Effect of secondary adhesion hysteresis on impact between elastic spherical particles and a half-space

Adhesive interactions play a crucial role in collisions involving soft and compliant materials, yet classical impact models based on the Johnson–Kendall–Roberts (JKR) theory often underestimate experimentally observed energy losses. Motivated by evidence of adhesion hysteresis, we develop a model for the collision of an elastic sphere with an elastic half-space in which the loading and unloading stages are governed by different contact mechanisms. The indentation phase is described by non-adhesive Hertzian contact, whereas the rebound phase follows the adhesive JKR theory. This asymmetric Hertz–JKR formulation captures the additional dissipation associated with secondary adhesion hysteresis. Universal expressions for the coefficient of restitution and the relative energy loss are obtained in dimensionless form as functions of a single adhesion parameter. These relationships constitute master curves that are independent of impact velocity, particle size, elastic properties, and work of adhesion. The model predicts significantly greater energy dissipation than the classical JKR approach across the entire range of adhesion parameters and yields a lower critical threshold for particle sticking after impact. The results provide a realistic framework for describing adhesive particle collisions in granular media, powders, aerosols, and other particulate systems.