Mechanical response of particle packings at jamming onset

The jamming onset of particle packings provides an ideal physical state for the comparison of mechanical properties. In this paper, we investigate the effects of size distribution and particle shape on the mechanical response of disordered jammed packings. For packings of bidisperse spheres, both species participate in the force network for the small particle volume fraction X_s ≤ 0.35, boosting the bulk modulus B by nearly 60% relative to the monodisperse case. On the other hand, the high rattler fraction induced by some polydispersity generally reduces B compared to the monodisperse case. Within the family of superellipsoids and spherocylinders studied, packings of nonspherical particles show higher B than that of spheres, with the self-dual ellipsoids achieving the maximum value, where B exhibits robust power-law scaling with pressure. Moreover, although B shows no direct correlation with packing density, it exhibits a robust linear scaling with the coordination number across different particle shapes. This linear relation persists in polydisperse sphere systems when a volume-weighted coordination number is employed to account for the size disparity. These findings advance our understanding of jamming transitions and facilitate rational granular material design.