A novel approach to predict the effective elastic moduli of matrix composites made from non-circular inclusions embedded in a continuous matrix is proposed. In this approach, those inhomogeneities are substituted by simple equivalent circularinclusions with modified elastic properties obtained from comparing the dilute solution results. | Vietnam Journal of Mechanics, VAST, Vol. 37, No. 2 (2015), pp. 123 – 132 DOI: EQUIVALENT-INCLUSION APPROACH FOR ESTIMATING THE ELASTIC MODULI OF MATRIX COMPOSITES WITH NON-CIRCULAR INCLUSIONS Tran Nguyen Quyet1 , Pham Duc Chinh2 , Tran Anh Binh3,∗ 1 Hanoi University of Industry, Vietnam 2 Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam 3 National University of Civil Engineering, Hanoi, Vietnam ∗ E-mail: Received December 03, 2014 Abstract. A novel approach to predict the effective elastic moduli of matrix composites made from non-circular inclusions embedded in a continuous matrix is proposed. In this approach, those inhomogeneities are substituted by simple equivalent circularinclusions with modified elastic properties obtained from comparing the dilute solution results. Available simple approximations for the equivalent circular-inclusion medium then can be used to estimate the effective elastic moduli of the original composite. Robustness of proposed approach is demonstrated through the numerical examples with elliptic inclusions. Keywords: Effective elastic moduli, isotropic multicomponent material, matrix composite, elliptic inclusion, circular inclusion. 1. INTRODUCTION Practical materials are often strongly heterogeneous and contain high volume fractions of inclusions with sizes spread over several spatial scales. Regarding the intensive use of these materials, predicting and optimizing their effective properties from a microscopic description represents a considerable industrial interest. In view of the microscopic morphological complexity, analytical results are limited, even in the linear case. Upper and lower bounds on the possible values of the effective properties [1–6] are not very useful in the case of high contrast of matrix-inclusion properties. Numerical homogenization techniques [7–12] allow overcoming these issues, but efficient strategies must be .
