Auxetic regions in large deformations of periodic frameworks

TL;DR

This paper explores the conditions under which periodic frameworks exhibit auxetic behavior during large deformations, using geometric and kinematic analysis of specific mechanisms.

Contribution

It introduces a method to identify auxetic regions in the deformation space of periodic frameworks, including novel case studies and geometric characterizations.

Findings

Identification of auxetic domains in specific frameworks

Relationship between geometric and kinematic descriptions of auxeticity

Analysis of large deformation behaviors in periodic mechanisms

Abstract

In materials science, auxetic behavior refers to lateral widening upon stretching. We investigate the problem of finding domains of auxeticity in global deformation spaces of periodic frameworks. Case studies include planar periodic mechanisms constructed from quadrilaterals with diagonals as periods and other frameworks with two vertex orbits. We relate several geometric and kinematic descriptions.