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Derivation of a mesoscopic model for nonlinear particle-reinforced composites from a fully microscopic model

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Abstract

Particle-reinforced composites (PRCs) are usually studied by some averaging or homogenization techniques. In this, the effective properties are derived by assuming that particles are dispersed within composites according to some given (probabilistic) distribution. Such approaches restrain the possibilities of studying the contribution of exact location and parameters of individual particles to the overall behavior of composites. In this paper, we attempt to fill this gap by deriving the mesoscopic model of such composites corresponding to a continuum with point inhomogeneities. We start from a fully microscopic model where the composite is regarded as a continuum with spherical inclusions. Letting the diameter of inclusions decrease to zero, material parameters of the composite are represented in terms of the Dirac distribution. The Mindlin–Reissner–von Kármán thick plate theory is considered as a particular case, and closed-form formulas are obtained for the plate stiffness coefficients. Numerical analysis of a thick composite plate reinforced over its mid-surface justifies the theoretical derivations.

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Acknowledgements

The support of the State Administration of Foreign Expert Affairs of China is thankfully acknowledged. Valuable remarks of unknown reviewers allowed to improve the presentation of the results substantially.

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Authors and Affiliations

  1. Department on Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia, Yerevan, Armenia

    Asatur Zh. Khurshudyan

  2. Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China

    Asatur Zh. Khurshudyan

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  1. Asatur Zh. Khurshudyan
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Correspondence to Asatur Zh. Khurshudyan.

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Khurshudyan, A.Z. Derivation of a mesoscopic model for nonlinear particle-reinforced composites from a fully microscopic model. Acta Mech 230, 3543–3554 (2019). https://doi.org/10.1007/s00707-019-02491-y

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  • DOI: https://doi.org/10.1007/s00707-019-02491-y

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