A systematic molecular dynamics simulation study is performed to assess the effects of temperature and free edges on the ultimate tensile strength and Young's modulus of a single-layer graphene sheet. It is observed that graphene sheets at higher temperatures fail at lower strains, due to the high kinetic energy of atoms. A numerical model, based on kinetic analysis, is used to predict the ultimate strength of the graphene under various temperatures and strain rates. As the width of a graphene reduces, the excess edge energy associated with free edge atoms induces an initial strain on the relaxed configuration of the sheets. This initial strain has a greater influence on the Young's modulus of the zigzag sheet compared with that of the armchair sheets. The simulations reveal that the carbon–carbon bond length and amplitude of intrinsic ripples of the graphene increases with temperature. The initial out-of-plane displacement of carbon atoms is necessary to simulate the physical behaviour of a graphene when the Nosé–Hoover or Berendsen thermostat is used.

A thorough understanding on the mechanical properties of carbon nanotube (CNT) is essential in extending the advanced applications of CNT based systems. However, conducting experiments to estimate mechanical properties at this scale is extremely challenging. Therefore, development of mechanistic models to estimate the mechanical properties of CNTs along with the integration of existing continuum mechanics concepts is critically important. This paper presents a comprehensive molecular dynamics simulation study on the size dependency and potential function influence of mechanical properties of CNT. Commonly used reactive bond order (REBO) and adaptive intermolecular reactive bond order (AIREBO) potential functions were considered in this regard. Young’s modulus and shear modulus of CNTs are derived by integrating classical continuum mechanics concepts with molecular dynamics simulations. The results indicate that the potential function has a significant influence on the estimated mechanical properties of CNTs, and the influence of potential field is much higher when studying the torsional behaviour of CNTs than the tensile behaviour