Computational modeling of elastic properties of carbon nanotube/ polymer composites with interphase regions. Part II: Mechanical modeling Fei Han, Yan Azdoud, Gilles Lubineau ⇑ King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering Division, COHMAS Laboratory, Thuwal 23955-6900, Saudi Arabia article info Article history: Received 24 April 2013 Accepted 1 July 2013 Available online 22 August 2013 Keywords: Carbon nanotube Composites Polymer interphase region Elasticity Non-local continuum Peridynamics abstract We present two modeling approaches for predicting the macroscopic elastic properties of carbon nano- tubes/polymer composites with thick interphase regions at the nanotube/matrix frontier. The first model is based on local continuum mechanics; the second one is based on hybrid local/non-local continuum mechanics. The key computational issues, including the peculiar homogenization technique and treat- ment of periodical boundary conditions in the non-local continuum model, are clarified. Both models are implemented through a three-dimensional geometric representation of the carbon nanotubes net- work, which has been detailed in Part I. Numerical results are shown and compared for both models in order to test convergence and sensitivity toward input parameters. It is found that both approaches provide similar results in terms of homogenized quantities but locally can lead to very different micro- scopic fields. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction Following the first part, ‘‘Computational modeling of elastic prop- erties of carbon nanotube/polymer composites with interphase re- gions. Part I: micro-structural characterization and geometric modeling’’ [1], we now assess the elastic mechanical properties of carbon nanotube (CNT)/polymer composites by large scale compu- tational models. CNT/polymer composites present peculiar micro-structural fea- tures. CNTs tend to create interwoven networks and to agglomer- ate together to form ‘‘clusters’’ due to the Van der Waals forces and Coulomb attractions [2–4]. These complex microstructures might result in strong heterogeneities in the nano-composites. An- other feature of CNT/polymer composites are the thick (with re- spect to the CNT diameter) polymer interphase regions at the CNT/bulk polymer frontier. Polymer chains easily wrap, crystallize or agglomerate around a CNT [5–8] to form a thick polymer inter- phase region [5,9,10]. The mechanical properties of this interphase region are much higher compared to the properties of the amor- phous phase [11,12]. Additionally, we proved in the first part [1] that, even at low CNT content, the volume fraction of these inter- phase regions can be quite high. Some experimental studies sug- gest that these interphase regions play, in fact, a major reinforcing role in nano-composites [11,13]. Multiple modeling and simulation strategies have been pro- posed to estimate the mechanical properties of CNT/polymer com- posites [14], such as, molecular dynamics [15–17], continuum mechanics [18,19] and multiscale approaches [20–24]. However, few simulations focus on both CNT networks and polymer inter- phase regions to study their effects on the mechanical behavior of nano-composites. The reason is that accounting for the CNT net- work and the surrounding interphase regions becomes quickly untraceable from the computational point of view at the scale of the representative volume element (RVE). Here, we intend to present two possible modeling approaches: classical local continuum mechanics, involving contact forces, and hybrid local/non-local continuum mechanics that involves both lo- cal and non-local interactions. While the first class of model is clas- sical, the second class is of interest for its future possible applications to failure simulation. It belongs to a more general framework known as ‘‘peridynamics’’. Peridynamics [25] has been recently proposed as a way to model the deformation of bodies, especially for discontinuity and fracture problems [26,27]. It has been proven to be an upscaling of molecular dynamics [28] and a limiting case of classical local models when the peridynamics length scale goes to zero [29–31]. The motivation for using a non-local continuum model is double: (1) it can be a way to simu- late the macroscopic behavior while capturing some specific fea- tures at the very low scale (non-local forces and interactions), and (2) it defines a consistent framework for failure simulations in the future. 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.07.008 ⇑ Corresponding author. Tel.: +966 28082983. E-mail address: gilles.lubineau@kaust.edu.sa (G. Lubineau). Computational Materials Science 81 (2014) 652–661 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci