The characteristics of elastic interfacial waves in pre-stressed compressible interlayers are examined. The interlayer is separated from an infinite surrounding solid of a generally different non-linear elastic compressible material by planar parallel boundaries. The underlying stress conditions in the two solids are homogeneous with their underlying finite strain having common principal axes, one axis being normal to the planar interfaces. For arbitrary materials and otherwise arbitrary stress, the dispersion equation of superposed small amplitude waves is derived in explicit form for propagation along a principal pre-strain axis lying on an interfacial plane. Analysis of the dispersion equation reveals the characteristics of propagating waves. In respect of the solids' material and pre-stress parameters, single or multiple mode propagation occurs or no propagation at all. The propagation characteristics are classified into categories defined by the material and pre-stress parameters. For wavelengths large as compared to the interlayer thickness, the interfacial wave speed is derive in explicit form yielding parameter conditions for the non-existence of interfacial waves. The bifurcation equation, a limiting case of the dispersion equation, is also examined yielding standing waves as solutions which define the boundaries of stability for the computations for the propagating waves. Graphical illustratiosn are also presented based on numerical computations for Blatz-Ko materia
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