Contact angle entropy and macroscopic friction in noncohesive two-dimensional granular packings

Parking spheres stochastically to model realistic granular packings

The packing geometry of granular solids and other amorphous materials is important to understand their macroscopic behaviors. However, their particle-scale assembly mechanism and the underlying statistical mechanical laws remain unclear. In this work, we develop a model to generate the local packing structures of granular spheres by parking them sequentially and stochastically, and connect the fluctuating structures to the thermodynamic equations of state. The influences of entropy, friction, and mechanical action on local configurations are decomposed with the aid of an effective interparticle interaction, a parking sequence of neighboring particles, and an external potential. Quasiuniversal laws of granular sphere packings observed in previous experiments are replicated by our model and their empirical dependences on particle friction and packing protocol are rationalized. This model provides a general statistical mechanical approach to understanding the nonequilibrium assembly mechanism of amorphous particle packing systems.

Bulk modulus along jamming transition lines of bidisperse granular packings

We present three-dimensional discrete element method simulations of bidisperse granular packings to investigate their jamming densities ϕ_{J} and dimensionless bulk moduli K as functions of the size ratio δ and the concentration of small particles X_{S}. We determine the partial and total bulk moduli for packings near their jamming densities, including a second transition that occurs for sufficiently small δ and X_{S} when the system is compressed beyond its first jamming transition. While the first transition is sharp, exclusively with large-large contacts, the second is rather smooth, carried by small-large interactions at densities much higher than the monodisperse random packing baseline, ϕ_{J}^{mono}≈0.64. When only nonrattlers are considered, all the effective transition densities are reduced, and the density of the second transition emerges rather close to the reduced baseline, ϕ[over ̃]_{J}^{mono}≈0.61, due to its smooth nature. At size ratios δ≤0.22 a concentration X_{S}^{*} divides the diagram-either with most small particles nonjammed or jammed jointly with large ones. For X_{S}<X_{S}^{*}, the modulus K displays different behaviors at first and second jamming transitions. Along the second transition, K rises relative to the values found at the first transition; however, is still small compared to K at X_{S}^{*}. Explicitly, for our smallest δ=0.15, the discontinuous jump in K as a function of X_{S} is obtained at X_{S}^{*}≈0.21 and coincides with the maximum jamming density where both particle species mix most efficiently. Our results will allow tuning or switching 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.

Reduction of the bulk modulus with polydispersity in noncohesive granular solids

We study the effect of grain polydispersity on the bulk modulus in noncohesive two-dimensional granular solids. Molecular dynamics simulations in two dimensions are used to describe polydisperse samples that reach a stationary limit after a number of hysteresis cycles. For stationary samples, we obtain that the packing with the highest polydispersity has the lowest bulk modulus. We compute the correlation between normal and tangential forces with grain size using the concept of branch vector or contact length. Classifying the contact lengths and forces by their size compared to the average length and average force, respectively, we find that strong normal and tangential forces are carried by large contact lengths, generally composed of at least one large grain. This behavior is more dominant as polydispersity increases, making force networks more anisotropic and removing the support, from small grains, in the loading direction thus reducing the bulk modulus of the granular pack. Our results for two dimensions describe qualitatively the results of three-dimensional experiments.