Normal and tangential force–displacement relations for frictional elasto-plastic contact of spheres

In this paper, we present the data obtained from numerical experiments that are at the foundation of our successful elasto-plastic force–displacement (FD) models in both the normal direction and tangential direction of spheres in collision. We also present in detail how these data were obtained. Our numerical experiments are in the form of frictional elasto-plastic finite-element analysis of spherical particles in contact. We use the numerical experiments to observe the behavior of various quantities involved in the contact (e.g. contact-area radius, contact curvature, stresses, FD relations, etc.). This observation has helped us to devise an accurate and consistent model for frictional elasto-plastic contact of spherical particles that are used in granular-flow simulations that may involve tens of thousands of these particles.