**Multiscale modeling of size-dependent elastic properties of carbon
nanotube/polymer nanocomposites with interfacial imperfections**

S Yang and S Yu and W Kyoung and DS Han and M Cho, POLYMER, 53, 623-633 (2012).

DOI: 10.1016/j.polymer.2011.11.052

We developed an efficient and extensible multiscale analysis to consider the carbon nanotube (CNT) size effect and weakened bonding effect at the interface on the effective elastic stiffness of CNT/polymer nanocomposites using molecular dynamics (MD) simulations and continuum micromechanics. Under the assumption that the CNT molecular structure is an equivalent solid cylinder, molecular mechanics calculation results for transversely isotropic elastic stiffness were found to decrease as the radius of the CNT increased. Similarly, the transversely isotropic elastic moduli of aligned pristine CNT-reinforced polypropylene composites obtained from molecular dynamics simulations exhibited the same CNT size dependency. However, a weakened interface effect was observed from the transverse Young's modulus and two shear moduli. To account for the size effect and the weakened interface in the micromechanics-based multiscale model, a modified multi-inclusion model is derived with an effective particle scheme. Also, an effective matrix concept is suggested to account for the formation of an interphase near the surface of the CNT, and the elastic stiffness of the CNT and the effective matrix is defined as a function of the CNT radius to describe size-dependent elastic stiffness in the micromechanics regime. (C) 2011 Published by Elsevier Ltd.

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