Deformation of chiral cylinders in the gradient theory of porous elastic solids

Abstract

Chiral effects cannot be described by means of the classical theories of continua. In the context of the strain gradient theory of porous elastic solids we study the deformation of a chiral cylinder subjected to torsion, extension and bending by terminal couples. This work is motivated by recent interest in using the chiral continuum as a model for some auxetic materials, bones and carbon nanotubes. The problem is reduced to the study of some two-dimensional problems. We show that the torsion of a chiral cylinder is accompanied by extension, bending, and a variation of the volume fraction field. The solution is used to investigate the deformation of a circular cylinder.

A finite element implementation of the stress gradient theory

“…This is in contrast to the stress gradient solution worked out in the previous section. However, the torsion stiffness is increased by a contribution of the higher order elasticity moduli [19,20], at least if the bar is long enough to fulfil the Saint-Venant conditions, see [23] which focuses on special boundary conditions at the bar's ends. This relative stiffness enhancement is proportional to 1 þ a x À2 m  à , where x m is the ratio of the bar radius divided by one strain gradient elastic length scale, and where a is a factor depending on the specific strain gradient model considered.…”