On Interfacial Waves in PreStressed Layered Incompressible Elastic Solids
Abstract
Interfacial waves along the plane boundary between two prestressed incompressible elastic solids are considered. One of the solids is a halfspace while the other has arbitrary uniform thickness. The principal axes of the underlying pure homogeneous deformation in the two solids are aligned, with one axis normal to the interface. For propagation along an inplane principal axis, the dispersion equation is derived in respect of a general strainenergy function. Conditions on the prestrain, prestress and material parameters that ensure the existence of a unique interfacial wavespeed at low frequencies are obtained, and it is shown that, in special circumstances, nondispersive waves can exist at the lowfrequency limit. Asymptotic results at the highfrequency limit are also obtained. For the case of equibiaxial prestrain, more specific conditions are derived for the existence of interfacial waves at the low and highfrequency asymptotes, and these provide information on the existence of waves for the whole frequency range. A particular feature of the structure considered is that it may act as a mechanical filter in different frequency regimes depending on the prestrain, prestress and material parameters. When the wavespeed vanishes, the dispersion equation reduces to a bifurcation equation, solutions of which define states of stress and deformation which form boundaries of the region of stability of the underlying state of stress and deformation in the two materials for given material properties. The bifurcation equation is examined separately and an explicit bifurcation criterion is given for equibiaxial deformations. The results are illustrated graphically by considering several numerical examples based on a certain class of strainenergy functions, which includes the neoHookean strainenergy function. The results highlight low and highfrequency features and demonstrate the influence of prestress and deformation on the multiplicity of propagating modes.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 August 1995
 DOI:
 10.1098/rspa.1995.0087
 Bibcode:
 1995RSPSA.450..319O