A Cosserat-type plate theory and its application to carbon nanotube microstructure

The predictive capabilities of plate and shell theories greatly depend on their underlying kinematic assumptions. In this study, we develop a Cosserat-type elastic plate theory which accounts for rotations around the normal to the mid-surface plane (so-called drilling rotations). Internal loads, equilibrium equations, boundary conditions and constitutive equations are derived. The case of a Single Walled carbon Nanotube (SWNT) modelled as a Cosserat medium is taken here as a reference example. Material parameters are identified and the proposed theory is used to solve analytically the problem of a polymer- SWNT composite tube under torsion. Predictions such as an absolute size effect are compared to those of the classical Cauchy-de Saint-Venant results.