Conclusion
The (virial) power series of the concentration of inhomogeneities (particles) obtained in principle solve the problem of calculating the effective characteristics. The proposed form of the virial expansions does not contain integrals requiring regularization. This was attained by considering virial expansions in finite bodies, where it can be shown that the principal parts of the integrals which give convergence in passing to an infinite body are equal to zero due to the equilibrium equations in summation of the effect of all surrounding particles on the isolated particle.
From a practical point of view, calculation of then-th term of the expansion requires solving the problem ofn inhomogeneities, which restricts the applicability of the method. However, the virial series are convenient for analysis of simpler approximate methods such as self-consistent methods, for example. The next communication will treat such an analysis.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 2, pp. 222–237, March–April, 1994.
We would like to thank the participants in the seminar “Mechanics and Physics of Rocks” (Moscow Mining Institute) and its director R. L. Salganik for their useful discussion of the results of the study.
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Germanovich, L.N., Dyskin, A.V. Virial expansions in problems of effective characteristics. 1. General concepts. Mech Compos Mater 30, 157–167 (1994). https://doi.org/10.1007/BF00635848
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DOI: https://doi.org/10.1007/BF00635848