General Model for Contact Law between Two Rough Spheres

An incremental elastic-plastic constitutive model is proposed to relate force and displacement at the contact between two identical elastic rough spheres. The model is formulated in a three-dimensional force space defined by the normal and two tangential contact force components. The normal and two tangential components of the relative displacement between the centers of the spheres are predicted for any arbitrary contact force history. The infinite yield surfaces in force space are cones parallel to each other, the apexes of which generally do not coincide with the origin of the force space; the axes of the cones translate without rotation during loading. It is a kinematic hardening model with a modified normality rule. The model identically reproduces all available closed solutions obtained by Mindlin, Deresiewicz and others for particular loading histories, leading to the conjecture that it may be a rigorous solution of the contact problem. The model has been coded into program CONTACT and used for numerical simulations of granular media using finite element and discrete element techniques.