CAVITATION FOR INCOMPRESSIBLE ANISOTROPIC NONLINEARLY ELASTIC SPHERES

In this paper, the effect of material anisotropy on void nucleation an d growth in incompressible nonlinearly elastic solids is examined. A b ifurcation problem is considered for a solid sphere composed of an inc ompressible homogeneous nonlinearly elastic material which is transver sely isotropic about the radial direction. Under a uniform radial tens ile dead-load, a branch of radially symmetric configurations involving a traction-free internal cavity bifurcates from the undeformed config uration at sufficiently large loads. Closed form analytic solutions ar e obtained for a specific material model, which may be viewed as a gen eralization of the classic neo-Hookean model to anisotropic materials. In contrast to the situation for a neo-Hookean sphere, bifurcation he re may occur locally either to the right (supercritical) or to the lef t (subcritical), depending on the degree of anisotropy. In the latter case, the cavity has finite radius on first appearance. Such a discont inuous change in stable equilibrium configurations is reminiscent of t he snap-through buckling phenomenon of structural mechanics. Such dram atic cavitational instabilities were previously encountered by Antman and Negron-Marrero [3] for anisotropic compressible solids and by Horg an and Pence [17] for composite incompressible spheres.