We consider a two-dimensional lattice model to describe the opening of a crack in hydraulic fracturing. In particular, we consider that the material only breaks under tension and the fluid has no pressure drop inside the crack. For the case in which the material is completely homogeneous (no disorder), we present results for pressure and elastic energy as a function of time and compare our findings with some analytic results from continuum fracture mechanics. Then we investigate fracture processes in strongly heterogeneous cohesive environments. We determine the cumulative probability distribution for breaking events of a given energetical magnitude (acoustic emission). Further, we estimate the probability distribution of emission free time intervals. Finally, we determine the fractal dimension(s) of the cracks.
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