A Network Approach to Fracture: The Effect of Heterogeneity and Loading Conditions

Fracture in a heterogeneous solid is simulated on a triangular network of bonds which figure the potential cracks of the medium. Heterogeneity is introduced by assuming a statistical strength distribution for the bonds. External stresses are applied to the network and the evolution of the bond population is analyzed when the stresses are increased. Bond-breaking is controlled by the crack-exten sion force which takes into account crack interactions by using an iterative procedure. Crack propaga tion leads to the coalescence of broken bonds crack clusters are formed. By using this kind of approach which combines fracture mechanics and network modelling, we are able to simulate the rupture of a rock specimen under various loading conditions without heavy computation. We discuss physical properties of the rupture process by examining the rupture stress and the geometric properties of the macroscopic fracture and their dependence on loading conditions and heterogeneity. Analysis of the geometric characteristics shows that the number of broken bonds can be fitted by a power law of the lattice size, the exponent depending on the loading conditions. Furthermore, an approximate computation of the mechanical response of the network demonstrates that the threshold secant modulus may be a more legitimate choice for a damage parameter in terms of system size independence.