Characterization of the mechanical properties of quasi-two-dimensional systems of rigid spheres

In this work, we perform event-chain Monte Carlo simulations to investigate the mechanical properties of quasi-two-dimensional systems of non-additive rigid spheres, with a specific focus on binary mixtures. We present numerical results for the shear and bulk elastic moduli and analyze how structural arrangements affect the mechanical response in various systems, including monodisperse and bidisperse configurations with disordered, crystalline, and quasicrystalline organization. Our results indicate that, for binary mixtures with intermediate size ratios, the configurations obtained at intermediate fractions of small spheres are generally softer and more mechanically isotropic. Although the simulations for binary mixtures were able to stabilize different spatial arrangements, including one with octagonal quasicrystalline order, our numerical results indicate that the symmetry found in the structure factors has no direct correspondence to the observed mechanical response of the system.