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The never-ending struggle to design new materials for supporting innovative engineering requirements gives composites a worthy focus. This endeavor is challenged by the anisotropic nature of composite material that needs virtual simulations based on non-linear multi-scale modeling. Unfortunately, to accurately characterize the nonlinear behavior of composite materials and to determine the optimized design, the existing micromechanical models are not up to the challenge. Therefore, there is a pressing need to help design engineers getting a clear view of their strengths and weaknesses both from the perspective of their ground hypotheses and their predictive capabilities. This work addresses this goal by ascertaining the accuracy of both prominent and recent micromechanical models and subsequently emphasizes the capability scope of each model. In effect, the different conclusions are summarized in a table. The drawn conclusion is that yet no particular micromechanical model could yield good estimates for different heterogeneous materials and various operating conditions; due mainly to the limitations of their underlying hypotheses even in the linear case. That leads us to argue that the development of a comprehensible linear model with a clear physical background is needed more than ever to help us circumvent the intricacy of the extension to the non-linear case.

Elastoplastic mean-field homogenization: recent advances review