Generalized Clausius–Mossotti Formula for Random Composite with Circular Fibers

摘要: An important area of materials science is the study effective dielectric, thermal and electrical properties two phase composite with very different constituents. The case small concentration well studied analytical formulas such as Clausius–Mossotti (Maxwell–Garnett) are successfully used by physicists engineers. We investigate analytically an arbitrary number unidirectional circular fibers in periodicity cell when not small, i.e., we account for interactions all orders (pair, triplet, etc.). next consider transversely-random parallel obtain a closed form representation conductivity (as power series v). express coefficients this expansion terms integrals elliptic Eisenstein functions. These evaluated explicit dependence parameter d, which characterizes random position centers, obtained. Thus have extended formula non dilute mixtures adding higher order qualitatively effect randomness locations. In particular, proven that periodic array provides extremum our class arrays (“shaking” geometries). Our approach based on complex analysis techniques functional equations, solved successive approximations method.