Modeling of geometric configuration and fiber interactions in short fiber reinforced composites via new modified Eshelby tensors and enhanced mean-field homogenization

Determination of the effective elastic properties of unidirectional short fiber reinforced composites (SFRCs) is a key fundamental requirement which is usually estimated by mean-field homogenization (MFH) methods. Available classical MFH methods only account for volume fraction and aspect ratio of the fibers and do not consider the physical cylindrical geometry of the fibers. Moreover, classical MFHs are not designed for predicting the effective properties of SFRCs with distinct packing configurations and order of fibers. In this work, new modified Eshelby tensors associated with an enhanced MFH are developed which resolve the mentioned limitations of the available MFH methods and preserve their computational efficiency. While classical Eshelby tensors used in MFHs depend only on the aspect ratio of the fictitious ellipsoidal inclusion and material properties of the matrix, the introduced modified Eshelby tensors additionally account for physical cylindrical geometry as well as interactions of the short fibers with different packing configurations. Moreover, non-uniform homogenizing eigenstrains required for accurate homogenization of the short fibers are also incorporated by the proposed analytical treatment. Predictions of the developed enhanced MFH for various packing configurations are compared with those obtained from Finite Element Method implementing periodic boundary conditions and very good agreements are observed. It is shown that packing configuration and geometrical specifications of short fibers can significantly affect the effective properties of the SFRC.