Due to the enhanced interaction among constituents and the resultant effect of particle size on the elastic modulus, nanocomposites with volume fractions higher than 12% show critical nondilute concentrations. In order to describe nondilute concentrations and the effect of particle size, a multi-inclusion model was adopted and a method was developed to transfer nanoscale physical information to a continuum-based analytical model. The accuracy and applicability of the present scale-bridging method at dilute and nondilute concentrations were verified by comparing results of the present method with those of molecular dynamics and finite element analysis.
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Yang et al. (2009) studied this question.
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