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In this study, the fundamental framework of analytical micromechanics isgeneralized to consider nano-composites with both interface stretching andbending effects. The interior and exterior Eshelby tensors for a sphericalnano-inclusion, with an interface defined by the Steigmann-Ogden model,subjected to an arbitrary uniform eigenstrain are derived for the first time.Correspondingly, the stress/strain concentration tensors for a sphericalnano-inhomogeneity subjected to arbitrary uniform far-field stress/strainloadings are also derived. Using the obtained concentration tensors, theeffective bulk and shear moduli are derived by employing the diluteapproximation and the Mori-Tanaka method, respectively, which can be used forboth nano-composites and nano-porous materials. An equivalent interfacecurvature parameter reflecting the influence of the interface bendingresistance is found, which can significantly simplify the complex expressionsof the effective properties. In addition to size-dependency, the closed formexpressions show that the effective bulk modulus is invariant to interfacebending resistance parameters, in contrast to the effective shear modulus. Wealso put forward for the first time a characteristic interface curvatureparameter, near which the effective shear modulus is affected significantly.Numerical results show that the effective shear moduli of nano-composites andnano-porous materials can be greatly improved by an appropriate surfacemodification. Finally, the derived effective modulus with the Steigmann-Ogdeninterface model is provided in the supplemental MATLAB code, which can beeasily executed, and used as a benchmark for semi-analytical solutions andnumerical solutions in future studies.

Eshelby tensors and overall properties of nano-composites considering both interface stretching and bending effects