Examination of Law of Mixture for Composites Using FEM Analysis.

Abstract

In this paper, effect of shape of inclusions on the elastic modulus of composite materials is considered when equally shaped 2D inclusions are arranged in matrix. The effective elastic modulus of the composite materials is numerically analyzed by the application of FEM. Accuracy of approximate formula based on law of mixture is examined. From the comparison between the results of rectangular and elliptical inclusions, it is found that the effective elastic modulus is determined by two major parameters, that is, (i) the area fraction of inclusions projected in tensile direction, and (ii) the volume fraction of inclusion, almost independent of shape of inclusion. A convenient method of calculation is newly proposed for the effective elastic modulus of composites by using the replacement of the equivalent rectangular inclusions.