  We revisit the classic problem of elastic cavitation within the framework of
stochastic elasticity. For the deterministic elastic problem, involving
homogeneous isotropic incompressible hyperelastic spheres under radially
symmetric tension, there is a critical dead-load traction at which cavitation
can occur for some materials. In addition to the well-known case of stable
cavitation post-bifurcation at the critical dead load, we show the existence of
unstable snap cavitation for some isotropic materials satisfying Baker-Ericksen
inequalities. For the stochastic problem, we derive the probability
distribution of the deformations after bifurcation. In this case, we find that,
due to the probabilistic nature of the material parameters, there is always a
competition between the stable and unstable states. Therefore, at a critical
load, stable or unstable cavitation occurs with a given probability, and there
is also a probability that the cavity may form under smaller or greater loads
than the expected critical value. We refer to these phenomena as `likely
cavitation'. Moreover, we provide examples of homogeneous isotropic
incompressible materials exhibiting stable or unstable cavitation together with
their stochastic equivalent.

Soft Condensed Matter;Probability