Influences of self-organization of granular materials on particle crushing based on discrete element method

Starting from the Apollonian sphere packing method in mathematics, four kinds of self-organization of breakage are established, and the linear expansion method is introduced to guarantee the mass conservation. On this basis, the numerical experiments on different self-organizations are carried out, and the influences of self-organization on gradation evolution and macro and micro mechanical behaviors of granular materials are studied. It is found that the fractal dimension and the average inter-particle stress decrease with the increase of fragment number, while the relative breakage B_r and the compressibility increase with the increase of particle number in the self-organization. The anisotropic rose diagram of contact orientation and contact normal force show that the larger the number of particles in the self-organization is, the lower the anisotropy of the specimens at the end of loading is. In addition, the number of particle contact increases with the increase of self-organized particles, while the normal contact force decreases. Furthermore, the probability distributions of coordination number and contact force are also closely related to the self-organization of fragmentation.