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Multi-scale fracture of random heterogeneous materials

This article presents new probabilistic models for generating microstructures and multi-scale fracture analysis of a random heterogeneous material. The microstructure model involves a level-cut, inhomogeneous, filtered Poisson field comprising a sum of deterministic kernel functions that are scaled by random variables and centred at Poisson points. The fracture model involves stochastic description of the particle volume fraction and locations and constituent material properties, two-scale algorithms including micro-scale and macro-scale analyses, and dimensional decomposition or Monte Carlo simulation for reliability analysis. Numerical results demonstrate that the random field model is capable of producing a wide variety of two- and three-dimensional microstructures containing particles of various sizes, shapes, densities, gradations and orientations. The results of fracture analysis indicate that the concurrent model developed is sufficiently accurate, gives probabilistic solutions very close to those generated from the micro-scale model and can reduce the computational effort of the latter model by more than a factor of two. In addition, the concurrent multi-scale model predicts crack trajectory as accurately as the micro-scale model. The stochastic models presented have the potential to fundamentally change the way advanced materials in high-technology applications, including the maritime industry, can be applied in the future.