Torsional characteristics of carbon nanotubes: Micropolar elasticity models and molecular dynamics simulation

Efficient application of carbon nanotubes (CNTs) in nano-devices and nano-materials requires comprehensive understanding of their mechanical properties. As observations suggest size dependent behaviour, non-classical theories preserving the memory of body’s internal structure via additional material parameters offer great potential when a continuum modelling is to be preferred. In the present study, micropolar theory of elasticity is adopted due to its peculiar character allowing for incorporation of scale effects through additional kinematic descriptors and work-conjugated stress measures. An optimisation approach is presented to provide unified material parameters for two specific class of single-walled carbon nanotubes (e.g., armchair and zigzag) by minimizing the difference between the apparent shear modulus obtained from molecular dynamics (MD) simulation and micropolar beam model considering both solid and tubular cross-sections. The results clearly reveal that micropolar theory is more suitable compared to internally constraint couple stress theory, due to the essentiality of having skew-symmetric stress and strain measures, as well as to the classical local theory (Cauchy of Grade 1), which cannot accounts for scale effects. To the best of authors’ knowledge, this is the first time that unified material parameters of CNTs are derived through a combined MD-micropolar continuum theory

Prediction of Breast Cancer Risk in Women over 35 Years Old Living in Villages of Zanjan: A Study Based on Gail Model

Background: Breast cancer is one of the most important malignancies in both developed and developing countries. Objectives: To reduce the burden of this disease, the prediction of individuals at risk and implementation of efficient preventive interventions can be effective. The present study was aimed at investigating five-year and lifetime risks of the breast cancer in a rural community in Zanjan province, Iran. Methods: A total of 435 subjects aged 35 years old were randomly selected using systematic randomization in a rural community in Zanjan. The participation rate was 92.4% (402 women). Data collection instrument was a questionnaire in which all associated variables of Gail model and demographic information were included. The data were analyzed using SPSS software version 18, and mean cancer risks were reported. Results: Family history of breast cancer and history of breast biopsy were found to be positive in 3.5% and 0.3% of participants, respectively. Out of all participants, 84.3% were under 60 years old and 13.2% were illiterate. Five-year and lifetime mean risks were fund to be 0.74% and 7.6%, respectively. About 2% of the participants had a higher cancer risk>1.66%. Conclusion: The findings demonstrated that based on the Gail model, the lifetime risk of the participants will be one out of 13 women. Given the lower estimations of Gail model in the prediction of breast cancer, we suggest general population interventions and high-risk strategies be implemented to decrease problems associated with the breast cancer in the future

Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation

Vibration responses were investigated for a viscoelastic Single-walled carbon nanotube (visco-SWCNT) resting on a viscoelastic foundation. Based on the nonlocal Euler-Bernoulli beam model, velocity-dependent external damping and Kelvin viscoelastic foundation model, the governing equations were derived. The Transfer function method (TFM) was then used to compute the natural frequencies for general boundary conditions and foundations. In particular, the exact analytical expressions of both complex natural frequencies and critical viscoelastic parameters were obtained for the Kelvin-Voigt visco-SWCNTs with full foundations and certain boundary conditions, and several physically intuitive special cases were discussed. Substantial nonlocal effects, the influence of geometric and physical parameters of the SWCNT and the viscoelastic foundation were observed for the natural frequencies of the supported SWCNTs. The study demonstrates the efficiency and robustness of the developed model for the vibration of the visco-SWCNT-viscoelastic foundation coupling system

Molecular dynamics simulations of structural instability of fullerene family under tension force

Fullerene molecules are cage-like nanoscopic structures with pentagonal and hexagonal faces. In practical applications such as fullerene-reinforced nanocomposites (FRNCs), these structures may be subjected to tension force. In this research, we employ molecular dynamics (MD) simulation to compute the behaviour and deformation of different fullerene molecules, ranging from C60 to C2000, under tension force. To model the interactions between carbon atoms in the MD simulations, the adaptive intermolecular reactive bond order (AIREBO) force field is used. The displacement–force and the displacement–strain energy curves are obtained. It is observed that a new type of structural instability occurs in the fullerene molecules when the applied tension force increases. This abnormal structural instability in the fullerenes is investigated for the first time in the literature. The critical tensile forces and the corresponding mode shapes are determined for different fullerenes. The results indicate that the critical forces and deformations strongly depend upon the number of carbon atoms

Elastic properties of polymer composites reinforced with C60 fullerene and carbon onion: Molecular dynamics simulation

In this paper, the elastic properties of polymer nanocomposites reinforced with C60 fullerene and C60@C240 carbon onion are estimated by using a molecular dynamic (MD) simulation. The nanocomposites are constructed by embedding the buckminsterfullerene and the carbon onion into an amorphous polymer matrix with different weight fractions. The poly methyl methacrylate (PMMA) is chosen as the polymer matrix. The results demonstrate that Young's modulus of the composite increases with increasing the weight fractions of the nanoscopic additives, which is consistent with experimental observations. The nanocomposite containing 4 wt% of C60 exhibits Young's modulus of 3.774 GPa that is 24% higher than pure PMMA. In addition, the validity of the present simulation is verified by the comparison with the experimental results

Combined molecular dynamics–micromechanics methods to predict Young's modulus of fullerene-reinforced polymer composites

In this paper, a multiscale method is developed to predict Young's modulus of fullerene-reinforced polymer nanocomposites (FRPNs). Polymethyl methacrylate is chosen as the polymer matrix, while C60 fullerene is considered as the reinforcement. First, molecular dynamics (MD) simulations are conducted to calculate the Young modulus of nanocomposite unit cell with different weight fractions of fullerene. Then, a micromechanics model for a composite with multi-inclusion reinforcements is developed based on the extension of the Mori–Tanaka model and generalized Eshelby's results. Numerical results obtained from the proposed micromechanics model are compared with those calculated from the MD simulations, and good agreement is achieved. In addition, we propose an extension for the Halpin–Tsai model to predict Young's modulus of the FRPNs