Geometric auxetics

Abstract

We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We demonstrate its usefulness by predicting or recognizing, without experiment, computer simulations or numerical approximations, the auxetic capabilities of several well-known structures available in the literature. We propose new principles of auxetic design and rely on the stronger notion of expansive behavior to provide an infinite supply of planar auxetic mechanisms and several new three-dimensional structures.

References in corpus (4)

• Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
• Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots
• Poisson's ratio in cubic materials
• Symmetry detection of auxetic behaviour in 2D frameworks

Cited by in corpus (5)

• An additive framework for kirigami design
• Analytic analysis of auxetic metamaterials through analogy with rigid link systems
• Disordered auxetic networks with no re-entrant polygons
• Corner-Sharing Tetrahedra for Modeling Micro-Structure
• Flexible placements of periodic graphs in the plane