Abstract：One of the main objectives of micromechanics is to predict the effective modulus of composites. Most of micromechanics models are based on Eshelby’s equivalent inclusion method under the hypothesis of ellipsoidal inclusion. An appropriate theoretical treatment for the non- ellipsoidal inclusion problems in an inhomogeneous media is still needed to be done. In this work, we proposed a principle of averaged equivalent eigenstrain, and then developed a new analytical micromechanics method for determining the effective elastic modulus of composites. By introducing the concept of averaged eigenstrain, the average stress and average strain in the matrix and inclusion of the representative volume element are analyzed. The principle of averaged equivalent eigenstrain is thus developed based on the principle of equivalent eigenstrain. Identical to the principle of equivalent eigenstrain which was built on the corner-stone of principle of virtual work, this new principle is also applicable to the inclusions with arbitrary shapes (either convex or concave), and multiple inclusions within a solid of finite volume. Then, focusing on the long-fiber-reinforced two-phase composites, we obtain the analytic relations of the average stresses and average strains in the matrix and fiber. A combination of the averaged equivalent eigenstrain and direct homogenization method of micro-mechanics thus can determine the effective elastic moduli of two-phase composites, by selecting the different deformation model and the corresponding boundary conditions. Finally, the effective moduli of composites is predicted using the mechanical properties of fiber and matrix constituents and the volume fraction of fiber, through a MATLAB program. The engineering constants such as tensile modulus, shear modulus and Poisson’s ratio of nine types of commonly used composites were discussed in detail. After comparing the predicted values with the experimental results and the predictions from other theoretical models, it is found that the averaged relative errors of the new approach are less as that of Halphin-Tsai model and Mori-Tanaka model, which thus the new analytical method is inherently suitable for the effective modulus of more general composites (either two-phase or multi-phase composites, containing inclusions/damage of either convex or concave shapes).
2022, Vol. 43 
