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In this article, nonlinear bending analysis of single-layered circular graphene sheet is studied. The equilibrium equations are derived based on the nonlocal continuum mechanics and principle of virtual work and first order shear deformation plate theory (FSDT). Differential quadrature method is used to discretize the equilibrium equations. In this method a non-uniform mesh point distribution (Chebyshev- Gauss- Lobatto) is used for provide accuracy of solutions and convergence rate. The effect of nonlocal parameter, thickness, number of grid points and lateral loading are investigated on deflection of graphene sheet. The results are compared with valid results reported in the literature.

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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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Biologic tissues modeling play an important role in understanding the tissue behavior and development of synthetic materials for medical applications. It is also a vital action to develop the predictive models for a wide range of uses including medical and tissue engineering. Various strain energy functions have been introduced to model arteries to date. The newest introduced strain energy function is the Nolan strain energy function. Two-layer arterial modeling using this strain energy function has not been performed so far. In this paper, modeling the arteries was carried out in the form of double layers including media and adventitia and hyperelastic material assumption. At first, governing equations were driven based on continuum mechanics. Boundary conditions including inner pressure of artery, axial load and torque as well as static equilibrium were applied. Moreover, Cauchy stress components were gotten by using the continuum mechanics relations. Then, the equilibrium equations in cylindrical coordinate were obtained by using the Cauchy stress. Stress distribution through the artery wall was specified by solving the resulting nonlinear partial differential equations based on generalized differential quadrature method. In the beginning, the artery modeling was conducted in the form of monolayer including the media layer and the results were compared with experimental ones, comparison between stresses in the artery wall and experimental data showed that the volcanic energy function of Nolan is suitable for modeling. After that, the stress distribution was obtained by artery modeling in the form of double layers including the media and adventitia layers.

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Persistent strength training can increase ventricular blood pressure and volume and the resultant loading in ventricles of the human heart. It is proved that pressure overload can increase ventricular thickness and volume. In this article, we modeled athlete’s heart syndrome macroscopically arising from pressure overload using continuum mechanics and finite elements methods. We tried to improve previous results by using a more precise geometry and loading and by modifying previous equations. Firstly, we saw that because the left ventricular pressure was more than the right ventricular pressure, increase in myocardium thickness started from the left ventricle and secondly, this increase in myocardium thickness started from lower regions that located far from the right ventricle. Then, it was shown that thicker regions with greater values of the growth multiplier had less stress than regions with less values of the growth multiplier. As time passed and more loading cycles were applied to the endocardium, myocardium thickness increased gradually until the growth multiplier reached its maximum threshold value. Finally, we demonstrated that when the ventricular pressure rises and hypertrophy occurs, residual stresses remain in the myocardium after unloading.