Interfacial waves in pre-stressed incompressible elastic interlayers

Abstract

Elastic interfacial waves along planar interfaces in pre-stressed incompressible layered solids are examined. The layered structure consists of an infinite solid which contains a layer of arbitrary uniform thickness. The material and pre-strain parameters of the interlayer are in general different from those of the surrounding solid. The underlying finite strain in the solids is homogeneous with common principal axes, one axis being normal to the planar interfaces. For arbitrary strain energy functions and propagation along a principal pre-strain axis lying on an interfacial plane, the dispersion equation is derived in explicit form. The interfacial wave speed is subsequently obtained explicitly in respect of the solids' material and prestrain parameters for wavelengths large as compared to the layer thickness, yielding parameter conditions for filtering low frequency interfacial waves. It is proven that it is under these same conditions that interfacial waves of any wavelength cannot exist. For arbitrary interlayer thickness necessary parameter conditions are derived for the existence of quasi-static interfacial deformations corresponding to standing waves. The dependence of interfacial propagating and standing wave characteristics on pre-strain parameters is also illustrated numerically by considering specific incompressible materials.