Eur. Phys. J. B (2018) 91: 271
https://doi.org/10.1140/epjb/e2018-90073-1

Regular Article

Mechanics of disordered auxetic metamaterials^★

¹ COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076 Aalto, Espoo, Finland
² Center for Complexity and Biosystems, Department of Physics, University of Milano, Via Celoria 16, 20133 Milano, Italy
³ CNR – Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l’Energia, Via R. Cozzi 53, 20125 Milano, Italy

^a e-mail: stefano.zapperi@unimi.it

Received: 15 February 2018
Received in final form: 7 June 2018
Published online: 5 November 2018

Abstract

Auxetic materials are of great engineering interest not only because of their fascinating negative Poisson’s ratio, but also due to the possibility to increase by design the toughness and indentation resistance. The general understanding of auxetic materials comes often from ordered or periodic structures, while auxetic materials used in applications are typically strongly disordered. Yet, the effect of disorder in auxetics has rarely been investigated. Here, we provide a systematic theoretical and experimental study of the effect of disorder on the mechanical properties of a paradigmatic two-dimensional auxetic lattice with a re-entrant hexagonal geometry. We show that disorder has a marginal effect on the Poisson’s ratio until the point when the lattice topology becomes altered, and in all cases examined disorder preserves the auxetic characteristics. Depending on the direction of loading applied to these disordered auxetic lattices, either brittle or ductile failure is observed. It is found that brittle failure is associated with a disorder-dependent tensile strength, whereas in ductile failure disorder does not affect strength. Our work thus provides general guidelines to design and optimize elasticity and strength of disordered auxetic metamaterials.