Effective properties of particulate nano-composites including Steigmann-Ogden model of material surface

Abstract

The objective of this work is inclusion of the Steigmann-Ogden interface in the Method of Conditional Moments to investigate the influence of surface effects on the effective properties of random particulate composites. The particular focus is centered on accounting for the surface bending stiffness. To this end, the notion of the energy-equivalent inhomogeneity developed for Gurtin–Murdoch interface is generalized to include the surface bending contribution. The crucial aspect of that generalization is identification of the formula defining energy associated with the surface bending. With the help of that formula, the real nano-particle and its surface are replaced by equivalent inhomogeneity with properties incorporating the surface effects. Closed-form expressions for the effective moduli of a composite with a matrix and randomly distributed spherical inhomogeneities are derived. The normalized shear moduli of nanoporous material as a function of void volume fraction is analyzed and evaluated in the context of other theoretical predictions.