Universality of stress-anisotropic and stress-isotropic jamming of frictionless spheres in three dimensions: Uniaxial vs isotropic compression

TL;DR

This study investigates whether stress-anisotropic and stress-isotropic jamming of frictionless spheres in three dimensions belong to the same universality class by analyzing critical scaling behaviors of pressure, shear stress, and contact number.

Contribution

It provides the first comprehensive critical scaling analysis comparing uniaxial and isotropic compression jamming in 3D frictionless spheres, demonstrating their universality.

Findings

Bulk viscosity diverges as $(J - )$ with an exponent of approximately 3.36.

Critical parameters show good agreement between uniaxial and isotropic cases.

Contact number scaling also confirms universality across compression types.

Abstract

We numerically study a three dimensional system of athermal, overdamped, frictionless spheres, using a simplified model for a non-Brownian suspension. We compute the bulk viscosity under both uniaxial and isotropic compression as a means to address the question of whether stress-anisotropic and stress-isotropic jamming are in the same critical universality class. Carrying out a critical scaling analysis of the system pressure $p$, shear stress $\sigma$, and macroscopic friction $\mu=\sigma/p$, as functions of particle packing fraction $\phi$ and compression rate $\dot\epsilon$, we find good agreement for all critical parameters comparing the isotropic and anisotropic cases. In particular, we determine that the bulk viscosity diverges as $p/\dot\epsilon\sim (\phi_J-\phi)^{-\beta}$, with $\beta=3.36\pm 0.09$, as jamming is approached from below. We further demonstrate that the average contact number per particle $Z$ can also be written in a scaling form as a function of $\phi$ and $\dot\epsilon$. Once again, we find good agreement between the uniaxial and isotropic cases. We compare our results to prior simulations and theoretical predictions.