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 σthA where σthis 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.