CONCAVITIES ON THE ZONAL SLOWNESS SECTION OF A TRANSVERSELY ISOTROPICELASTIC-MATERIAL

The section of the slowness surface of a, transversely isotropic elast ic material in a zonal plane consists of an ellipse and a quartic curv e with two nested branches, the inner of which is convex. Concavities can therefore occur only on the outer branch S and five possibilities arise: (I) S is convex; (II) S has two axial concavities (centred on t he points of intersection of S with the axis of transverse isotropy); (III) S has two basal concavities (centred on the points of intersecti on of S with the basal plane); (IV) S has two axial and two basal conc avities; (V) S has four oblique concavities, neither axial nor basal. The first and last of these are commonly realized in actual materials, the others only rarely. A unified treatment of stationary points and concavities on S is given in the course of which some previous results are simplified and their relationship clarified.