  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. How- ever, the elastic instability is reversible and rate-independent,
dis- appearing 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.
