Elasto-plastic models for composites can be classified into three categories in terms of a length scale, i.e., macro scale, meso scale, and micro scale (micromechanics) models. In general, a so-called multi-scale model is a combination of those at various length scales with a micromechanics one as the foundation. In this paper, a critical review is made for the elastoplastic models at the micro scale, and a comparative study is carried out on most popular analytical micromechanics models for the elastoplastic behavior of long fibrous composites subjected to a static load, meaning that creep and dynamic response are not concerned. Each model has been developed essentially following three steps, i.e., an elastic homogenization, a rule to define the yielding of a constituent phase, and a linearization for the elastoplastic response. The comparison is made for all of the three aspects. Effects of other issues, such as the stress field fluctuation induced by a high contrast heterogeneity, the stress concentration factors in the matrix, and the different approaches to a plastic Eshelby tensor, are addressed as well. Correlation of the predictions by different models with available experimental data is shown.

Bridging Model is an efficient micromechanical theory which can be used to predict the effective thermomechanical as well as strength properties of a fiber reinforced composite. The key to the Bridging Model is a bridging tensor, which was obtained on Eshelby's inclusion method [Huang and Zhou, Strength of Fibrous Composites, Vol. 53, Zhejiang University Press, Springer, Hangzhou, (2011)]. A different approach to the closed‐form expressions for the elements of a bridging tensor is presented in this work. The method is based on averaging the stress fields of a single‐fiber inclusion embedded within an infinite matrix subjected to various load conditions. By solving the bridging equations between the averaged stress components in the fiber and those in the matrix, the exact expressions for the bridging tensor elements are obtained. The Bridging Model can be established by neglecting some small quantities in the bridging tensor elements. Effective elastic moduli of a unidirectional (UD) composite are expressed as functions of a bridging tensor. Comparisons of predicted elastic properties of a total number of 18 UD composites on simplified and the exact bridging tensors are made. POLYM. COMPOS., 36:1417–1431, 2015. © 2014 Society of Plastics Engineers

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