  When a fluid is pumped into a cavity in a confined elastic layer, at a
critical pressure, destabilizing fingers of fluid invade the elastic solid
along its meniscus (Saintyves, Dauchot, and Bouchaud, 2013). These fingers
occur without fracture or loss of adhesion and are reversible, disappearing
when the pressure is decreased. We develop an asymptotic theory of pressurized
highly elastic layers trapped between rigid bodies to explain these
observations, with predictions for the critical fluid pressure for fingering,
and the finger wavelength. We also show that the theory links this fluid-driven
fingering with a similar transition driven instead by transverse stretching of
the elastic layer. We further verify these predictions by using finite-element
simulations on the two systems which show that, in both cases, the fingering
transition is first-order (sudden) and hence has a region of bistability. Our
predictions are in good agreement with recent observations of this elastic
analog of the classical Saffman-Taylor interfacial instability in
hydrodynamics.
