Quarterly Journal of Mechanics and Applied Mathematics
Materials science has adopted the term of auxetic behavior for structural deformations where stretching in some direction entails lateral widening, rather than lateral shrinking. Most studies, in the last three decades, have explored repetitive or cellular structures and used the notion of negative Poisson's ratio as the hallmark of auxetic behavior. However, no general auxetic principle has been established from this perspective. In the present article, we show that a purely geometric approach to periodic auxetics is apt to identify essential characteristics of frameworks with auxetic deformations and can generate a systematic and endless series of periodic auxetic designs. The critical features refer to convexity properties expressed through families of homothetic ellipsoids.
© The Author(s) 2017
Borcea, Ciprian S. and Streinu, Ileana, "Periodic Auxetics: Structure and Design" (2018). Computer Science: Faculty Publications, Smith College, Northampton, MA.