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Random Versus Periodic Microstructures for the Thermal Conductivity of Fiber-Reinforced Composites


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DOI: https://doi.org/10.15866/ireme.v12i10.13711

Abstract


Periodic models are often used for the homogenization of fiber-reinforced materials. The periodic distribution of the inclusions is a simplifying assumption that fails to give a realistic representation of the actual materials which demonstrate a random arrangement of fibers. The present study is a comparison between the periodic model and the random one. An intermediate configuration was introduced in which a periodic hexagonal cell of varying size is embedded inside a microstructure of a random distribution of fibers. The results of the homogenization showed similarities between the macroscopic behavior of the random model and the intermediate models. It also highlighted the discrepancies between the effective thermal conductivities of the periodic model and the random one. Furthermore, the analysis of the thermal field maps of the three types of configurations helped determine the reason behind the difference in the macroscopic response of the random model and the periodic one based on their local behavior. Lastly, it was concluded that the periodic model should solely be used to determine the macroscopic behavior of the fiber-reinforced composites, only if no significant precision is required.
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Keywords


Fiber-Reinforced Composites; Numerical Homogenization; Periodic Microstructures; Random Microstructures; Thermal Conductivity; Unidirectional Fibers

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