Modeling the tensile stress–strain response of carbon nanotube/polypropylene nanocomposites using nonlinear representative volume element Ehsan Mohammadpour a , Mokhtar Awang a , Saeid Kakooei a , Hazizan Md Akil b,c,⇑ a Department of Mechanical Engineering, Universiti Teknologi PETRONAS, Malaysia b School of Materials and Mineral Resources Engineering, Universiti Sains Malaysia, Malaysia c Cluster of Polymer Composites (CPC), Engineering and Technology Research Platform, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Penang, Malaysia article info Article history: Received 1 June 2013 Accepted 2 January 2014 Available online 10 January 2014 Keywords: Carbon nanotube Polymer composites Non-bonded interface Finite element modelling Representative volume element abstract This paper presents a finite element model for predicting the mechanical behavior of polypropylene (PP) composites reinforced with carbon nanotubes (CNTs) at large deformation scale. Existing numerical mod- els cannot predict composite behavior at large strains due to using simplified material properties and inefficient interfaces between CNT and polymer. In this work, nonlinear representative volume elements (RVE) of composite are prepared. These RVEs consist of CNT, PP matrix and non-bonded interface. The nonlinear material properties for CNT and polymer are adopted to solid elements. For the first time, the interface between CNT and matrix is simulated using contact elements. This interfacial model is capable enough to simulate wide range of interactions between CNT and polymer in large strains. The influence of adding CNT with different aspect ratio into PP is studied. The mechanical behavior of com- posites with different interfacial shear strength (ISS) is discussed. The success of this new model was verified by comparing the simulation results for RVEs with conducted experimental results. The results shows that the length of CNT and ISS values significantly affect the reinforcement phenomenon. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Carbon nanotubes (CNTs) have attracted huge interest in most areas of engineering due to their unique physical and chemical properties. Carbon nanotubes are considered to be excellent rein- forcement to improve toughness and fracture resistant [1], wear sliding [2], impact behavior [3] and thermal conductivity [4] of polymer composites. Experimental studies showed that the ability of carbon nanotubes to enhance the performance of polymer com- posites mostly depends on the strength of the interface and inter- actions between the polymer and CNTs [5,6]. The load carrying capacity of CNTs, polymer/CNT wetting and interfacial adhesion in CNT/polymer composites have been extensively studied using electron microscopy [7] and spectroscopic techniques [8]. Cadek et al. [6] studied the effects of interfacial surface area on the tensile behavior of poly(vinyl alcohol) films loaded with different types of CNTs. Results indicated that total nanotubes surface area is directly proportional to the tensile reinforcement. They concluded that reinforcement is significantly dependent on the interfacial interac- tions between polymer–CNTs. Advanced atomic force microscopy (AFM) method was used to understand and improve interfacial bonding between nanotubes and polymer [9]. They attempted to directly measure the interfacial energy between nanotubes and matrix. These observations demonstrated that the reinforcement potential of CNTs in composites can be substantial. Coleman et al. [10] discussed mechanical properties of CNTs, production and processing of composites in order to obtain system require- ments for maximum mechanical performance. While experimental studies in this field needs costly and time consuming characteristic tools, numerical approaches have been introduced to handle these investigations. Recent literature has shown that molecular dynamics and continuum simulations can play important roles in characterization of CNTs and CNT enabled composites [11]. Frankland et al. [12] studied the effect of func- tionalization on the nanotube/polymer shear strength using molecular dynamics (MD). Simulation of single-walled carbon nanotube (SWCNT) embedded in polyethylene matrix showed that shear strength at interface can be increased by chemical cross-link- ing between nanotube and polymer. Zheng et al. [13] simulated pullout of SWCNT from polymer matrix using molecular dynamics. They found out certain degree of functionalization may signifi- cantly increase the interfacial bonding between CNT and polymer. http://dx.doi.org/10.1016/j.matdes.2014.01.007 0261-3069/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: School of Materials and Mineral Resources Engineer- ing, Universiti Sains Malaysia, Malaysia. Tel.: +60 45996161; fax: +60 45941011. E-mail address: hazizan@eng.usm.my (H.M. Akil). Materials and Design 58 (2014) 36–42 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes