© 1979 by Oxford University Press
INTERFACIAL WAVES IN A PRE-STRAINED NEO-HOOKEAN BODY
II. TRIAXIAL STATES OF STRAIN
( School of Mathematics and Physics, University of East Anglia Norwich )
The study of interfacial waves in an infinite neo-Hookean elastic body whose two halves have been differently pre-strained on common axes, one of them normal to the interface, is here extended to the case in which the magnitudes of the in-plane stretches are unrestricted. To render the generalized analysis tractable the stretches on one of the in-plane axes are regarded as given a priori and the other in-plane pair are treated as controllable variables. In this setting there arise families of neutral and limiting curves, situated in the quadrant spanned by the variable stretches and parametrized by the angle defining the direction of wave propagation. The form of the neutral curves is broadly the same as in the case of biaxial pre-strain, considered in Part I, but the limiting curves are altogether more elaborate. As regards the existence of interfacial waves, three possibilities now emerge: a wave can propagate in every in-plane direction; in some directions only, forming one or more pairs of opposite sectors; or in no direction at all. The domain of total existence (associated with the first possibility) consists of two finite subdomains which are disjoint and, as described by numerical results for a variety of particular cases, of small extent.