On the Instability and Folding Deformation of a Layered Viscoelastic Medium in Compression

Abstract

Abstract When a layer of material embedded in an infinite medium is subject to a compression parallel with the layer an instability tends to develop which manifests itself in the folding of the layer. This phenomenon is examined here for the general case where the layer and the surrounding medium are both viscoelastic. This problem which was examined in preliminary form in an earlier publication [6] is treated here with particular attention to the effect of interfacial adherence of the layer and the medium, and to an evaluation of the amplitude of the folding. In general there is a lower and upper-critical value of the compressive load between which folding occurs with a finite rate of deformation. There appears also a dominant wave length, for which the rate of folding is maximum under a given load. The dominant wave length may or may not depend on the load. The effect of interfacial adherence while not negligible is not generally significant. The rate of folding increases very rapidly beyond a certain value of the viscosity ratio of the two media. A brief discussion is also included of the thermodynamic implications of incremental stress-strain relations in prestressed media.