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H. J. Böhm, F. G. Rammerstorfer, E. Weissenbek:
"Some Simple Models for Micromechanical Investigations of Fiber Arrangement Effects in MMCs";
Computational Materials Science, 1 (1993), 3; 177 - 194.

The influence of the fiber arrangement on the microscale stress and strain fields and on the overall thermoelastoplastic properties of two classes of unidirectional metal matrix composites (MMCs) is investigated. A micromechanical approach employing the Finite Element (FE) method is used, which is based on analyzing the nonlinear response of periodically repeating unit cells. By applying suitable boundary conditions, microgeometries which are modified from regular fiber arrays are modeled at relatively low computational cost. When applied to discontinuously reinforced composites, this strategy allows the investigation of materials containing regular arrangements of two or more different types of aligned short fibers. In the case of continuously reinforced composites, periodic hexagonal arrays as well as regular, modified and clustered square arrangements of parallel fibers are considered. The influence of the fiber arrangement on the overall thermomechanical properties of the damage-free composites is generally found to be small, the main exception being the overall response to transverse mechanical loading. The computed microfields, however, are predicted to depend noticeably on the microgeometry, and consequently, damage-related parameters such as the hydrostatic microstresses, the interfacial stress distributions and the shakedown limits show a marked sensitivity to the fiber arrangement.

http://dx.doi.org/10.1016/0927-0256(93)90010-K