ABSTRACT
In this chapter, several approaches and methods of the analysis of the interrelations between the microstructures, and the mechanical behavior and strength of materials in particular have been discussed. This chapter reviews and evaluates models that predict the stiffness of short-fiber composites. These include the dilute model based on Eshelby’s equivalent inclusion, the self-consistent model for finite-length fibers, Mori–Tanaka-type models, bounding models, the Halpin–Tsai equation, and shear-lag models. Several models are found to be equivalent to the Mori–Tanaka approach, which is also equivalent to the generalization of the Hashin–Shtrikman–Walpole lower bound. The essential ideas and numerical implementation of fast Fourier transform (FFT)-based homogenization and asymptotic homogenization have been reviewed.
