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Static discrete models are advantageously used for the simulation of fracture in quasibrittle heterogeneous materials. In order to correctly capture strain localization during the fracture process, it is often necessary to represent material heterogeneity in the model directly via its discrete geometry. Depending on the specimen size and the size of the heterogeneities, these simulations are typically extremely computationally demanding. The contribution aims to reduce this computational cost via the implementation of adaptivity in the construction of the discrete model geometry. The simulation starts with coarse discretization, which provides correct elastic behavior and is then adaptively refined during the simulation in regions that suffer high stresses that induce cracking and strain localization. The technique is applied in deterministic and probabilistic simulations and demonstrated on several examples. [ABSTRACT FROM AUTHOR]