16. Simple Semi-auxetic Solids

Upon defining two types of semi-auxetic solids—directional and positional semi-auxetic solids—this chapter develops the elastic properties of a directional semi-auxetic solid based on a combined hexagonal and re-entrant honeycomb structure and the 3D kinematic characteristics of another directional semi-auxetic solid based on rotating units. This is followed by an analysis and proposed fabrication methods of directional semi-auxetic yarns. An analysis is then given for a functionally-graded beam from positive Poisson’s ratio on one surface to a negative Poisson’s ratio on the opposite surface. Finally analyses are given for the mechanical properties of positional semi-auxetic structures in the form of compound rods and sandwich structures. Results for positional semi-auxetic structures show that the extent of auxeticity depends not only on the auxeticity of the constituent structures and the relative volume fractions, but also on the modes of deformation, i.e. these structures exhibit overall conventional properties under one type of loading mode, but overall auxetic properties under a different type of loading mode.