Voronoi neighbor statistics of homogeneously sheared inelastic hard disks and hard spheres

V. Senthil Kumar and V. Kumaran

Phys. Rev. E 73, 051305 – Published 19 May 2006

Abstract

In this work we extend our earlier Voronoi neighbor analysis [J. Chem. Phys. 123, 074502 (2005)] to homogeneously sheared inelastic hard-particle structures, the simplest model for rapid granular matter. The pair distribution function is partitioned into the $n th$ neighbor coordination number $(C_{n})$ , and the $n th$ neighbor position distribution $[f_{n} (r)]$ . The distribution of the number of Voronoi faces $(P_{n})$ is also considered since $C_{1}$ is its mean. We report the $C_{n}$ and $P_{n}$ for the homogeneously sheared inelastic hard-disk and hard-sphere structures. These statistics are sensitive to shear ordering transition, the nonequilibrium analogue of the freezing transition. In the near-elastic limit, the sheared fluid statistics approach that of the thermodynamic fluid. On shear ordering, due to the onset of order, the $C_{n}$ for sheared structures approach that of the thermodynamic solid phase. The suppression of nucleation by the homogeneous shear is evident in these statistics. As inelasticity increases, the shear ordering packing fraction increases. Due to the topological instability of the isotropically perturbed face-centered cubic lattice, polyhedra with faces 12 to 18, with a mean at 14, coexist even in the regular close packed limit for the thermodynamic hard-sphere solid. In shear ordered inelastic hard-sphere structures there is a high incidence of 14-faceted polyhedra and a consequent depletion of polyhedra with faces 12, 13, 15–18, due to the formation of body-centered-tetragonal (bct) structures. These bct structures leave a body-centered-cubic-like signature in the $C_{n}$ and $P_{n}$ data. On shear ordering, close-packed layers slide past each other. However, with a velocity-dependent coefficient of restitution, at a critical shear rate these layers get disordered or amorphized. We find that the critical shear rate for amorphization is inversely proportional to the particle diameter, as compared to the inverse square scaling observed in dense colloidal suspensions.