Pull-off of a rigid cone from a viscoelastic substrate

The pull-off of a sphere from an elastic substrate follows the well-known JKR solution, and a similar but less known solution is valid for a cone. The two differ qualitatively in the parametric dependences of the pull-off load, so we study the case of a viscoelastic substrate using a well-known Gent and Schultz approach for the effective work of adhesion, with the assumption that the elastic modulus in the bulk of the specimen is the relaxed one. The rate of peeling of the contact line (for given remote withdrawing speed) depends on elastic modulus for the spherical case, and not for the cone. However, for the spherical geometry, we predict that the highest load amplification should be actually smaller than the highest work of adhesion amplification, while for the cone the opposite is true, although of a smaller factor.