Numerical approaches to the modelling of quasi-brittle crack propagation

. Computational analysis of quasi-brittle fracture in cement-based and similar composites, supplied by various types of rod, fibre, etc. reinforcement, is crucial for the prediction of their load bearing ability and durability, but rather difficult because of the risk of initiation of zones of microscopic defects, followed by formation and propagation of a large number of macroscopic cracks. A reasonable and complete deterministic description of relevant physical processes is rarely available. Thus, due to significance of such materials in the design and construction of buildings, semi-heuristic computational models must be taken into consideration. These models generate mathematical problems, whose solvability is not transparent frequently, which limits the credibility of all results of ad hoc designed numerical simulations. In this short paper such phenomena are demonstrated on a simple model problem, covering both micro-and macro-cracking, with references to needful generalizations and more realistic computational settings.