Additional Transition Line in Jammed Asymmetric Bidisperse Granular Packings.

We present numerical evidence for an additional discontinuous transition, upon compression, inside the jammed regime for an asymmetric bidisperse granular packing. This additional transition line separates jammed states with networks of predominantly large particles from jammed networks formed by both large and small particles, and the transition is indicated by a discontinuity in the number of particles contributing to the jammed network. The additional transition line emerges from the curves of jamming transitions and terminates in an end point where the discontinuity vanishes. The additional line is starting at a size ratio around δ=0.22 and grows longer for smaller δ. For δ→0, the additional transition line approaches a limit that can be derived analytically. The observed jamming scenarios are reminiscent of glass-glass transitions found in colloidal glasses.

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}

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.

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

We study the relationship between the granular contact angle distribution and local particle friction on the macroscopic friction and bulk modulus in noncohesive disk packings. Molecular dynamics in two dimensions are used to simulate uniaxial loading-unloading cycles imposed on the granular packings. While macroscopic Mohr friction depends on the granular pack geometric details, it reaches a stationary limit after a finite number of loading-unloading cycles that render well-defined values for bulk modulus, grain coordination, porosity, and friction. For random packings and for all polydispersities analyzed, we found that as interparticle friction increases, the bulk modulus for the limit cycle decreases linearly, while the mean coordination number is reduced and the porosity increased, also as approximately linear functions. On the other hand, the macroscopic Mohr friction increases in a monotonous trend with interparticle friction. The latter result is compared to a theoretical model that assumes the existence of sliding planes corresponding to definite Mohr-friction values. The simulation results for macroscopic friction are well described by the theoretical model that incorporates the local neighbor angle distribution that can be quantified through the contact angle entropy. As local friction is increased, the limit entropy of the neighbor angle distribution is reduced, thus introducing the geometric component to granular friction. Surprisingly, once the limit cycle is reached, the Mohr friction seems to be insensitive to polydispersity as has been recently reported.