Abstract
The finite cluster model (FCM)-based homogenization scheme has been formulated in terms of the dipole moments of the representative volume element (RVE) of actual composite and equivalent inclusion. Provided the interactions between the inclusions were taken into account, this scheme is asymptotically exact in the sense that the effective properties converge to its exact value with increasing RVE size and thus can be regarded as a rigorous method of micromechanics. To demonstrate its potential, the conductivity problem for a composite with non-randomly oriented elliptic inclusions is considered. The convergence of the solution is illustrated, and an effect of the microstructure including the orientation factor on the effective conductivity of the composite has been explored. The methodological issues of FCM application are discussed including an appropriate shape of the composite cluster and equivalent inclusion. The practical importance of the FCM consists in its direct applicability to the image of the microstructure obtained by the instrumental methods which makes it a convenient tool for estimating the effective properties of a composite in situ.
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Kushch, V.I., Knyazeva, A.G. Finite cluster model and effective conductivity of a composite with non-randomly oriented elliptic inclusions. Acta Mech 227, 113–126 (2016). https://doi.org/10.1007/s00707-015-1413-4
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DOI: https://doi.org/10.1007/s00707-015-1413-4