Auxetic deformations and elliptic curves

Infinitesimal Periodic Deformations and Quadrics

We describe a correspondence between the infinitesimal deformations of a periodic bar-and-joint framework and periodic arrangements of quadrics. This intrinsic correlation provides useful geometric characteristics. A direct consequence is a method for detecting auxetic deformations, identified by a pattern consisting of homothetic ellipsoids. Examples include frameworks with higher crystallographic symmetry.

Novel Design and Comparison of Structural and Modal Analyses of Auxetic Geometry versus Honeycomb Geometry

Auxetic structures are popular, since they have many applications in defense, textile and sport industries. The advantages of providing comfort and protection to people for the impact energy increase the usability of auxetic structures in these areas. Within the scope of this study, two structures were designed as honeycomb and auxtetic structures with lateral displacements in opposite directions. The auxetic and honeycomb structures were modeled in Ansys software by keeping the boundaries of these two structures close to each other. Structural and modal analysis were applied to these structures and the auxetic structure gave better results in terms of the tensile strength.

Periodic Auxetics: Structure and Design

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.