ALGORITHM FOR RANDOM CLOSE PACKING OF SPHERES WITH PERIODIC BOUNDARY-CONDITIONS

The isotropic algorithm is constructBd for random close packing of equ isized spheres with triply periodic boundary conditions. All previousl y published packing methods with periodic boundaries were kinetics-det ermined; i.e., they contained a densification rate as an arbitrary par ameter. In contrast, the present algorithm is kinetic-independent and demonstrates an unambiguous convergence to the experimental results. T o suppress crystallization, the main principles of our algorithm are ( 1) to form a contact network at an early stage and (2) retain contacts throughout the densification, as far as possible. The particles are a llowed to swell by the numerical solution of the differential equation s of densification. The RHS of these equation is calculated efficientl y from a linear system by a combination of conjugate gradient iteratio ns and exact sparse matrix technology. When an excessive contact occur s and one of the existing bonds should be broken to continue the densi fication, an efficient criterion based on multidimensional simplex geo metry is used for searching the separating bond. The algorithm has a w ell-defined termination point resulting in a perfect contact network w ith the average coordination number six (for particle number N much gr eater than 1) and a system of normal reactions between the spheres mai ntaining the structure. These forces are the counterpart of the algori thm and can be used to calculate small elastic particle deformations i n a granular medium. Extensive calculations are presented for 50 less- than-or-equal-to N less-than-or-equal-to 400 and demonstrate very good agreement with the experimental packing density (about 0.637) and str ucture. (C) 1994 Academic Press, Inc.