Mechanics of Anisotropic Composite Materials

Abstract

Mechanics of composite materials was in the last decade one of the most rapidly explored engineering area, basically due to huge progress in composite fabrication and use. The main problem referred in this chapter is how to correctly predict averaged effective properties by implementation of numerous homogenization techniques. Useful classification of composites with respect to the format of effective stiffness matrix, based on the analogy between the crystal lattice symmetry and respective configuration of reinforcement in the RUC, is given. Extended section is focused on conventionally used Hill’s theorem on upper and lower bounds by Voigt and Reuss’ isotropic estimation for approximate determination of stiffness and compliance matrices of anisotropic composite. Consistent application of the Hill theorem to the elements of elastic stiffness or compliance matrices (but not to engineering anisotropy constants) enable to explain some peculiarities of the Poisson ratio diagrams, met in respective bibliography (e.g., Aboudi et al., Micromechanics of Composite Materials, 2013; Sun and Vaidya, Compos. Sci. Technol. 56:171–179, 1996; Gan et al., Int. J. Solids Struct. 37:5097–5122, 2000). The new effective proposal to achieve approximation of the mechanical modules of unidirectionally reinforced composites by the use of hybrid-type rule of weighted average between the Voigt and Reuss upper and lower estimates is proposed. Capability of this averaged interpolation was checked based on selected findings by Gan et al. (Int. J. Solids Struct. 37:5097–5122, 2000) for Boron/Al composite, which show good convergence and enable to treat weighting coefficients as universal ones over the full $V_\mathrm{f}$ range.