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Maxwell’s methodology of estimating effective properties: alive and well. (English) Zbl 1425.74405

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 J. C. Maxwell [A treatise on electricity and magnetism. Clarendon Press: Clarendon Press Oxford (1873; JFM 05.0556.01)] 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.

MSC:

74Q20 Bounds on effective properties in solid mechanics
78A25 Electromagnetic theory (general)
74E30 Composite and mixture properties

Citations:

JFM 05.0556.01
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References:

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