A Theory of Chiral Cosserat Elastic Plates

Abstract

The mechanical behaviour of chiral materials is of interest for the investigation of carbon nanotubes, honeycomb structures, auxetic materials and bones. This paper is concerned with a theory of chiral Cosserat elastic plates. In this theory, in contrast with the case of achiral plates, the stretching and flexure cannot be treated independently of each other. First, we derive the basic equations which characterize the deformation of chiral plates. Then we establish a uniqueness result in the dynamical theory. In the equilibrium theory we establish conditions under which the Neumann problem admits solutions. Finally, the deformation of an infinite plate with a circular hole is studied. It is shown that, in contrast with the theory of Cosserat achiral plates a uniform pressure acting on the boundary of the hole produces a microrotation of the material particles.