INTERFACIAL WAVES IN A PRE-STRAINED NEO-HOOKEAN BODY .1. BIAXIAL STATES OF STRAIN

The two parts of this paper report an investigation of the conditions under which an interfacial wave can propagate in a medium formed by welding together two semi-infinite neo-Hookean elastic bodies which have been subjected to triaxial extensions of different magnitudes in directions in and normal to the interface. In Part I the secular equation, determining the speed of propagation of an interfacial wave, is derived by standard methods and the analysis is then specialized to the case in which the in-plane stretches (in directions parallel to the interface) are equal in each of the constituent bodies. The domain of existence of interfacial waves in the quarter-plane spanned by the distinct in-plane stretches is shown to be bounded by two curves to which the designations neutral and limiting are given. These curves, which do not depend upon material or geometrical parameters when the pre-strain is biaxial, are plotted by a combination of asymptotic analysis and numerical computation. A discussion of the dependence of the wave speed and the particle paths on the in-plane stretches concludes Part I. © 1979 Oxford University Press.