3. Analogies Across Auxetic Models

This chapter views 2D auxetic models, including 3D deformation models with 2D auxetic behavior, from mechanism perspective instead of geometrical perspective. On this basis, auxetic models across different geometrical groups can be regrouped into clusters that exhibit analogy in deformation mechanism. Factors that are taken into consideration include the identification of corresponding rotation and non-rotation units, as well as linkages/joints between rotation and non-rotation units and non-linkages/non-joints across various auxetic models. As a result, five clusters of auxetic models have been identified, in which auxetic models within each cluster are analogous to each other. The identified clusters are those that exhibit: (1) double periodicity in the rotation direction of their rotating units, (2) synchronized rotation direction of their rotation units, (3) single periodicity in the rotation direction of their rotating units, (4) random rotation of their rotation units, and (5) non-rotation of units. Results from this analogy identification place auxetic models in a systematic representation and will enrich the future development of auxetic models, particularly, those that do not fall within these five clusters.