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The purpose of this paper is to deal with fracture behavior of carbon nanotubes with presenting a revised structural molecular mechanics model in the finite element method. Structural molecular mechanics modified model, uses a three-dimensional beam element with general section to make nanotube structural model in which bending stiffness and inversion are defined independently. In analysis which are done, a bridged carbon nanotube with constant strain rate is examined under tensile stress until the failure of nanotube. Carbon-carbon bonds behavior has been assumed nonlinearly and will be ruptured when the strain reaches 19%. It is predicted that fracture behavior in carbon nanotubes depends on the environment temperature due to mechanical behavior of carbon nanotube's bonds. Based on the present research, we found that by increasing the temperature, Poisson's ratio increases and Young's modulus decreases. Further, it can be said while the temperature increases, both the fracture ultimate strain and stress decrease. Finally, a nonlinear relationship is presented in which the constants depend on chirality of the carbon nanotubes.

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In structural engineering, concrete is known as a material with brittle behavior that the tensile strength of which is negligible compared to its compressive strength and show low resistance to crack propagation. Moreover, the concrete can be considered as a quasi-brittle material, which is due to the type of behavior related to the crack propagation and is also existed around the crack tip of fracture process zone (FPZ) that involves a set of microcracks. From the perspective of structural behavior, the size effect of the structure is one of the most important concepts provided by the fracture mechanics; therefore, it is important to provide an equation between concrete fracture properties such as fracture toughness (K_IC) and fracture energy (G_f) and its correlation with the size effect mechanism. The fracture energy is one of the most important characteristics for analysis of fracture behavior in concrete, evidenced to be a concrete property, showing its strength to cracking and fracture toughness. Given that the fracture energy (G_f) is sufficient to calculate the fracture behavior evaluation for the brittle materials in range of linear fracture mechanics, for the quasi-brittle materials such as concrete, this is not a sufficient parameter due to the presence of microcracks in the fracture process zone, and the length of fracture process zone (C_f) is one of the important properties of fracture in the unlimited-size structures. For determining the fracture parameters of concrete, various methods have been proposed. One of the most important methods that is presented by Bazant is the size effect method (SEM). The use of high strength concretes is increasing due to the expansion of the construction technology of these concretes. This research studies and analyzes the fracture behavior of high strength concrete (HSC) with various amounts of silica fume, along with a change in water to cement (w/c) ratio with SEM. In this experimental study, a total of 10 mixing designs have been tested. To investigate the effects of different w/c ratios in the range of HSC and the effect of silica fume, four w/c ratios of 0.24, 0.3, 0.35 and 0.4 Examined and in two w/c ratios of 0.24 and 0.35 a mix design for plain concrete without silica fume and three mix designs prepare with silica fume content of 5%, 10% and 15% by weight of cement. To determine the fracture characteristics of concrete, a total of 120 beams were tested. The results show that by decreasing the w/c ratio from 0.35 in the range of HSC, the value of initial fracture energy (G_f), the effective length of fracture processing zone (C_f) and the critical crack tip opening displacement (CTOD_c) has decreased and on the other hand the brittleness number (β) has increased. Also, by increasing the amount of silica fume in the w/c ratios of 0.35 and 0.24, the fracture energy, the length of the fracture processing zone, the fracture toughness (K_IC), the critical crack tip opening displacement has reduced, and the brittleness number has increased. The results show that by using the fracture parameters obtained from the SEM, the maximum load on the high strength concrete specimen can be predicted correctly.