Effects of particle shape on the macroscopic and microscopic linear behaviors of particle reinforced composites Azra Rasool, Helmut J. Böhm ⇑ Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology, Vienna, Austria article info Article history: Received 14 November 2011 Accepted 16 January 2012 Available online 19 April 2012 Keywords: Composites Thermoelastic properties Conduction properties Particle shape effects abstract A systematic comparison of inhomogeneity shape effects on the linear elastic, thermoelas- tic and thermal conduction responses of particle reinforced composites is carried out. For this purpose, multi-particle unit cells that contain randomly positioned and, where appli- cable, oriented, identical particles having the shapes of spheres, regular octahedra, cubes or regular tetrahedra, respectively, and a volume fraction of 20% are employed. The macro- scopic moduli and microscopic responses, such as phase averages, as well as phase-level standard deviations and distribution functions of the microfields are evaluated and com- pared to analytical estimates. The results indicate the presence of relatively small but con- sistent effects of the particle shape on the effective behavior of particulate composites. Effects on the microscopic stress and flux fields are predicted to be more pronounced. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction A well-known mean field expression for the effective elastic tensor of two-phase composites, E / , can be written in the form E  ¼ n ðmÞ E ðmÞ A ðmÞ þ n ðiÞ E ðiÞ A ðiÞ : ð1Þ From this equation it is evident that the leading parameters determining E / are the elastic tensors, E (m) and E (i) , as well as the volume fractions, n (m) and n (i) , of the matrix (m) and the inhomogeneity (i) phases, respectively. The phase averaged strain concentration tensors, A ðmÞ and A ðiÞ , contain information, on the one hand, on the macroscopic symmetry of the materials, i.e., on the two-point statistics of the phase arrangement. On the other hand, they also depend on details of the microgeometry, such as clustering, size distributions and shape(s) of the reinforcement phase. The latter descriptors can be captured by high- er correlations and have more limited effects on the effective tensors. Analogous considerations hold for the thermoelastic and thermal conduction responses of inhomogeneous materials. The present work concentrates on one of these details, par- ticle shape, in particle reinforced composites. Among the established methods for modeling the behavior of particle reinforced composites, the classical equivalent inclusion approach of Eshelby (1957) and the standard mean field methods based on it are capable of handling ellipsoidal inhomogeneities of different aspect ratios. Non-ellipsoidal inclusions are known to give rise to Eshelby tensors that are posi- tion dependent (Kang & Milton, 2008). Accordingly, extensions of mean field models to more general inhomogeneity shapes have, on the one hand, been based on inclusion averaged Eshelby tensors (Gao & Liu, 2012; Nozaki & Taya, 2001; Onaka, 2001; Rodin, 1996; Zheng, Zhao, & Du, 2006). On the other hand, numerically evaluated compliance contribution (Eroshkin & Tsukrov, 2005; Kachanov, Tsukrov, & Shafiro, 1994; Sevostianov, Kachanov, & Zohdi, 2008) or replacement concentration 0020-7225/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijengsci.2012.03.022 ⇑ Corresponding author. E-mail address: hjb@ilsb.tuwien.ac.at (H.J. Böhm). International Journal of Engineering Science 58 (2012) 21–34 Contents lists available at SciVerse ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci