the material parameters of the medium.