Bulk Modulus along Jamming Transition Lines of Bidisperse Granular Packings

Abstract

We present 3D DEM simulations of bidisperse granular packings to investigate their jamming densities, ${\varphi }_J$, and dimensionless bulk moduli, $K$, as a function of the size ratio, $\delta$, and the concentration of small particles, $X_{\mathrm{S}}$. We determine the partial and total bulk moduli for each packing and report the jamming transition diagram, i.e., the density or volume fraction marking both the first and second transitions of the system. At a large enough size difference, e.g., $\delta \le 0.22$, $X_{\mathrm{S}}^{\ast }$ divides the diagram with most small particles either non-jammed or jammed jointly with large ones. We find that the bulk modulus $K$ jumps at $X_{\mathrm{S}}^{\ast }(\delta =0.15)\approx 0.21$, at the maximum jamming density, where both particle species mix most efficiently, while for $X_{\mathrm{S}}<X_{\mathrm{S}}^{\ast }$ $K$ is decoupled in two scenarios as a result of the first and second jamming transition. Along the second transition, $K$ rises relative to the values found at the first transition, however, is still small compared to $K$ at $X_{\mathrm{S}}^{\ast }$. While the first transition is sharp, the second is smooth, carried by small-large interactions, while the small-small contacts display a transition. This demonstrates that for low enough $\delta$ and $X_{\mathrm{S}}$, the jamming of small particles indeed impacts the internal resistance of the system. Our new results will allow tuning the bulk modulus $K$ or other properties, such as the wave speed, by choosing specific sizes and concentrations based on a better understanding of whether small particles contribute to the jammed structure or not, and how the micromechanical structure behaves at either transition.

15 pages, 18 figures

References in corpus (8)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• The Jamming Transition in Granular Systems
• Do Binary Hard Disks Exhibit an Ideal Glass Transition?
• Percolation of disordered jammed sphere packings
• Sub-Jamming Transition in Binary Sphere Mixtures
• Unjamming due to local perturbations in granular packings with and without gravity
• Force Percolation Transition of Jammed Granular Systems
• Phase transition in the binary mixture of jammed particles with large size dispersity

Cited by in corpus (3)

• Structural transitions in jammed asymmetric bidisperse granular packings
• Additional jamming transition in 2D bidisperse granular packings
• Vibrational similarities in jamming-unjamming of polycrystalline and disordered granular packings