On Maxwell's concept of equivalent inhomogeneity: When do the interactions matter?

The concept of Maxwell's equivalent inhomogeneity is re-evaluated in the context of the effective elastic properties of unidirectional multi-phase composite materials with the fibers of circular cross-section. The following key questions are addressed in this paper. Is the concept of equivalent...

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Bibliographic Details
Published in:Journal of the mechanics and physics of solids 2012-03, Vol.60 (3), p.391-417
Main Authors: Mogilevskaya, Sofia G., Stolarski, Henryk K., Crouch, Steven L.
Format: Article
Language:English
Subjects:
Cross sections (physics)
Elastic constants
Elastic properties
Equivalence
Estimates
Fibers
Inhomogeneity
Maxwell approximation formula
Multi-phase fiber-reinforced composites
Volume fraction
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Summary:The concept of Maxwell's equivalent inhomogeneity is re-evaluated in the context of the effective elastic properties of unidirectional multi-phase composite materials with the fibers of circular cross-section. The following key questions are addressed in this paper. Is the concept of equivalent inhomogeneity valid only for the materials with low volume fractions, as originally suggested by Maxwell? When do the interactions among the fibers matter? Could Maxwell's concept be generalized to allow for accurate estimates of the effective properties? The approach advocated in the paper provides an unique opportunity to study, in the framework of one model, the effects of the interactions among fibers on the effective transversely isotropic elastic properties of multi-phase composite materials.
ISSN:0022-5096
DOI:10.1016/j.jmps.2011.12.008