Infinitesimal Periodic Deformations and Quadrics

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

Archived as published.

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.