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.
Highlights
Interphases between the inhomogeneities and the matrix may have a very pronounced influence on the overall properties of composite materials
The main goal of this work is to show that the new concept of energy-equivalent inhomogeneity (EEI), recently presented in [37,38,39], permits direct evaluation of effective properties of nanomaterials, which includes SteigmannOgden interface model
The variation of the normalized shear modulus ∗∕ 2 with the void volume fractions calculated by the method of conditional moments (MCM) in combination with EEI approach for the spherical cavities of radius a = 5 nm with Steigmann-Ogden model of interface is shown in Fig. 1
Summary
Interphases between the inhomogeneities and the matrix may have a very pronounced influence on the overall properties of composite materials. The generalization of Gurtin–Murdoch model was proposed by Steigmann and Ogden [19, 20] who introduced the resistance of the surface to both stretch and bending. The main goal of this work is to show that the new concept of energy-equivalent inhomogeneity (EEI), recently presented in [37,38,39], permits direct evaluation of effective properties of nanomaterials, which includes SteigmannOgden interface model. The main contribution of the proposed approach, which is determination of properties of the equivalent spherical inhomogeneity with Steigmann-Ogden interface, is presented in general terms, with the development quantifying those contributions relegated to Appendices 1 and 2.
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