Whitepapers

5 W H I T E P A P E R (7) (8) (9) (10) where e ∞ , d o , and φ are model parameters that should be fitted to experimental data, and L is the particle size. Whenever a particle enters in the simulation, a random strength is assigned to it, following an upper-truncated lognormal distribution based on the breakage parameters that describe the material. This property can be interpreted as the value of P o at which the particle will break during a simulation. Then, the specific fracture energy of the particle, e , can be determined considering equations (8), (9), and (10). Particle collisions will result in a decrease in the fracture specific energy due to the accumulated damage to the particle during the loading process. Thus, for every new loading cycle without breakage, a new particle specific fracture energy, e n , is computed based on the previous specific fracture energy, e n-1 , and the fractional damage in the particle during the n th loading cycle, D * n . The expressions considered for these variables are: where γ is the damage accumulation coefficient, and e c,n is the instantaneous specific contact energy in the particle at the end of the n th loading cycle. The instantaneous specific contact energy in a particle at a given time t is defined here as e t c , thus when a particle is in its n th loading cycle, and the value of e t c is greater than e n-1 , particle breakage will occur. Fragments size will be related to the stressing energy according to the value of t 10 , which is given by: where A and b' are model parameters fitted to experimental data, e c,b is the value of the specific contact energy in the particle at the instant of breakage, and ê c is a measure of the specific fracture energy of the broken particles.

• Cover