Interfacial waves in an inextensible elastic composite

Abstract

The composite considered here is formed by welding together two semi-infinite bodies, made of different transversely isotropic elastic materials, each inextensible along the symmetry axis. It is known from previous work that a small-amplitude wave can propagate along the plane interface only when the directions of inextensibility in the constituent bodies coincide. The case chosen for detailed study in the present paper is that in which the common direction is parallel to the interface: this is mathematically the simplest and physically the most interesting situation. The secular equation governing the speed of propagation is derived and reformulated by a matrix method which yields a necessary and sufficient condition for the existence of an interfacial wave and a proof that whenever such a wave exists it is unique. The domain of existence of interfacial waves is seven-dimensional, the coordinates being the angle between the directions of propagation and inextensibility and six dimensionless combinations of the material constants. Four of the combinations relate to one of the constituent materials and the others to both. The bimaterial combinations and the quotient of two of the others effectively control the set of directions in which an interfacial wave can travel. Some representative cases are discussed numerically.