  In the present short note, we generalize simple approximate
Johnson-Jaffar-Barber solutions for the indentation by a rigid punch of a thin
elastic layer on a rigid foundation to the case of adhesion. This could be an
interesting geometry for an adhesive system, a limit case of the more general
class of layered systems, or FGMs (Functionally Graded Materials). We show that
ultrastrong adhesion (up to theoretical strength) can be reached both in line
contact or in axisymmetric contact for thin layers (typically of nanoscale
size), which suggests a new possible strategy for "optimal adhesion". In
particular, in line contact adhesion enhancement occurs as an increase of the
actual pull-off force, while in axisymmetric case the latter is apparently very
close to the classical JKR case. However, it appears in closer examination that
also for axisymmetric case, the enhancement occurs by reducing the size of
contact needed to sustain the pull-off force. These effects are further
enhanced by Poisson's ratio effects in the case of nearly incompressible layer.
