A Continuum Mechanics Model of Adhesive Contact Based on the Lennard-Jones Potential

A continuum model of adhesive interaction between elastic surfaces is presented. Surface interaction between two elastic spheres is modeled by the Lennard-Jones (L-J) potential. The analysis is based on the equivalent system of a rigid sphere of reduced radius in close proximity with an elastic half-space of effective elastic modulus. The critical gap at the instant of the “jump-in” and “jump-out” contact instabilities is determined by an elastic solution of the half-space surface displacement. A finite element model, in which surface interaction is modeled by nonlinear springs of a prescribed force-displacement governed by the L-J potential, is also used to analyze adhesive surface interaction. The analytical model is validated by finite element results of the critical central gap at the instant of jumpin and jump-out instabilities for different values of the Tabor parameter.