Issue 29

L. Cabras et alii, Frattura ed Integrità Strutturale, 29 (2014) 9-18; DOI: 10.3221/IGF-ESIS.29.02 9 Focussed on: Computational Mechanics and Mechanics of Materials in Italy Effective properties of a new auxetic triangular lattice: an analytical approach L. Cabras Università degli Studi di Cagliari, Dipartimento di Ingegneria Civile, Ambientale e Architettura luigi.cabras@unica.it M. Brun Università degli Studi di Cagliari, Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali; University of Liverpool, Department of Mathematical Sciences mbrun @unica.it A BSTRACT . In this article we propose a new auxetic periodic lattice with negative Poisson's ratio which tends to the limit ν=-1 under particular conditions. We have studied its generation and kinematic, and we give a full description of the mechanical properties of this innovative model. Calibrating the geometrical configuration of the lattice and the mechanical properties of the constituent material we are able to have a Poisson's ratio which is arbitrarily close to -1. K EYWORDS . Auxetic lattice; Negative Poisson’s ratio; Mechanical properties. I NTRODUCTION oisson's Ratio, usually represented by ν, is defined as the ratio of transverse contraction strain to longitudinal extension strain with respect to the direction of stretching force applied. Since tensile deformation is considered positive and compressive deformation is considered negative in the definition of Poisson's ratio is introduced a minus sign, so that common materials have a positive ratio. However, there are particular materials that expand laterally when stretched longitudinally with a negative Poisson's ratio, they were named for the first time auxetic materials by Ken Evans in an article in Nature (1991). For isotropic materials it may be shown that Poisson's ratio is between -1≤ν≤ ½ in 3D and -1≤ν≤1 in 2D, for anisotropic materials ν is not restricted by the above limits. The value of the Poisson's ratio has also important consequences for other aspects of the behavior of materials, in fact the most materials resist a change in volume as determined by the bulk modulus K more than they resist a change in shape, as determined by the shear modulus μ, the values of K are typically larger than the values of μ. By changing the microstructure of a material in such a way that the Poisson's ratio ν is lower, the values of K and μ can be altered. Decreasing the value of ν to negative value, it would result into a material with a higher shear modulus μ than the bulk modulus K. Different geometrical structures and models are created trying to reproduce some observed feature in auxetic materials, ranging from the macroscopic to microscopic and to the molecular levels. A simple classification can be based on mechanical considerations. Almost all of these models are based on a simple mechanism that is treated as a unit cell leading to a global stiffening effect. One of the earliest models used to describe these special materials was that with re-entrant structure, firstly suggested in [1]. Over the years, many more sophisticated models have been proposed. Another model is based on chiral structure, the researchers in this area use the adjective "chiral" to mean a physical property of spinning. In this type of structures, basic chiral units P