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27.07.2019 | Original Paper | Ausgabe 10/2019

Acta Mechanica 10/2019

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

Zeitschrift:
Acta Mechanica > Ausgabe 10/2019
Autor:
Asatur Zh. Khurshudyan
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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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