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[References: 33 tit.]

An approach to solving the known problem on determination of the effective physical and mechanical properties of dispersedly filled compositions is presented. The solution is based on the formulation and numerical implementation of boundary-value problems based on the fundamental equations of the theories of elasticity, thermal conductivity, electrostatics, and electrical conductivity. The general concept is to obtain detailed parameters of state of the composition under external actions with account of the real structure of the material. Averaging procedures are used to determine the effective properties of the compositions. The formulation and solution of boundary-value problems, in all cases, is reduced to the formulation of corresponding variational principles and their implementation by the methods of computational mechanics, in particular, by the finite element method. The effective characteristics of the composite under mechanical, thermal, and electromagnetic actions are calculated on the basis of energy considerations: the stored energy of a structurally inhomogeneous body is equal to the energy of a homogeneous comparison body under various actions. A comparison of calculated and experimental values of the effective characteristics attests to the applicability of the models proposed and the methods of their implementation.