  A slender thread of elastic hydrogel is susceptible to a surface instability
that is reminiscent of the classical Rayleigh-Plateau instability of liquid
jets. The final, highly nonlinear states that are observed in experiments arise
from a competition between capillarity and large elastic deformations.
Combining a slender analysis and fully three-dimensional numerical simulations,
we present the phase map of all possible morphologies for an unstable
neo-Hookean cylinder subjected to capillary forces. Interestingly, for softer
cylinders we find the coexistence of two distinct configurations, namely,
cylinders-on-a-string and beads-on-a-string. It is shown that for a given set
of parameters, the final pattern is selected via a dynamical evolution. To
capture this, we compute the dispersion relation and determine the
characteristic wavelength of the dynamically selected profiles. The validity of
the "slender" results is confirmed via simulations and these results are
consistent with experiments on elastic and viscoelastic threads.
