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Determination of effective conductivities of imperfect contact composites with first-passage simulation.

A first-passage simulation scheme is developed to determine the effective conductivities of composites with matrix-inclusion interfaces of imperfect contact. The necessary mean hitting probabilities and mean scaled traveling times of the probing walkers in the close vicinity of the imperfect contact interface are derived by solving proposed boundary value problems. The developed scheme is first validated through application in the effective conductivity problem of composites containing periodically arranged spherical inclusions for which accurate results are available for comparison, and is then further applied to the effective conductivity problem of composites containing randomly distributed spherical inclusions. The present development treats the more general imperfect contact problem, with the perfect contact problem as one special case.