Differential scheme for the effective elastic properties of nano-particle composites with interface effect

The differential scheme is developed to evaluate the effective elastic properties of nano-composites with interface effect through the solution of an infinitely dilute dispersion of nano-particles in a matrix. The differential equations presented in this paper for overall modulus of composites extend the application of classic differential scheme to the nano-scale, and they are valid for both mono-sized and poly-sized nano-particle composites. Particle size distribution functions are introduced. Continuous and discrete size distributions are taken into consideration for poly-sized filled nano-particles. The numerical examples exhibit that the effective properties of mono-sized nano-particle composite are size dependent, which agrees well with previous studies. As for poly-sized particle composite, the results show that the elastic properties are dependent on particle size distributions. Some distribution parameters, such as the mean size and the standard deviation, may significantly affect the effective mechanical properties. The proposed differential equations can be reduced to the classic ones, and are supposed to be in wider application.