A CONTRIBUTION TO THE BOUNDS ON REAL EFFECTIVE MODULI OF 2-PHASE COMPOSITE-MATERIALS

Effective transport coefficients of two-phase composite materials lamb da(e)(x) can be represented by power expansions of four Stieltjes func tions: (e),lambda(e)(y)/lambda(2),lambda(1)(y)/lambda(e), where x = (l ambda(2)/lambda)(1)) - 1 and y = -x/(x + 1), while lambda(1) and lambd a(2) denote the real moduli of a matrix and inclusions respectively.(5 ) By constructing Pade approximants to power expansions of these funct ions, we derive an infinite set of fundamental inequalities identifyin g real-valued Milton's bounds(20) as a lower and upper estimations of lambda(e)(s). From coefficients of a power expansion of lambda(e)(x) n ot exactly known, but only within the limits, the infinite set of new bounds on lambda(e)(x) has been derived. Due to Schulgasser inequality (21) some improvement of existing bounds(20) is proposed. For an illus tration of the results achieved, the improved bounds on the effective conductivity lambda(e)(x) of a regular array of spheres are evaluated.