Emerging contact force heterogeneity in ordered soft granular media

TL;DR

This study reveals that mechanical heterogeneity alone can induce force heterogeneity in soft granular media, with lattice geometry influencing force distribution and nonlocal effects, providing new insights into granular material behavior.

Contribution

It demonstrates through FEM modeling that mechanical heterogeneity causes force heterogeneity, highlighting the influence of lattice geometry and nonlocal effects in granular packings.

Findings

Hexagonal packing shows more force heterogeneity than square packing.

Outliers indicate nonlocal effects, with softer disks bearing larger forces.

Force distribution and nonlocal effects vary with mechanical heterogeneity and lattice geometry.

Abstract

Under external perturbations, inter-particle forces in disordered granular media are well known to form a heterogeneous distribution with filamentary patterns. Better understanding these forces and the distribution is important for predicting the collective behavior of granular media, the media second only to water as the most manipulated material in global industry. However, studies in this regard so far have been largely confined to granular media exhibiting only geometric heterogeneity, leaving the dimension of mechanical heterogeneity a rather uncharted area. Here, through a FEM contact mechanics model, we show that a heterogeneous inter-particle force distribution can also emerge from the dimension of mechanical heterogeneity alone. Specifically, we numerically study inter-particle forces in packing of mechanically heterogeneous disks arranged over either a square or a hexagonal lattice and under quasi-static isotropic compression. Our results show that, a hexagonal packing exhibit a more heterogeneous inter-particle force distribution than a square packing does. For both packing lattices, preliminary analysis shows the consistent coexistence of outliers (i.e., softer disks sustaining larger forces while stiffer disks sustaining smaller forces) in comparison to their homogeneous counterparts, which implies the existence of nonlocal effect. Further analysis on the portion of outliers and on spatial contact force correlations suggest that the hexagonal packing shows more pronounced nonlocal effect over the square packing under small mechanical heterogeneity. However, such trend is reversed when assemblies becomes more mechanically heterogeneous. Lastly, we confirm that, in the absence of particle reorganization events, contact friction merely plays the role of packing stabilization while its variation has little effect on inter-particle forces and their distribution.