Abstract
Consider 2D multi-phase random composites with different circular inclusions. A finite number n of inclusions on the infinite plane forms a cluster. The corresponding boundary value problem for Muskhelishvili's potentials is reduced to a system of functional equations. Solution to the functional equations can be obtained by a method of successive approximations or by the Taylor expansion of the unknown analytic functions. Next, the local stress-strain fields are calculated and the averaged elastic constants are obtained in symbolic form. An extension of Maxwell's approach and other various self-consisting cluster methods from single- to n-inclusions problems is developed. An uncertainty when the number of elements n in a cluster tends to infinity is analyzed by means of the conditionally convergent series. Application of the Eisenstein summation yields new analytical approximate formulas for the effective constants for macroscopically isotropic random 2D composites.
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