Applicability of Micropolar Theory to Describe the Size Dependency in Torsional and Bending Deformations of Carbon Nanotubes

The efficient application of carbon nanotubes in nanodevices and nanomaterials requires a comprehensive understanding of their mechanical properties [1]. As observations suggest size-dependent behaviour, non-classical theories preserving the memory of internal structure via additional material parameters offer great potential for continuum modelling [2]. The work aims at evaluating non-classical continuum parameters for single-walled armchair and zigzag CNTs focusing on size-dependent behaviour in both torsional [3] and flexural [4] deformations observed in molecular dynamics simulations. A non-linear optimisation approach is adopted to find unified material parameters minimising the difference between shear/ bending modulus from atomistic simulation and continuum description. Acknowledging that in the current problem, internal length is comparable to the macroscopic length, the results suggest the adopted non-classical theories, notably micropolar theory, provide reasonable predictions with an evident deficiency of classical Cauchy theory. The micropolar parameters are then used to obtain mechanical properties of a randomly oriented CNT reinforced nanocomposite to demonstrate the practicality of employing micropolar theory in the description of carbon nanotubes.