Theoretical bounds on the electrical conductivity of sintered materials and their relation to bounds on the Young's modulus

The constraints to the effective electrical conductivity were derived as function of distribution of material electrical conductivity throughout the sample. If the sample consists only of homogeneous isotropic matrix and pores, the constraints to effective electrical conductivity take the form very similar to the constraints derived previously for the effective Young's modulus of porous materials. The differences occurring in expressions are due to the fact that elastic properties of an isotropic matrix material are characterized by two quantities, e.g. Young's modulus and Poisson's ratio, while the conductivity is characterized.only by one quantity. But regardless of the small differences, in the both cases the key role in determining the properties is played by the minimum load-bearing cross section of the sample considered.