Determination of shape and force attractors for brittle granular materials through numerical experiments

Evidence indicates that crushing drives the coevolution of the size and shape of brittle particles towards states characterized by specific mechanical and topological attractors. This study explores this self-organization process through synthetic numerical experiments based on the discrete element method (DEM). Oedometric compression is imposed to synthetic assemblies consisting of particles with a wide range of initial aspect ratios, ranging from spheres to rods, blades, plates, as well as mixtures of such unit classes. The simulation results reveal that at the macroscale the spherical particles exhibit higher yield stress, more significant cushioning, and a narrower dispersed contact force distribution at the microscale, relative to non-spherical particles. Most notably, it is found that the particle shape distributions converge towards a consistent aspect ratio (AR) after extensive fragmentation, which is irrespective of their initial particle shape, loading history, and material composition. Using a proposed shape index, the evolution occurs faster in shape than in size, consistent with prior predictions from shape-enhanced continuum breakage mechanics (CBM). The concurrent evolution of the probability density function (PDFs) of contact forces suggests that these distributions also converge towards a state of mechanical self-organization, manifesting in the form of a microscopic “force attractor” that underpins the observed shape attractor. These findings pave the way for refining breakage mechanics theories to incorporate particle shape, offering insights into the self-organizing characteristics of fragmented granular systems.