Abstract
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.
Highlights
When elastic material is stretched, it becomes longer in the direction of stretching and is typically thinner in the orthogonal direction
Since our approach to the matter is a geometric one we have explained the structure of such materials in a precise way, without computer simulation or approximation
The examples shown in this paper, which can be described precisely in a geometric way, can be scaled to any size
Summary
When elastic material is stretched, it becomes longer in the direction of stretching and is typically thinner in the orthogonal direction. Auxetic materials show a completely opposite behavior compared to general elastic material, since it is stretched in the transverse direction of the applied forces and so the volume increases and Poisson’s ratio becomes negative, due to its definition. In this case we use a parallel four-bar linkage instead of a diamond-shaped one This allows us to construct a system where we start from a closed version of the pattern and end in a closed one and the hinges do not collide. A much bigger variety for design purposes are given using the whole wallpaper group It is still an open question, which of the patterns allow a precise planar geometric motion and represent monostable auxetics. The way out for this situation is use flexible materials and to bend the individual parts
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