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In the present short note, we generalize simple approximateJohnson-Jaffar-Barber solutions for the indentation by a rigid punch of a thinelastic layer on a rigid foundation to the case of adhesion. This could be aninteresting geometry for an adhesive system, a limit case of the more generalclass of layered systems, or FGMs (Functionally Graded Materials). We show thatultrastrong adhesion (up to theoretical strength) can be reached both in linecontact or in axisymmetric contact for thin layers (typically of nanoscalesize), which suggests a new possible strategy for "optimal adhesion". Inparticular, in line contact adhesion enhancement occurs as an increase of theactual pull-off force, while in axisymmetric case the latter is apparently veryclose to the classical JKR case. However, it appears in closer examination thatalso for axisymmetric case, the enhancement occurs by reducing the size ofcontact needed to sustain the pull-off force. These effects are furtherenhanced by Poisson's ratio effects in the case of nearly incompressible layer.

Ultrastrong adhesion in the contact with thin elastic layers on a rigid foundation