Pull-off of viscoelastic spherical contact

This paper studied the adhesive contact between a viscoelastic sphere and a rigid plane, and presented a dimensionless first-order differential equation to directly describe the relationship between the applied load and the contact radius. By adopting a combination strategy, the singularity of Muller’s dimensionless first-order differential equation was avoided well. To study the dependence of the pull-off force on the initial applied load, a table-based linear and logarithmic interpolation method was presented to determine the contact radius at the pull-off. The dependence of the square root (ζmax) of the ratio of the effective adhesion work at the upper bound to the equilibrium adhesion work on Muller’s parameter β and material constant n was deduced theoretically. And the relationship between the contact radius at the upper bound and ζmax was also deduced theoretically. In addition, the ratio of the pull-off force to the maximum pull-off force was determined to be cubic function of the ratio of the contact radius at the pull-off to that at the upper bound numerically. If β, n and the initial applied load were given, utilizing these relationships, the pull-off force and the maximum pull-off force could be predicted well. Lastly, Violano-Chateauminois-Afferrante JKR-like formula for the pull-off force and the upper bound was verified.