A shape design of discrete cylindrical structures tiled with auxetic hexagonal units

Author

Sakai, Yusuke and Ohsaki, Makoto

Abstract

We propose a method for shape design of a cylindrical structure tiled with hexagonal units. Auxetic structures, which have a negative Poissons ratio, compressed in a uniaxial direction shrink in the transverse direction. Their specific mechanical property is caused by the geometrical configuration. A cylindrical structure consisting of auxetic units designed by discrete members is used as a flexible actuator, energy absorber, and so on. However, there have been still few shape design methods for discrete cylindrical structures. To develop a variety of discrete cylindrical structures, it is crucial to propose a shape design method easy to use by general designers. We utilize the existing formulation representing a geometrical configuration of carbon nanotube, and extended it to obtain a surface of a discrete cylinder by rolling up a parallelogram filled with uniform hexagonal units with 2-rotational symmetry. This extended method enables us to generate a variety of geometrical configurations of discrete cylindrical structures from those close to a carbon nanotube to those composed of units with negative Poissons ratio arranged in spiral. In the numerical examples, various shapes of discrete cylindrical structures are parametrically generated, and we investigate the mechanical properties of several models by carrying out large-deformation analysis. Note that the models exhibit a remarkable specific deformation behavior, namely a torsioncompression coupling.