K. Z. Markov. On the sink strength and permeability of microcracked arrays. Proc. Roy. Soc. Lond. A (2003) 459, 1035–1051

The effective absorption coefficient (the sink strength or the trapping constant) g of a statistically isotropic random array of penny-shaped cracks is considered. The cracks are treated as oblate spheroids with vanishing aspect ratio. A variational procedure, based on Rubinstein-Torquato's principle [J. Chem. Phys. 88, 6372-6380 (1988)] is employed which yields nontrivial lower bound on g using appropriate trial fields of `particle' and `surface' type. The bounds include the crack density parameter for the array as well as the two-point correlation function for the set of crack's centers. The bounds also provide useful and nontrivial information concerning cracks competition at nondilute concentration. The straightforward `transition' of the obtained results as upper bounds on the effective permeability of an array of randomly distributed disk-like obstacles is finally indicated.
Keywords: microcracked media; absorption problem; permeability; variational estimates; effective properties