Geometrical-parameter bounds on the effective moduli of composites

L. V. Gibiansky; S. Torquato

doi:10.1016/0022-5096(95)00049-O

Geometrical-parameter bounds on the effective moduli of composites

L. V. Gibiansky, S. Torquato

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

We study bounds on the effective conductivity and elastic moduli of two-phase isotropic composites that depend on geometrical parameters that take into account up to three-point statistical information concerning the composite microstructure. We summarize existing bounds, apply a special fractional linear transformation to simplify their functional forms, and describe two approaches to improve such bounds. These approaches allow us to get new and improved geometrical-parameter bounds on the elastic moduli of two-dimensional composites. Applications of the bounds for effective-medium geometries as well as random arrays of aligned fibers in a matrix are discussed.

Original language	English (US)
Pages (from-to)	1587-1613
Number of pages	27
Journal	Journal of the Mechanics and Physics of Solids
Volume	43
Issue number	10
DOIs	https://doi.org/10.1016/0022-5096(95)00049-O
State	Published - Oct 1995

All Science Journal Classification (ASJC) codes

Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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10.1016/0022-5096(95)00049-O

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title = "Geometrical-parameter bounds on the effective moduli of composites",

abstract = "We study bounds on the effective conductivity and elastic moduli of two-phase isotropic composites that depend on geometrical parameters that take into account up to three-point statistical information concerning the composite microstructure. We summarize existing bounds, apply a special fractional linear transformation to simplify their functional forms, and describe two approaches to improve such bounds. These approaches allow us to get new and improved geometrical-parameter bounds on the elastic moduli of two-dimensional composites. Applications of the bounds for effective-medium geometries as well as random arrays of aligned fibers in a matrix are discussed.",

author = "Gibiansky, {L. V.} and S. Torquato",

note = "Funding Information: The authorst hank GraemeM ilton for helpful discussionsW. e gratefullya cknowledgeth e supporto f the Air Force Officeo f ScientificR esearchu nder Grant No. F49620-92-J-050a1n d of the Departmento f Energyu nder Grant. No. DEFG02-92ER14275.",

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T1 - Geometrical-parameter bounds on the effective moduli of composites

AU - Gibiansky, L. V.

AU - Torquato, S.

N1 - Funding Information: The authorst hank GraemeM ilton for helpful discussionsW. e gratefullya cknowledgeth e supporto f the Air Force Officeo f ScientificR esearchu nder Grant No. F49620-92-J-050a1n d of the Departmento f Energyu nder Grant. No. DEFG02-92ER14275.

PY - 1995/10

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N2 - We study bounds on the effective conductivity and elastic moduli of two-phase isotropic composites that depend on geometrical parameters that take into account up to three-point statistical information concerning the composite microstructure. We summarize existing bounds, apply a special fractional linear transformation to simplify their functional forms, and describe two approaches to improve such bounds. These approaches allow us to get new and improved geometrical-parameter bounds on the elastic moduli of two-dimensional composites. Applications of the bounds for effective-medium geometries as well as random arrays of aligned fibers in a matrix are discussed.

AB - We study bounds on the effective conductivity and elastic moduli of two-phase isotropic composites that depend on geometrical parameters that take into account up to three-point statistical information concerning the composite microstructure. We summarize existing bounds, apply a special fractional linear transformation to simplify their functional forms, and describe two approaches to improve such bounds. These approaches allow us to get new and improved geometrical-parameter bounds on the elastic moduli of two-dimensional composites. Applications of the bounds for effective-medium geometries as well as random arrays of aligned fibers in a matrix are discussed.

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Geometrical-parameter bounds on the effective moduli of composites

Abstract

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