Due to limitations in their manufacturing stage, many composites can exhibit a considerable level of randomness in their microstructure. Such variations can affect the mechanical response of the resulting specimens, especially when localized phenomena are involved. When multi-phase materials exhibit statistically inhomogeneous characteristics, as in the case of random media with a built in gradient in composition, the analysis becomes considerably more complex as the spatial dependency of their probabilistic descriptors cannot be disregarded.; This thesis presents a probabilistic simulation approach to the issue of characterizing and generating samples of such composites. Furthermore, the effects of randomness on the mechanical properties of these materials are investigated using micromechanical-based techniques.; A novel method that is capable of generating non-Gaussian, non-stationary samples through a non-linear translation technique is introduced and applied to the generation of two-phase random media. The effect of spatial fluctuations on the local material response is measured by coupling the probabilistic framework of the analysis with micromechanical homogenization techniques. Two distinct cases are presented as an illustration of the difficulties involved in the analysis of statistically inhomogeneous composites and to measure the performance of the methods developed here.
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