Maxwell’s methodology of estimating effective properties: Alive and well

This paper presents a comprehensive review of the far-field-based methodology of estimation of the effective properties of multi-phase composites that was pioneered by Maxwell in 1873 in the context of effective electrical conductivity of a particle-reinforced material. Maxwell suggested that a clus...

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Bibliographic Details
Published in:International journal of engineering science 2019-07, Vol.140, p.35-88
Main Authors: Sevostianov, I., Mogilevskaya, S.G., Kushch, V.I.
Format: Article
Language:English
Subjects:
Composite materials
Conductivity
Effective properties
Electrical resistivity
Heat conductivity
Magnetic fields
Maxwell’s methodology
Methodology
Microstructure
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Summary:This paper presents a comprehensive review of the far-field-based methodology of estimation of the effective properties of multi-phase composites that was pioneered by Maxwell in 1873 in the context of effective electrical conductivity of a particle-reinforced material. Maxwell suggested that a cluster of particles embedded in an infinite medium subjected to a uniform electrical field has the same far-field asymptotic as an equivalent sphere whose conductivity is equal to the effective one; this yields closed-form formula for the effective conductivity. Our review focuses on subsequent developments of Maxwell’s idea in various applications and on its range of applicability. The conclusion is that, 145 years later, the methodology is still alive and well.
ISSN:0020-7225
1879-2197
DOI:10.1016/j.ijengsci.2019.05.001