Optimal shapes for adhesive binding between two elastic bodies

The pull-off force required to separate two elastic bodies in adhesive binding depends on the surface shapes of the corresponding binding regions on the two bodies. Given a fixed binding area A  , the optimal shapes are those which give the maximum pull-off force σthAσthA where σthσth is the theoretical strength of interactive forces between the two solids. Here we study closed form solutions to the optimal shapes for adhesive binding over a small circular region where slip is allowed whenever shear stress along the contact interface exceeds a critical value.

Graphical abstractThe pull-off force required to separate two elastic bodies in adhesive binding depends on the surface shapes of the corresponding binding regions on the two bodies. Here we study closed form solutions of optimal surface shapes that lead to the maximum pull-off force adhesive binding over a fixed circular area which is divided into a slipping (a⩽r⩽Ra⩽r⩽R) and nonslipping (r