Frictionless bead packs have macroscopic friction, but no dilatancy

TL;DR

This study demonstrates that frictionless bead packs exhibit macroscopic friction and anisotropic stress-induced fabric formation under shear, despite lacking microscopic friction, with results supported by numerical simulations in the quasistatic limit.

Contribution

It reveals that frictionless bead packs develop macroscopic friction and anisotropic fabrics through stress-induced network rearrangements, challenging the assumption that microscopic friction is necessary for macroscopic friction.

Findings

Internal friction angle is approximately 5.76 degrees, independent of pressure.

Solid fraction remains near the random close packing value (~0.64) under shear.

Stress and volume fluctuations diminish with increasing system size.

Abstract

The statement of the title is shown by numerical simulation of homogeneously sheared packings of frictionless, nearly rigid beads in the quasistatic limit. Results coincide for steady flows at constant shear rate γ in the limit of small γ and static approaches, in which packings are equilibrated under growing deviator stresses. The internal friction angle ϕ, equal to 5.76 $\pm$ 0.22 degrees in simple shear, is independent on the average pressure P in the rigid limit. It is shown to stem from the ability of stable frictionless contact networks to form stress-induced anisotropic fabrics. No enduring strain localization is observed. Dissipation at the macroscopic level results from repeated network rearrangements, like the effective friction of a frictionless slider on a bumpy surface. Solid fraction Φ remains equal to the random close packing value ≃ 0.64 in slowly or statically sheared systems. Fluctuations of stresses and volume are observed to regress in the large system limit, and we conclude that the same friction law for simple shear applies in the large psystem limit if normal stress or density is externally controlled. Defining the inertia number as I = γ m/(aP), with m the grain mass and a its diameter, both internal friction coefficient $\mu$∗ = tan ϕ and volume 1/Φ increase as powers of I in the quasistatic limit of vanishing I, in which all mechanical properties are determined by contact network geometry. The microstructure of the sheared material is characterized with a suitable parametrization of the fabric tensor and measurements of connectivity and coordination numbers associated with contacts and near neighbors.