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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.

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.

We study the local structural changes along the jamming transitions in asymmetric bidisperse granular packings. The local structure of the packing is assessed by the contact orientational order, $$\tilde{Q}_{\ell }$$ Q ~ ℓ , that quantifies the contribution of each contact configuration (Large–Large, Small–Small, Large–Small, Small–Large) in the jammed structure. The partial values of $$\tilde{Q}_{\ell }$$ Q ~ ℓ are calculated with respect to known ordered lattices that are fixed by the size ratio, $$\delta $$ δ , of the particles. We find that the packing undergoes a structural transition at $$\phi _J$$ ϕ J , manifested by a sudden jump in the partial $$\tilde{Q}_{\ell }$$ Q ~ ℓ . Each contact configuration contributes to the jammed structure in a different way, changing with $$\delta $$ δ and concentration of small particles, $$X_{\textrm{S}}$$ X S . The results show not only that the packing undergoes a structural change upon jamming, but also that bidisperse packings exhibit local HCP and FCC structures also found in monodisperse packings. This suggests that the jammed structure of bidisperse systems is inherently endowed with local structural order. These results are relevant in understanding how the arrangement of particles determines the strength of bidisperse granular packings. Graphic abstract

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 mono J ≈ 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, φmono J ≈ 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.