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Maxwell’s concept of equivalent inhomogeneity- revisited

Maxwell’s (1873) approximation formula, based on the idea of an equivalent inhomogeneity, is regarded as one of the oldest estimates for the effective electrical conductivity of a composite material. Similar approximations were independently obtained for dielectric, magnetic, and optical effective properties, and some of these approximation methods remain extremely popular.
In this talk, the Maxwell’s concept of equivalent inhomogeneity is re-evaluated in the context of the effective elastic properties of two-phase unidirectional composite materials. It will be demonstrated that the modified Maxwell’s approach allows for obtaining accurate effective properties of periodic composites without solution of periodic boundary value problems. The main idea is to choose the right shape of equivalent inhomogeneity and accurately account for the interactions between the reinforcements.

Author(s):

Sonia Mogilevskaya    
University of Minnesota
United States

Dmitry Nikolskiy    
University of Minnesota
United States