Determination of the overall moduli in second order incompressible elasticity

Ali Imam; George C. Johnson; Mauro Ferrari

doi:10.1016/0022-5096(95)00027-G

Determination of the overall moduli in second order incompressible elasticity

Ali Imam, George C. Johnson, Mauro Ferrari

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

13 Scopus citations

Abstract

The problem of finding the overall second order elastic moduli for a biphase material is considered. The material consists of an incompressible isotropic matrix containing a dilute concentration of spherical inhomogeneities which are also incompressible and isotropic. To evaluate the effective moduli, the second order elastic field of a single inhomogeneity in an infinite matrix under homogeneous displacement boundary conditions is determined. This elastic field is assumed to approximate that of the composite with a dilute concentration of the second phase. No interaction between the particles is considered. Subsequently, through the equality of the strain energies of the inhomogeneous material and an equivalent homogeneous material, explicit expressions for the overall elastic constants are obtained.

Original language	English (US)
Pages (from-to)	1087-1104
Number of pages	18
Journal	Journal of the Mechanics and Physics of Solids
Volume	43
Issue number	7
DOIs	https://doi.org/10.1016/0022-5096(95)00027-G
State	Published - Jul 1995

ASJC Scopus subject areas

Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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title = "Determination of the overall moduli in second order incompressible elasticity",

abstract = "The problem of finding the overall second order elastic moduli for a biphase material is considered. The material consists of an incompressible isotropic matrix containing a dilute concentration of spherical inhomogeneities which are also incompressible and isotropic. To evaluate the effective moduli, the second order elastic field of a single inhomogeneity in an infinite matrix under homogeneous displacement boundary conditions is determined. This elastic field is assumed to approximate that of the composite with a dilute concentration of the second phase. No interaction between the particles is considered. Subsequently, through the equality of the strain energies of the inhomogeneous material and an equivalent homogeneous material, explicit expressions for the overall elastic constants are obtained.",

author = "Ali Imam and Johnson, {George C.} and Mauro Ferrari",

note = "Funding Information: MF is grateful to NSF for support under the National Young Investigatorp rogram.T he authorsb enefitedc onsiderablyf rom the commentso f Dr Frank Rooney during the courseo f this work.",

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T1 - Determination of the overall moduli in second order incompressible elasticity

AU - Imam, Ali

AU - Johnson, George C.

AU - Ferrari, Mauro

N1 - Funding Information: MF is grateful to NSF for support under the National Young Investigatorp rogram.T he authorsb enefitedc onsiderablyf rom the commentso f Dr Frank Rooney during the courseo f this work.

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Y1 - 1995/7

N2 - The problem of finding the overall second order elastic moduli for a biphase material is considered. The material consists of an incompressible isotropic matrix containing a dilute concentration of spherical inhomogeneities which are also incompressible and isotropic. To evaluate the effective moduli, the second order elastic field of a single inhomogeneity in an infinite matrix under homogeneous displacement boundary conditions is determined. This elastic field is assumed to approximate that of the composite with a dilute concentration of the second phase. No interaction between the particles is considered. Subsequently, through the equality of the strain energies of the inhomogeneous material and an equivalent homogeneous material, explicit expressions for the overall elastic constants are obtained.

AB - The problem of finding the overall second order elastic moduli for a biphase material is considered. The material consists of an incompressible isotropic matrix containing a dilute concentration of spherical inhomogeneities which are also incompressible and isotropic. To evaluate the effective moduli, the second order elastic field of a single inhomogeneity in an infinite matrix under homogeneous displacement boundary conditions is determined. This elastic field is assumed to approximate that of the composite with a dilute concentration of the second phase. No interaction between the particles is considered. Subsequently, through the equality of the strain energies of the inhomogeneous material and an equivalent homogeneous material, explicit expressions for the overall elastic constants are obtained.

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Determination of the overall moduli in second order incompressible elasticity

Abstract

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