The restructuring of the elastic layer wave-like relief under the load

A promising direction in creating biocompatible polymer implants is using ion-plasma treatment of surface being in contact with biological tissues. This treatment allows production of implants with a carbonized nanolayer which does not provoke rejection. However, some problems arise when a soft polymeric material, e.g. bio-inert polyurethane, is used for the manufacture of this medical product. The material can be severely deformed by the movement of biological tissue, which causes the occurrence of time-varying stresses in the nanolayer. Moreover, the carbonized layer emerging in course of the ion-plasma treatment has a wave-like surface, which is an indication of initial stresses. This paper focuses on mathematical modeling of possible rearrangements of a thin elastic layer. The obtained analytical solutions provide an explanation for the behavior of the elastic layer and for the conditions of loss in stability of one or another deformed state. It has been found that changes in loads may provoke a new orientation of the wave-like relief. The solution presented in the paper can be used to gain better understanding of the phenomena related to geometrical changes in nanolayers formed on soft materials.