Contact behavior of spherical elastic particles: a computational study of particle adhesion and deformations

When two elastic particles are brought into contact, the effect of short-range intermolecular forces may become significant especially in the contact region. Due to the intermolecular interaction forces around the contact region, the elastic particles usually deform from their original shape. The deformation of the particles changes the distance between interacting molecules that in turn alters the force of interaction. Thus, the contact behavior of elastic particles constitutes a non-linear mathematical problem that defies the traditional analytical methods for general solution. In theoretical analyses, the behavior of contacting particles has often been considered by approximating the shape of undeformed particles as spheres. The discrepancy between simplified models for elastic spheres based on different analytical treatments led to a heated debate over many years. Computer-aided numerical solutions were resorted to as a final arbitrator. However, the existing numerical results for contacting elastic spheres are quite limited because of the requirement of large number of iterations with primitive computational techniques. The purpose of the present work is to demonstrate an efficient computational method that yields each converged solution in a few iterations. Using an arc-length continuation algorithm enables tracking solution branches around turning points to accurately determine jumping-on and jumping-off behavior of contacting surfaces when the value of Taborʹs parameter is not small. Detailed features such as secondary turning points associated with the secondary hysteresis are revealed in load–approach curves when the value of Taborʹs parameter becomes large.