Several representative micro-mechanical models for the analysis of the effective elastic properties of unidirectional fiber-reinforced composites and textile composites are briefly reviewed, and their characteristics are pointed out. In view of the limitations of the classical mechanical models for the prediction of the overall elastic behaviors of textile composites, a more generalized method is established. According to the fact that the in-plane components of strain tensor and the out-of-plane components of stress tensor are continuous across a perfect interface, interactions between phases are considered, and the perfect interface based formulas for homogenization are derived. This method has been applied to determine the effective elastic modulus of a unidirectional fiber-reinforced composite, and satisfactory results are obtained.
Hashin Z,Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphase materials[J].Journal of the Mechanics and Physics of Solids.1963,11(2):127-140
Hill R. Elastic properties of reinforced solids:some theoretical principles[J].Journal of the Mechanics and Physics of Solids.1963, 11(5):357-372
Hashin Z, Rosen R W. The elastic moduli of fiber-reinforced materials . Journal of Applied Mechanics,1964,31(1):223~232.
Hill R. Theory of mechanical properties of fiber-strengthened materials—IIIself-consistent model[J].. Journal of the Mechanics and Physics of Solids.1965,13(4):189-198
Christensen R M, Lo K H. Solutions for effective shear properties in three-phase sphere and cylinder models[J].Journal of the Mechanics and Physics of Solids.1979,27(4):315-330
Ishikawa T, Chou T W. Stiffness and strength behaviour of woven fabric composites[J].Journal of Materials Science.1982, 17(1):3211-3220
Yang J M, Ma C L, Chou T W. Fiber inclination model of three-dimensional textile structure composites[J].Journal of Composite Materials.1986,20(5):472-484
Laws N. On interfacial discontinuities in elastic composites[J].Journal of Elasticity.1975,5(3-4):227-235
Hill R. Interfacial operators in the mechanics of composite media[J].Journal of the Mechanics and Physics of Solids.1983, 31(4):347-357
Gu Zhongming, Zhu Dechao. Micro-mechanical analysis of the strength of fiber composites with unidirectional undulation . In:Proceedings of the Asian-Pacific Conference on Strength of Materials and Structures . Beijing:International Academic Publishers, 1996. 307~311.
Hashin Z. Analysis of properties of fiber composites with anisotropic constituents[J]. Journal of Applied Mechanics, 1979, 46(3):543~550.