Three-dimensional compaction of soft granular packings

TL;DR

This study investigates how soft spherical particle assemblies compact under increasing stress, revealing a transition from granular to continuous-like behavior and developing a predictive equation for packing evolution.

Contribution

It introduces a new equation modeling packing fraction evolution under pressure, based on micromechanical principles, applicable from jamming to high densities.

Findings

Packing fraction approaches 1 with increasing stress.

Coordination number scales as the square root of packing fraction.

Transition from exponential to Gaussian shear stress distributions.

Abstract

This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized using the evolution of the packing fraction, the coordination number, and the von Misses stress distribution within the particles as the confining stress increases. The packing fraction increases and tends toward a maximum value close to $1$, and the mean coordination number increases as a square root of the packing fraction. As the confining stress increases, a transition is observed from a granular-like material with exponential tails of the shear stress distributions to a continuous-like material characterized by Gaussian-like distributions of the shear stresses. We develop an equation that describes the evolution of the packing fraction as a function of the applied pressure. This equation, based on the micromechanical expression of the granular stress tensor, the limit of the Hertz contact law for small deformation, and the power-law relation between the packing fraction and the coordination of the particles, provides good predictions from the jamming point up to very high densities without the need of tuning any parameters.