Effective medium models for conductivity of randomly cracked locally non-homogeneous materials Original Research Article

A refined effective medium scheme is developed to estimate the conductivity (thermal and electrical) of randomly cracked materials (the cracks are assumed to be insulating), accounting for possible locally non-homogeneous distribution of the cracks. Certain spaces within the materials are modelled as forbidden regions for the cracks. Up to relatively high values of the crack density, the conductivities of different disordered models do not differ much from each other. However the differences become pronounced if the distribution of the cracks follows certain local orders: a particulate aggregate can still retail relatively high values of conductivity if the cracks are concentrated in the isolated inner parts of the grains, while those distributed at the grain boundary should reduce the aggregate conductivity considerably. Approximations for cracked porous materials are given, which indicate a pore–crack relative size effect.