Abstract of the paper ``Contact force-displacement laws and the
mechanical behavior of random packs of identical spheres,'' with D. Elata
The contact force-displacement law of two identical elastic spheres can
independently display: nonlinear response, path dependence and dissipation due to slip.
Omitting relative roll and torsion between the two spheres, a general ontact force-displacement law is derived analytically by integrating the differential form of the
Hertz-Mindlin solution along the contact displacement path.
The Hertz-Mindlin contact law and a different contact law formulated by K. Walton
are special cases of this general contact law. Implementation of the contact law in
numerical 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 shown to be
thermodynamically inconsistent (i.e., unphysical) since they permit
energy generation at no cost. The mean-field approximation and statistical averaging for
calculating macroscopic stress-strain relations are discussed with respect to
various contact force-displacement laws.
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