Infinitesimal Periodic Deformations and Quadrics

Abstract

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.

Keywords

• kinematics
• periodic framework
• auxetics
• crystallographic symmetry
• quadrics