Several properties of aftershock series related to the main shocks of Landers, Northridge and Hector Mine (southern California, USA) are reproduced by the Dynamic Fiber Bundle Model, DFBM. Optimum values for the three parameters governing DFBM are determined by searching for the best agreement of real aftershock series properties and those of synthetic sequences generated by this model. The analysis of the model parameter values provides details on the underlying physical mechanism of the aftershock sequence generation. First, the ratio of seismic energy radiated as seismic waves and transferred as stress-strain to adjacent faults; second, the degree of stress heterogeneity reproducing the complex behavior of real aftershock series. Additionally, the results of simulations support the coexistence of two types of relaxation processes. One of them is associated with the well-known modified Omori's (MO) law, which involves elapsed times between consecutive aftershocks monotonically increasing; the other is manifested by episodes of sudden stress release, with inter-event times much shorter than those predicted by MO law. These episodes are assumed to be a consequence of the complex distribution of tectonic stresses and fault geometry. The first process is associated to events designed as leading aftershocks, LA. The second process generates series of events which are designed as cascades, CA. It is worth of mention that several properties concerning CAs can be reasonably related to critical changes on stress field along the simulation process.