Auxetics Abounding

Ciprian S. Borcea, Rider University
Ileana Streinu, Smith College

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Auxetic behavior refers to lateral widening upon stretching. Although a structural origin for this rather counterintuitive type of deformation was often suggested, a theoretical understanding of the role of geometry in auxetic behavior has been a challenge for a long time. However, for structures modeled as periodic bar-and-joint frameworks, including atom-and-bond frameworks in crystalline materials, there is a complete geometric solution which opens endless possibilities for new auxetic designs. We construct a large family of three-dimensional auxetic periodic mechanisms and discuss the ideas involved in their design.