Folding instability of a layered viscoelastic medium under compression

Abstract

A preliminary theory is established for the stability of a viscoelastic layer sandwiched in an infinitely extended medium of another viscoelastic material when a compressive force is acting in a direction parallel with the layer. The instability is manifested by a folding of the layer. It is shown that in general there exists a lower and a higher critical load between which folding occurs at a finite rate with a dominant wavelength. This is the wavelength whose amplitude increases at the fastest rate. Special cases are also discussed in more detail such as that of a purely viscous layer in a viscous fluid, an elastic layer in a viscous fluid, a viscous layer in an elastic medium, and of two Maxwell materials. Results indicate that the ratio of the relaxation times of the two materials is an important parameter.