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For extraordinary properties of carbon nanotube (CNT), a lot of research has been done about its application to reinforce different materials such as electronic and building materials, and good effects of CNT have been observed. Experimental approach for determining the properties of composites containing fibers, especially carbon nanotubes, needs using of complex experimental methods and expensive laboratorial equipments. Theoretical approach can lower the cost of predicting properties of these composites. So, in this paper, an analytical relation is presented by continuum mechanics method to predict the compressive strength of cement composite reinforced with carbon nanotube. For simplicity of computations, carbon nanotubes were assumed to be isotropicand firstly oriented unidirectionally and uniformly in the cement composite. Representative Elementary Volume(REV), as anindicatorelement of this nanocompositeis, was chosen and analyzed by continuum mechanics method. A fiber embedded in a cylinder of cement with certain radius is named REV. The strains under loads were calculated and the stresses were obtained by Hook’s law. Then, for prediction failure of composite, von Mises’ yield criterion was applied and by that, the compressive strength of cement composite reinforced with unidirectionally oriented carbon nanotubes was obtained. For real cases, the results of this analysis should be generalized to cement composites reinforced with random orientation of nanotubes, since there is no control on the distribution of fibers in the laboratory and they are oriented randomly in composites, although researchers are studying on production of CNT/cement composites with arbitrary orientation of fibers.To apply the random orientation effect, Cox’s method was used. For this purpose, the fibers' distribution function f ( ) was assumed and it was observed that the random orientation of fibers reduces the effect of fiber reinforcing with respect to unidirectional orientation. Therefore, an orientation factor  1 was used considering random orientation in comparison with unidirectional orientation. As a suggestion, this factor can be experimentally obtained too. Experimental method was used to determine the orientation factor of fibers incomposites and good results were obtained. Then the presented analytical relationship was compared with experimental data. Matches and differences between the analytical method and the experimental data were studied and the suggestions were presented to lower the differences between the analytical and experimental methods. The effect of some parameters such as compressive strength of cement and the amount of carbon nanotubes added on the compressive strength of CNT/cement composite were obtained too. Accordingly that an ideal nanocomposite with regard to economical considerations can be obtained.

Keywords: Cement nanocomposite, Carbon nanotube (CNT), compressive strength, Representative Elementary Volume (REV), Isotropic behavior

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