Based on the concepts of statistical mesoscopic damage mechanics, the ruptu
re of a heterogeneous medium is investigated in terms of numerical simulati
ons of a network model, subjected to simple shear loading. The heterogeneit
ies are simulated by varying the sizes and fracture strains of the elements
of the network. Progressive damage is governed by a damage field equation
and a dynamic function of damage (DFD). From the damage field equation, a c
riterion for damage localization can be derived, and the DFD can be extract
ed from the simulations of the network. Importantly, the DFD intrinsically
governs the damage localization. Both stress-free and periodic boundary con
ditions for the network are examined. It is found that damage localization
may be the underlying mechanism of eventual rupture and thus could be used
as a possible precursor of earthquake rupture.