On the strange behaviour of Young’s Modulus for tensile analysis of a nanorod/nanotube based on nonlocal elasticity theory

It has been a known fact in classical mechanics of materials that Young’s modulus is an indicator of material stiffness and materials with higher Young’s modulus are more stiff. At the nanoscale, within the scope and under specific circumstances described here, however, a nanorod (or a nanotube) with a smaller Young’s modulus (smaller stress-strain rate) is more stiff. In such a scenario, Young’s modulus is not a stiffness indicator for nanostructures. Furthermore, the nonlocal stress-strain rate is dependent on types of load, boundary conditions and location. This is likely to be one of the many possible reasons why numerous experiments in the past obtained significantly varying values of Young’s modulus for a seemingly identical nanotube, i.e. because the types of loading and/or boundary conditions in the experiments were different, as well as at which point the property was measured. Based on the nonlocal elasticity theory and within the scope of material and geometric linearity, it is reported here for the first time the strange and hitherto unrealized effect that a nanorod (or a nanotube) with lower Young’s modulus (smaller stress-strain rate) indicates smaller extension in tensile analysis. Similarly, it is also predicted that a nanorod (or a nanotube) with lower Young’s modulus results in smaller bending deflection, higher critical buckling load, higher free vibration frequency and higher wave propagation velocity, which are at all consequences of a stiffer nanostructure.