The elastic moduli of simple twohyphen;dimensional isotropic composites: Computer simulation and effective medium theory

摘要

An algorithm, combining digitalhyphen;image with spring network techniques, has been developed that enables computation of the elastic moduli of random twohyphen;dimensional multiphase composites. This algorithm is used to study the case of isotropic, randomly centered, overlapping circular inclusions in an isotropic elastic matrix. The results of the algorithm for the fewhyphen;inclusion limit, as well as the case where both phases have the same shear moduli, agree well with the exact results for these two problems. The case where the two phases have the same Poissonrsquo;s ratio, but different Youngrsquo;s moduli, is also studied, and it is shown that the effective medium theory developed by Thorpe and Sen agrees well with the numerical results. A surprising result is that the effective moduli of systems with nonoverlapping circular inclusions are almost identical with the overlapping inclusion case, up to an inclusion area fraction of 50percnt;. Using the validated effective medium theory, we illustrate how the effective Poissonrsquo;s ratio ngr; behaves as a function of ngr;0, the pure phase Poissonrsquo;s ratio, and the stiffness ratio between the two components. Two distinct regions of behavior are found, defined by ngr;0gsim;ngr;ast; and ngr;0ngr;ast;, where ngr;ast; is approximately 1/3 for the geometry of this model.