Equivalent Modulus Of Composites With Randomly Distributed Nanosized Ellipsoidal Inclusions

The calculation of the equivalent modulus of the particle reinforced composite materials is an important part of composite material mechanics,there are two kinds of the analytic methods for the equivalent modulus.One is the bound approaches and the other is direct estimations.Both methods simplify the model and merely consider composite materials with the random distributions of cylinders or balls.Later,Bornert has obtained the equivalent modulus of composite materials containing ellipsoidal inclusions by using the finite element method.In order to solve grid division and calculation increasing exponentially problem,Riccardi and Montheillet have improved 3PM method proposed by Luo and Weng to estimate the equivalent modulus of elliptical inclusion compound material.Even so,they have neglected the influence of interface stress when the scale of ellipsoidal inclusion is nanometer size.We improve the methods mentioned above and obtain the local stress field of the nanosized ellipsoidal inclusion based on the energy equivalence principle.The equivalent moduli of composite materials containing randomly distributed nano-ellipsoidal inclusions are also estimated in this paper.