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Explicit estimates versus numerical bounds for the electrical conductivity of dispersions with dissimilar particle shape and distribution. (English) Zbl 1453.74074

Summary: An effective-medium theory for the electrical conductivity of Ohmic dispersions taking explicit account of particle shape and spatial distribution independently is available from the work of P. Ponte Castañeda and J. R. Willis [J. Mech. Phys. Solids 43, No. 12, 1919–1951 (1995; Zbl 0919.73061)]. When both shape and distribution take particular “ellipsoidal” forms, the theory provides analytically explicit estimates. The purpose of the present work is to evaluate the predictive capabilities of these estimates when dispersions exhibit dissimilar particle shape and distribution. To this end, comparisons are made with numerical bounds for coated ellipsoid assemblages computed via the finite element method. It is found that estimates and bounds exhibit good agreement for the entire range of volume fractions, aspect ratios, and conductivity contrasts considered, including those limiting values corresponding to an isotropic distribution of circular cracks. The fact that the explicit estimates lie systematically within the numerical bounds hints at their possible realizability beyond the class of isotropic dispersions.

MSC:

74Q20 Bounds on effective properties in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
78A48 Composite media; random media in optics and electromagnetic theory

Citations:

Zbl 0919.73061
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References:

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