Contacts and Coordination Numbers in a Compact of Polyhedral Particles

Abstract

Model experiments were carried out with plastic polyhedra (cuboctahedra, in particular) contained in a beaker. The packing structures of these polyhedra were characterized in terms of three different types of contacts‐point, line, and face contacts‐along with the coordination numbers, nc. The present data indicate that the numerical distribution of nc shifted to larger values of nc with increasing distance from the beaker wall. On the other hand, the fractional values with respect to each specific type of contact, np/(np+nI+nf), nI/(np+nI+nf), and nf/(np+nI+nf), changed little with location, except at the beaker wall. The small changes of these fractional values were explained with ignorance of the numerical distribution of contact angles and also of the contact areas in counting the three kinds of contacts. The measured percentages of point, line, and face contacts in the central region ranged from 17% to 20%, 60% to 65%, and 15% to 23%, respectively. The larger percentage of line contacts is attributable to the cooperation of two tendencies inducing opposite orders, namely (1) the stability of a contact between polyhedra free from the array of polyhedra around it, which gives np < nI < nf and (2) the adaptability of a contact to an array of polyhedra around it, which gives nf < nI < np. The number of contacts with small contact angles was substantial in the case of the point and line contacts.