Bonded-cell model for particle fracture

Duc-Hanh Nguyen, Emilien Azema, Philippe Sornay, and Farhang Radjai

Particle degradation and fracture plays an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of 2D disk-like particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter escribing cell size distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell size distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength as inverse square root of particle diameter, in excellent agreement with our simulation data.