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General Interface Integral Equations in Elasticity of Random Structure Composites

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Micromechanics and Nanomechanics of Composite Solids

Abstract

One considers linearly elastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of a noncanonical shape. The new general integral equations connecting the stress and strain fields in the point being considered with the stress and strain fields in the surrounding points are obtained for the random fields of heterogeneities. The method is based on a recently developed centering procedure where the notion of a perturbator is introduced in terms of boundary interface integrals that makes it possible to reconsider basic concepts of micromechanics such as effective field hypothesis, quasi-crystalline approximation, and the hypothesis of “ellipsoidal symmetry.” The results of this reconsideration are quantitatively estimated for some modeled composite reinforced by aligned homogeneous heterogeneities of a noncanonical shape. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.

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Notes

  1. 1.

    It is known that for 2-D problems the plane-strain state is only possible for material symmetry no lower than orthotropic (see, e.g., Lekhnitskii 1963) that will be assumed hereafter in 2-D case.

  2. 2.

    Exponential decreasing of this function was obtained by Willis (1978) for spherical inclusions; Hansen and McDonald (1986), Torquato and Lado (1992) proposed a faster decreasing function for aligned fibers of circular cross-section.

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Acknowledgements

The author acknowledges the support of the US Air Force Office of Scientific Research.

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    Valeriy Buryachenko

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  1. Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada

    Shaker A. Meguid

  2. Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey, USA

    George J Weng

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Buryachenko, V. (2018). General Interface Integral Equations in Elasticity of Random Structure Composites. In: Meguid, S., Weng, G. (eds) Micromechanics and Nanomechanics of Composite Solids. Springer, Cham. https://doi.org/10.1007/978-3-319-52794-9_17

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