Design and optimization of microstructure of auxetic materials Akbar A. Javadi, Asaad Faramarzi and Raziyeh Farmani College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK Abstract Purpose – Auxetic materials differ from conventional materials by the manner in which they respond to stretching; they tend to get fatter when stretched, resulting in a negative Poisson’s ratio. The purpose of this paper is to present a numerical methodology for design of microstructure of 2D and 3D auxetic materials with a wide range of different negative Poisson’s ratios. Design/methodology/approach – The proposed methodology is based on a combination of finite element method and a genetic algorithm. The problem is formulated as an optimization problem of finding microstructures with prescribed behavioral requirements. Different microstructures are generated and evolved using the genetic algorithm and the behavior of each microstructure is analyzed using the finite element method to evaluate its fitness in competition with other generated structures. Findings – Numerical examples show that it is possible to design a large number of new auxetic materials, each with a different value of negative Poisson’s ratio. Originality/value – The proposed methodology can be used as an effective method to tailor new materials with prescribed values of negative (or positive) Poisson’s ratio. The methodology can also be used to optimize other material properties. Keywords Mechanical properties of materials, Elasticity, Deformation, Poisson ratio, Auxetic materials, Negative Poisson’s ratio, Evolutionary optimization, Finite element method Paper type Research paper 1. Introduction Poisson’s ratio is defined as the ratio of lateral contractual strain to longitudinal tensile strain in a stretched material, i.e. how much a material thins when it is stretched. Majority of engineering materials have positive Poisson’s ratios, i.e. they tend to get thinner when they are stretched. Some materials, on the other hand, are known to possess negative Poisson’s ratio. These are a class of auxetic materials. Auxetic materials differ from conventional materials by the manner in which they respond to stretching; they tend to get fatter when stretched, resulting in a negative Poisson’s ratio. Auxetic behaviour has been proven to add significant improvement to some materials, especially to their mechanical properties related to Poisson’s ratio such as indentation resistance, shear modulus, impact absorption and damage tolerance (Yang et al., 2004). These materials with their improved properties have proved their efficiency in several practical fields such as automotive and aerospace industries, smart mattresses and in manufacturing smart filters. They have also shown great potential to be used in sensors, molecular sieves and as structural materials. Since the discovery of auxetic materials, investigations have been focused on examining their properties and applications, finding new materials with negative Poisson’s ratio and developing new procedures to produce such materials. The current issue and full text archive of this journal is available at www.emeraldinsight.com/0264-4401.htm EC 29,3 260 Received 3 February 2011 Revised 8 June 2011 Accepted 23 June 2011 Engineering Computations: International Journal for Computer-Aided Engineering and Software Vol. 29 No. 3, 2012 pp. 260-276 q Emerald Group Publishing Limited 0264-4401 DOI 10.1108/02644401211212398