  The problem of the Rivlin cube is to determine the stability of all
homogeneous equilibria of an isotropic incompressible hyperelastic body under
equitriaxial dead loads. Here, we consider the stochastic version of this
problem where the elastic parameters are random variables following standard
probability laws. Uncertainties in these parameters may arise, for example,
from inherent data variation between different batches of homogeneous samples,
or from different experimental tests. As for the deterministic elastic problem,
we consider the following questions: what are the likely equilibria and how
does their stability depend on the material constitutive law? In addition, for
the stochastic model, the problem is to derive the probability distribution of
deformations, given the variability of the parameters.
