Geometrical Elaboration of Auxetic Structures

This paper analyzes the basic geometric and kinematic characteristics of auxetic structures. The geometric principles are then transferred to a family of new possible forms. We investigate and elaborate auxetic behavior in a purely geometric way which is based on the kinematic movement of different frameworks. We then demonstrate its usefulness by analyzing the involved geometry with computer software but without computer simulations or numerical approximations. Instead, using cut flat material and, depending on the cuts and the material used, we enable the kinematical movement of the structures. We also analyze monostable auxetic structures whose movements can be described as geometrically precise, as well as bistable ones. Based on geometric considerations, we combine rigid materials and composites and select appropriate joint connections to allow the application of this system in an architectural scale in, for example, facades, screens or shading systems.