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Abstract Based on the theory of Gurtin-Murdoch surface/interface model, a rigorous whole-field solution is obtained for the inhomogeneity/matrix/equivalent medium model, in terms of which a generalized self-consistent approach is developed for predicting the effective anti-plane shear modulus of nano composites. Closed-form solution of the effective anti-plane shear modulus was presented. The numerical results reveal that the effective anti-plane shear modulus is size dependent when the size of the inhomogeneity is on the order of nanometer. With the increase of the size of the inhomogeneity, the present solution approaches to the classical results obtained in the linear elasticity theory. In comparison to the effective bulk modulus and shear modulus (isotropic materials), the present effective anti-plane shear modulus of the nano composites is influenced by the size of the inhomogeneity at a smaller range. The interface property and the stiffness of the inhomogeneity play an important role in the effective anti-plane shear modulus of the nano composites.
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Received: 27 November 2009
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2011, Vol. 32 
