Parametric optimization of selected auxetic structures

Abstract Auxetic materials exhibit an interesting, counterintuitive behavior—when subjected to uniaxial tension, they stretch laterally, and when uniaxially compressed, they shrink laterally. In contrast to conventional materials, in auxetics, the value of Poisson’s ratio is negative. Behavior of auxetic materials is an effect of their internal structures. The auxetic effect depends mostly on the geometry of their internal unit cells and not on the properties of the bulk material. This paper presents the results of parametric optimization of selected two-dimensional auxetic unit cells with the aim to identify the geometrical parameters which exhibit the strongest influence on the value of Poisson’s ratio in each unit cell, and to identify geometries which exhibit the strongest auxetic effect. The optimization was conducted through numerical simulation with the use of the finite element method in commercial software. Response surface optimization and multi-objective genetic algorithm (MOGA) were applied. Obtained candidate geometries were verified via additional FEM analyses and confirmed to have improved auxetic effect and reduced equivalent stress. 5 × 5 structures composed of reference and optimized geometries of analyzed unit cells were subjected to similar analyses and it was confirmed that the optimization of singular unit cells caused an improvement of auxetic effect and reduction in equivalent stress in regular structures composed of multiple unit cells.