Critical behaviour in the fracture of disordered media

In this paper we investigate the influence of different boundary conditions on the final breakdown of a lattice model for the fracture of heterogeneou s media. Experimental evidence shows that disordered media subject to stres s display some features that are characteristic of critical systems, theref ore suggesting an interpretation of the global breakdown of the system as a kind of critical transition. Many of the observed features are well reprod uced at least at a qualitative level by lattice models; however, mechanisms at the base of the onset of criticality are not well understood. Besides d isorder, there are many parameters that seem to influence the critical prop erties of the system. The system size and the boundary conditions are among these. We find that the statistical properties of the final breakdown are strongly influenced by the boundary condition. In particular constant-stres s relaxation leads to a final breakdown always involving the breaking of a finite number of bonds, which is also large if compared with the number of bonds broken during the formation of each localized crack preceding the fin al breakdown. When the lattice undergoes constant-strain relaxation instead , the breakdown may involve a vanishingly small number of bond-breaking eve nts.