CONTACT FORCE-DISPLACEMENT LAWS AND THE MECHANICAL-BEHAVIOR OF RANDOMPACKS OF IDENTICAL SPHERES

The contact force-displacement law of two identical elastic spheres ca n independently display: nonlinear response, path dependence and dissi pation due to slip. Omitting relative roll and torsion between the two spheres, a general contact force-displacement law is derived analytic ally by integrating the differential form of the Hertz-Mindlin solutio n along the contact displacement path. The Hertz-Mindlin contact law a nd a different contact law formulated by K, Walton are special cases o f this general contact law. Implementation of the contact law in numer ical codes may be cumbersome because it requires a full description of the contact load history. Some simplified contact force-displacement laws proposed in the literature that overcome this difficulty are show n to be thermodynamically inconsistent (i.e,, unphysical) since they p ermit energy generation at no cost. The mean-field approximation and s tatistical averaging for calculating macroscopic stress-strain relatio ns are discussed with respect to various contact force-displacement la ws.