Conductivity tensor of anisotropic composite media from the microstructure

Journal Article · Thu Feb 01 00:00:00 EST 1990 · Journal of Applied Physics; (USA)

DOI:https://doi.org/10.1063/1.345711· OSTI ID:7185643

Torquato, S ^[1]; Sen, A K ^[2]

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1. Department of Mechanical and Aerospace Engineering Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (US)
2. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (US)

Perturbation expansions and rigorous bounds on the effective conductivity tensor {sigma}{sub {ital e}} of {ital d}-dimensional anisotropic two-phase composite media of arbitrary topology have recently been shown by the authors to depend upon the set of {ital n}-point probability functions {ital S}{sup ({ital i})}{sub 1},..., {ital S}{sup ({ital i})}{sub {ital n}}. {ital S}{sup ({ital i})}{sub {ital n}} gives the probability of simultaneously finding {ital n} points in phase {ital i} ({ital i}=1,2). Here we describe a means of representing these statistical quantities for distributions of identical, oriented inclusions of arbitrary shape. Our results are applied by computing second-order perturbation expansions and bounds for a certain distribution of oriented cylinders with a finite aspect ratio. We examine both cases of conducting cylindrical inclusions in an insulating matrix and of insulating {ital cracks} or {ital voids} in a conducting matrix.

• DOE Contract Number: FG05-89ER45384
• OSTI ID: 7185643
• Journal Information: Journal of Applied Physics; (USA), Vol. 67:3, Issue 3; ISSN 0021-8979
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPOSITE MATERIALS
ELECTRIC CONDUCTIVITY
ANISOTROPY
INCLUSIONS
MICROSTRUCTURE
PERTURBATION THEORY
PROBABILITY
TENSORS
TOPOLOGY
CRYSTAL STRUCTURE
ELECTRICAL PROPERTIES
MATERIALS
MATHEMATICS
PHYSICAL PROPERTIES
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics