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Generalized Mori–Tanaka Approach in Micromechanics of Peristatic Random Structure Composites

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Abstract

A statistically homogeneous random matrix medium with the bond-based peridynamic properties (see Silling, J Mech Phys Solids 48:175–209, 2000) of constituents is considered. For the media subjected to remote homogeneous volumetric boundary loading, one proved that the effective behavior of this media is described by conventional effective constitutive equation which is intrinsic to the local elasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional elasticity of CMs and adapted to peristatics. This is extraction from the material properties a constituent of the matrix properties. Effective properties moduli are expressed through the introduced local stress polarization tensor averaged over the extended inclusion phase rather than in an entire space. One proposes a generalization of a dilute approximation method to their peristatic counterpart in the sense that the volume fraction of the particles is small and their mutual interaction can be neglected. As in a classical approach, the essential assumption in the generalized Mori–Tanaka method (MTM) states that each extended inclusion behaves as an isolated one in the infinite matrix and subject to some effective strain field coinciding with the average strain in the truncated matrix. Comparative numerical analyses of both the dilute approximation and MTM method are performed for 1D case.

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Acknowledgements

Both the helpful comments of reviewers and their encouraging recommendations are gratefully acknowledged.

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  1. Micromechanics & Composites LLC, Dayton, Ohio, 45459, USA

    Valeriy A. Buryachenko

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  1. Valeriy A. Buryachenko
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Buryachenko, V.A. Generalized Mori–Tanaka Approach in Micromechanics of Peristatic Random Structure Composites. J Peridyn Nonlocal Model 2, 26–49 (2020). https://doi.org/10.1007/s42102-019-00023-9

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  • DOI: https://doi.org/10.1007/s42102-019-00023-9

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