  The cavitation of solid elastic spheres is a classical problem of continuum
mechanics. Here, we study this problem within the context of "stochastic
elasticity" where the constitutive parameters are characterised by probability
density functions. We consider homogeneous spheres of stochastic neo-Hookean
material, composites with two concentric stochastic neo-Hookean phases, and
inhomogeneous spheres of locally neo-Hookean material with a radially varying
parameter. In all cases, we show that the material at the centre determines the
critical load at which a spherical cavity forms there. However, while under
dead-load traction, a supercritical bifurcation, with stable cavitation, is
obtained in a static sphere of stochastic neo-Hookean material, for the
composite and radially inhomogeneous spheres, a subcritical bifurcation, with
snap cavitation, is also possible. For the dynamic spheres, oscillatory motions
are produced under suitable dead-load traction, such that a cavity forms and
expands to a maximum radius, then collapses again to zero periodically, but not
under impulse traction. Under a surface impulse, a subcritical bifurcation is
found in a static sphere of stochastic neo-Hookean material and also in an
inhomogeneous sphere, whereas in composite spheres, supercritical bifurcations
can occur as well. Given the non-deterministic material parameters, the results
can be characterised in terms of probability distributions.
