M. M. Shokrieh*, M. Salamat-talab Development of a Full Range Multi-scale Modeling to Obtain Elastic Properties of CNT/Polymer M. M. Shokrieh*, M. Salamat-talab Composites Research Laboratory, Center of Excellence in Solid Mechanics and Dynamics, Department of Mechanical Engineering, Iran University of Science & Technology, Narmak, 1684613114, Tehran, Iran shokrieh@iust.ac.ir Abstract The main goal of this research is to develop a full range multi-scale modeling approach to extract Young’s modulus and Poisson’s ratio of carbon nanotube reinforced polymer (CNTRP) covering all nano, micro, meso and macro scales. The developed model consists of two different phases as top-down scanning and bottom-up modeling. At the first stage, the material region will scanned from the macro level downward to the nano scale. Effective parameters associated with each and every scale will be identified through this scanning procedure. Introduction The supreme mechanical properties of carbon nanotubes (CNTs) are rendered them as a potential candidate of reinforcing agents for new generation of polymeric composites [1-4]. There are some evidences in literature [5-7] mentioning the significant enhancement in mechanical properties of polymeric resins by utilizing small portion of CNTs. Consequently, prediction of mechanical properties of carbon nanotube- based composites plays an important role in understanding their behavior and can pave the road toward their industrial application. Material and Method The modeling procedure constructed on the basis of bottom-up modeling starts from the nano-scale and lasting in macro-scale, passing the in- between scales as micro and meso. Since the developed multi-scale modeling is a full-range multi-scale modeling covering all scales of Nano, Micro, Meso and Macro, it will be called as N3M multi-scale modeling. The modeling technique required an accurate and careful definition of representative volume elements (RVE) at each level which are identified on the basis of top-down scanning method. Table 1: Longitudinal effective modulus of developed equivalent fiber for different lengths Results and Discussion The results of simulation procedure explained in previous section are presented in Fig. 5 for the case of Young’s modulus and Poisson’s ratio versus different pattern of volume fractions. Young’s modulus of simulated material region is varying from 15.21 GPa to 15.26 GPa representing 0.3% fluctuation in result. On the other hand, Poisson’ ratio can be considered 0.28 for all cases when the accuracy is considered as two order of magnitudes. So, it is inferred that one can simply replace the random volume fraction with the mean value of the volume fraction regardless of its deviations. Figure 1: Comparison between utilized random and mean length approaches Conclusion A stochastic multi-scale modeling is developed in this study to predict the mechanical properties of carbon nano-tube reinforced polymers. The developed modeling technique scans the whole scales starting from nano and lasting at macro-scale on the basis of bottom-up modeling. In each scale, effective parameters are identified and studied and the results are fed into the immediate upper level. Three main parameters as orientations, length and volume fraction of the CNTs accounts for random behavior of the material region. It was shown that volume fraction and length of CNTs can be simply replaced by their associated mean values with a very good approximation. References [1] Dai, H. (2002), Surface Science 500, 218–241. [2] Salvetat-Delmotte and J.P., Rubio, A. (2002), Carbon 40, 1729–1734. [3] Lau, K.T. et al. (2006), Composites: Part B 37, 425–436. [4] Shokrieh, M. M. and Rafiee, R. (2010), Journal of Mechanics of Composite Materials 37(2), 235-240. [5] Qian, D. et al. (2000), Applied Physics Letter 76(20), 2868-2870. [6] Schadler, L. (1998), Applied Physics Letter 73(26), 3842–3844.