Account for Random Microstructure in Multiscale Models

The accumulated in last decades knowledge of fibre-reinforced composite materials, their effective properties as well as deformation and damage processes in them confirms a random (probabilistic) character of their failure (see, e.g. [1–4] and references therein). Such a character is determined by the specificity of microstructure of composites – a result of a manufacturing process of embedding of a huge number of reinforcing elements into a matrix. The resulting microscopic heterogeneity linked to randomness in positions of fibres, their bonding with the matrix, presence of microdefects, etc. causes a spatially and temporally non-uniform response to external loading even under macroscopically uniform loading conditions. The resulting pattern of deformation localisation and stress concentrations is neither uniform nor periodic; it defines macroscopic nonuniformity in evolution of various damage mechanisms.