Periodic auxetics: a geometric approach
Seminar Room 1, Newton Institute
AbstractCo-author: Ciprian S. Borcea (Rider University, USA)
We propose a purely geometric criterion for characterizing auxetic one-parameter deformations of periodic bar-and-joint frameworks. This concept is valid in arbitrary dimension. Auxetic mechanisms are then compared with expansive mechanisms defined by the stronger property that the distance between any pair of vertices increases or stays the same. For two-dimensional periodic frameworks, expansive behaviour can be explained and explored in terms of a remarkable new class of structures. We show how to generate this type of planar periodic frameworks and discuss their geometry. Since expansive implies auxetic, we obtain an endless resource for auxetic designs.
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