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IMA Journal of Applied Mathematics Advance Access originally published online on December 17, 2004
IMA Journal of Applied Mathematics 2005 70(1):3-14; doi:10.1093/imamat/hxh057
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IMA Journal of Applied Mathematics Vol. 70 No. 1 © Institute of Mathematics and its Applications 2005; all rights reserved.

On interface waves in misoriented pre-stressed incompressible elastic solids*

M. Destrade

Laboratoire de Modélisation en Mécanique, CNRS, Université Pierre et Marie Curie (UMR 7607), 4 place Jussieu, case 162, 75252 Paris Cedex 05, France

Some relationships, fundamental to the resolution of interface wave problems, are presented. These equations allow for the derivation of explicit secular equations for problems involving waves localized near the plane boundary of anisotropic elastic half-spaces, such as Rayleigh, Scholte, or Stoneley waves. They are obtained rapidly, without recourse to the Stroh formalism. As an application, the problems of Stoneley wave propagation and of interface stability for misaligned predeformed incompressible halfspaces are treated. The upper and lower half-spaces are made of the same material, subject to the same prestress, and are rigidly bonded along a common principal plane. The principal axes in this plane do not, however, coincide, and the wave propagation is studied in the direction of the bisectrix of the angle between a principal axis of the upper half-space and a principal axis of the lower half-space.

Keywords: bimaterials; interface stability; pre-stress; Stoneley waves.

* Dedicated to Ray W. Ogden on the occasion of his 60th birthday


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