Design and optimization of microstructure 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. 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.

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.

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.

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.