Explicit cross-property correlations for anisotropic two-phase composite materials

Sevostianov, Igor; Kachanov, Mark

doi:10.1016/s0022-5096(01)00051-5

Cited by 204 publications

(85 citation statements)

References 12 publications

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“…Explicit analytic expressions for eff H are available for the ellipsoidal shapes only [13], and in this case equation (4) can be explicitly solved for the effective properties. In the following, we consider domains  of the ellipsoidal shape, assuming that it provides sufficient flexibility.…”

Section: Maxwell Scheme In Terms Of Property Contribution Tensorsmentioning

confidence: 99%

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Maxwell Homogenization Scheme in Micromechanics: an Overview

Sevostianov

2017

MATEC Web Conf.

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Abstract. The paper discuss the classical Maxwell's (1873) homogenization method and the problems appearing in its practical implications. The method equates the far fields produced by a set of inhomogeneities and by a fictitious domain with unknown effective properties. It is re-written in terms of the property contribution tensors. The shape of the effective inclusion substantially affects the overall elastic properties. The choice of this shape in the case of anisotropic composite is a non-trivial problem. Another problem is related to the possible appearance of artificial singularities in the process of homogenization. We illustrate the method by several examples.

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Section: Maxwell Scheme In Terms Of Property Contribution Tensorsmentioning

confidence: 99%

“…In the following, we consider domains  of the ellipsoidal shape, assuming that it provides sufficient flexibility. Then equation (4) can be specified as follows [13]:…”

Section: Maxwell Scheme In Terms Of Property Contribution Tensorsmentioning

confidence: 99%

Maxwell Homogenization Scheme in Micromechanics: an Overview

Sevostianov

2017

MATEC Web Conf.

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“…The key quantity in this problem is the resistivity contribution tensor that gives the extra temperature gradient produced by the introduction of the inhomogeneity into a material subjected to an otherwise uniform heat flux. This tensor was introduced by Sevostianov & Kachanov [25] in the context of the crossproperty connection between the elastic and conductive properties of heterogeneous materials. Following this work, we assume that the background material of volume V having the isotropic thermal conductivity k 0 contains an isolated inhomogeneity of volume V 1 of the isotropic thermal conductivity k 1 .…”

Section: Introductionmentioning

confidence: 99%

Toroidal insulating inhomogeneity in an infinite space and related problems

Radi

Sevostianov

2016

Proc. R. Soc. A.

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An analytic solution for the steady-state temperature distribution in an infinite conductive medium containing an insulated toroidal inhomogeneity and subjected to remotely applied uniform heat flux is obtained. The temperature flux on the torus surface is then determined as a function of torus parameters. This result is used to calculate the resistivity contribution tensor for the toroidal inhomogeneity required to evaluate the effective conductive properties of a material containing multiple inhomogeneities of this shape.

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“…Different physical and mechanical properties of composite materials-the elastic and the conductive ones, in particular-can be explicitly related to one another [1][2][3][4]. The practical usefulness of such relations lies in the fact that one physical property (for example, electrical conductivity) may be easier and cheaper to measure than the other (for example, elastic constants, tensile strength), and very often the non-destruction of samples is of primary interest.…”

Section: Introductionmentioning

confidence: 99%

Cross-property connections for copper–graphite composites

2015

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Copper-graphite composite materials in the range of 0-10 vol% of carbon phase were prepared from the mixture of copper and graphite powders by hot isostatic pressing. The microstructure, mechanical (tensile strength, elongation to fracture) and physical (electrical and thermal conductivity) properties of composite samples were investigated, and the cross-property connections were calculated. It was shown that electrical and thermal conductivity cross-property (Lorenz number) is almost constant and increases only slightly (no more than 10 % increase was observed). This implies that in the investigated composition range the Lorenz number of a copper-graphite composite system behaves according to Franz-Wiedemann law for pure metals at constant temperature. On the contrary, the conductivity to tensile strength cross-property connections showed significant linear increase (over 200 % in the investigated composition range) for both electrical conductivity and thermal conductivity of composite materials. The cross-property connections of conductivity to the elongation to fracture exhibit a nonlinear dependence on the volume fraction of graphite.

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Explicit cross-property correlations for anisotropic two-phase composite materials

Cited by 204 publications

References 12 publications

Maxwell Homogenization Scheme in Micromechanics: an Overview

Maxwell Homogenization Scheme in Micromechanics: an Overview

Toroidal insulating inhomogeneity in an infinite space and related problems

Cross-property connections for copper–graphite composites

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