Geometric Underpinnings of Auxetic Behavior
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In materials science, auxetic behavior is characterized by negative Poisson's ratios. We have recently developed a purely geometric theory of auxetic behavior for periodic framework materials. In this talk I will present the main ideas (rooted in rigidity theory) as well as the algorithmic consequences, which lead to efficient methods for detecting the local (infinitesimal) behavior. The design of novel two dimensional auxetic structures is facilitated by our theory of expansive mechanisms, fully characterized as periodic pseudo-triangulations. I will conclude with some recent results for designing three dimensional auxetic structures. Joint work with Ciprian Borcea, Rider University.
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