Micromechanics of Composite Materials Governed by Vector Constitutive Laws
The high-fidelity generalized method of cells micromechanics theory has been extended for the prediction of the effective property tensor and the corresponding local field distributions for composites whose constituents are governed by vector constitutive laws. As shown, the shear analogy, which can predict effective transverse properties, is not valid in the general three-dimensional case. Consequently, a general derivation is presented that is applicable to both continuously and discontinuously reinforced composites with arbitrary vector constitutive laws and periodic microstructures. Results are given for thermal and electric problems, effective properties and local field distributions, ordered and random microstructures, as well as complex geometries including woven composites. Comparisons of the theory's predictions are made to test data, numerical analysis, and classical expressions from the literature. Further, classical methods cannot provide the local field distributions in the composite, and it is demonstrated that, as the percolation threshold is approached, their predictions are increasingly unreliable. XXXX It has been observed that the bonding between the fibers and matrix in composite materials can be imperfect. In the context of thermal conductivity, such imperfect interfaces have been investigated in micromechanical models by Dunn and Taya (1993), Duan and Karihaloo (2007), Nan et al. (1997) and Hashin (2001). The present HFGMC micromechanical method, derived for perfectly bonded composite materials governed by vector constitutive laws, can be easily generalized to include the effects of weak bonding between the constituents. Such generalizations, in the context of the mechanical micromechanics problem, involve introduction of a traction-separation law at the fiber/matrix interface and have been presented by Aboudi (1987), Bednarcyk and Arnold (2002), Bednarcyk et al. (2004) and Aboudi et al. (2013) and will be addressed in the future.