© 1991 by Oxford University Press
ON THE OCCURRENCE OF THE CAVITATION INSTABILITY RELATIVE TO THE ASYMMETRIC INSTABILITY UNDER SYMMETRIC DEAD-LOAD CONDITIONS
( Department of Mechanical Engineering, Massachusetts Institute of Technology Cambridge, Massachusetts 02139, USA )
Deformations of an isotropic, incompressible, elastic sphere or cylinder, which is subjected to a uniformly-distributed, radial, nominal traction on its boundary, are considered. One deformation that this body can undergo is the trivial one in which the body remains undeformed and the stress state is uniform and hydrostatic. However, at least two other types of deformations can bifurcate from this fundamental one, viz. a ‘cavitated deformation’ which leads to the presence of a concentric internal cavity, and an ‘asymmetric deformation’ which carries the sphere into an ellipsoid. This paper examines the relationship between the occurrence of these two types of instabilities. In particular, we show that if there is a stable cavitated configuration corresponding to a given value of the applied stress, then necessarily there also exists a stable asymmetric configuration at that same stress; moreover, the total potential energy associated with the asymmetric configuration is less than that of the cavitated configuration.