The bulk behavior of short-fiber composite materials in mechanical, thermal, and electrical applications is of great engineering interest. The reliability of analytical and numerical studies dedicated to these topics depends to a large extent on the postulated, or prescribed, microstructure configurations. Of course, different spatial distributions of fibers lead to different configurations, which in turn influence the effective properties. There are no established (or benchmarked) microstructure configurations (or models) to be used in investigations aimed at calculating the macroscopic behavior of classes of real composite material bodies. In the present numerical study of heat conduction in composites, accurate results for the longitudinal and transverse effective thermal conductivities of short-fiber composites with single-fiber uniform hexagonal prism cell are calculated and validated. The three-dimensional periodic cell microstructure consists of one short circular cylindrical fiber placed at the center, and perpendicular to the two parallel regular hexagons, of the prism. Previous continuous formulation and computational implementation are employed, based on the method of homogenization and finite element discretization. A procedure for generating the domain of the uniform hexagonal prism cell, and the respective tetrahedral finite-element mesh, has been realized using a third-party software. The numerical effective conductivity results obtained in the 3-D calculations are validated against analytical results for the 2-D hexagonal array of circular cylinders.
Effective properties of short-fiber composites with Gurtin-Murdoch model of interphase