  Adhesive peeling of a thin elastic film from a substrate is a classic problem
in mechanics. However, many of the investigations on this topic to date have
focused on peeling from substrates with flat surfaces. In this paper, we study
the problem of peeling an elastic thin film from a rigid substrate that has
periodic surface undulations. We allow for contact between the detached part of
the film with the substrate. We give analytical results for computing the
equilibrium force given the true peeling angle, which is the angle at which the
detached part of the film leaves the substrate. When there is no contact we
present explicit results for computing the true peeling angle from the
substrate's profile and for determining an equilibrium state's stability solely
from the substrate's surface curvature. The general results that we derive for
the case involving contact allow us to explore the regime of peeling at large
surface roughnesses. Our analysis of this regime reveals that the peel-off
force can be made to become independent of the peeling direction by roughening
the surface. This result is in stark contrast to results from peeling on flat
surfaces, where the peel-off force strongly depends on the peeling direction.
Our analysis also reveals that in the large roughness regime the peel-off force
achieves its theoretical upper bound, irrespective of the other particulars of
the substrate's surface profile.
