Analyzed is the mutual deformation of adhesive particles that interact with
van der Waals forces using a viscoelastic theory that accounts for the tim
e dependence of the phenomenon. The particle shape and interaction is calcu
lated self-consistently for finite-ranged forces. Typical loading-unloading
trajectories display hysteresis that increases with driving velocity, as d
oes the particles' adhesion. An analytic approximation that accounts for th
e precontact deformation is tested against the exact numerical benchmarks a
nd found to be accurate.