Homogeneous crystallization in cyclically sheared frictionless grains

TL;DR

This study uses numerical simulations to demonstrate that frictionless spherical grains can undergo homogeneous crystallization under cyclic shear at a specific volume fraction, independent of friction or gravity.

Contribution

It shows that homogeneous crystallization occurs in frictionless, purely repulsive spheres under cyclic shear, revealing friction and gravity are not necessary for this process.

Findings

Homogeneous crystallization occurs at a volume fraction of 0.646.

Crystallization is achieved with small strain amplitudes.

Friction and gravity are not essential for crystallization.

Abstract

Many experiments over the past half century have shown that, for a range of protocols, granular materials compact under pressure and repeated small disturbances. A recent experiment on cyclically sheared spherical grains showed significant compaction via homogeneous crystallization (Rietz et al., 2018). Here we present numerical simulations of frictionless, purely repulsive spheres undergoing cyclic simple shear with dissipative Newtonian dynamics at fixed vertical load. We show that for sufficiently small strain amplitudes, cyclic shear gives rise to homogeneous crystallization at a volume fraction $\phi = 0.646 \pm 0.001$. This result indicates that neither friction nor gravity is essential for homogeneous crystallization in driven granular media.