Thin soft elastic layers serving as joints between relatively rigid
bodies may function as sealants, thermal, electrical, or mechanical
insulators, bearings, or adhesives. When such a joint is stressed,
even though perfect adhesion is maintained, the exposed free
meniscus in the thin elastic layer becomes unstable, leading to the
formation of spatially periodic digits of air that invade the elastic
layer, reminiscent of viscous fingering in a thin fluid layer. However, the elastic instability is reversible and rate-independent, disappearing when the joint is unstressed. We use theory, experiments,
and numerical simulations to show that the transition to the
digital state is sudden (first-order), the wavelength and amplitude
of the fingers are proportional to the thickness of the elastic layer,
and the required separation to trigger the instability is inversely
proportional to the in-plane dimension of the layer. Our study
reveals the energetic origin of this instability and has implications
for the strength of polymeric adhesives; it also suggests a method
for patterning thin films reversibly with any arrangement of
localized fingers in a digital elastic memory, which we confirm
experimentally.