Random field models for two-phase microstructures

Level-cut filtered Poisson fields are defined by cuts of filtered Poisson fields above prescribed levels and used to model two-phase microstructures. The filtered Poisson fields are sums of deterministic functions h scaled by random variables and centered at random points generated by a Poisson field N. The structure of the level-cut filtered Poisson fields depends on the functional form of h, the properties of the random variables scaling h, and the intensity of N. Level-cut Gaussian fields used extensively to represent two-phase microstructures are special cases of level-cut filtered Poisson fields. A Monte Carlo algorithm was developed for generating two-phase composites based on level-cut filtered Poisson fields. It is shown by examples that level-cut filtered Poisson fields can produce a broad range of two-phase microstructures.