The objective of this thesis is to study the fracture behavior of brittle materials by an approach which relates crack initiation to crack growth. We adopt the discrete element method (DEM) and we represent the material by a 2D regular set of particles in contact. This allows us to derive an expression for the stress intensity factor as a function of the forces and relative displacements of two adjacent contacts at the crack tip. A classical failure criterion, based on the material’s toughness, is then adopted for the analysis of crack propagation, represented by the loss of contacts forces between particles. The formulation is verified by the comparison of numerical simulations to classical solutions of fracture mechanics in mode I, mode II and mixed mode. Afterwards, we apply our discrete criterion to uncracked materials under homogenous stress conditions, obtaining a Rankine like behavior.. The work results in a simple discrete model which is totally compatible to continuum mechanics, where no calibration tests are required, in contrast to most of discrete approaches.
