Critical resistance for multi-phase composite materials

The effect of interfacial resistance on the effective conductivity of a multi-phase composite material was studied. The composite under study is composed of a matrix surrounding different types of circular cylinders arranged in rectangular order. It was assumed that the interfacial resistance is concentrated on the surface of the cylinders. For any direction of calculating the effective conductivity of the system, a condition was found in which the effect of cylinders of one type can be neglected. This condition may be estimated by R k − 1, where R and k are the non-dimensional interfacial resistance and the relative conductivity of the neglected cylinders, respectively. The case R = k − 1 applies when the same relation exists between the interfacial resistance and conductivity of all types of cylinders.  2003 Elsevier Science B.V. All rights reserved. PACS: 44.10.+i; 72.80.Tm; 41.20.Cv