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

Abstract

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. © 2014 Science Publication.