Stochastic damage model for brittle materials subjected to monotonic loading

A one-dimensional stochastic micromechanical model is developed for brittle materials subjected to monotonic uniaxial loading. The material is represented by a set of brittle linear-elastic springs of equal stiffness that are joined in parallel. The failure strengths of the springs are modeled as either a discrete or a continuous correlated random field. The statistics of the random force-displacement and damage-displacement functions are analytically derived for the structural element. The stochastic model is shown to be capable of representing the experimentally observed scatter in the structural response. To demonstrate the validity of the model, comparisons are made with experimental data for unlaxial compressive tests on concrete specimens. The present model is shown to offer a viable alternative to empirical methods proposed in the literature for exploring the statistical behavior of brittle materials.