Isogeometric shape optimization of missing rib auxetics with prescribed negative Poisson’s ratio over large strains using genetic algorithm

Abstract

This paper presents an isogeometric shape optimization framework using genetic algorithm to design 2D auxetic structures with prescribed Poisson’s ratio over large tensile or compressive strains in the nonlinear deformation regime. The design domain is parametrized using NURBS to allow smoother shape variation of the structure and enable accurate fabrication of the optimized structures. The versatility of the framework is illustrated through the optimization of a missing rib structure with four ligaments under different loading conditions. The manufacturability of specimens using the NURBS and PolyJet 3D printing technology is also shown. The first example focuses on achieving constant negative Poisson’s ratio up to -0.7 within the applied tensile strain of 50% under plane stress condition. As auxetics experiments under large compressive strain are rarely performed and published, the second example demonstrates the optimization for compressive loading. The Poisson’s ratio determined from experiments matches well with the numerical results. The experiments highlight that for very flexible materials, deformation under self-weight and contacts between adjacent unit cells are significant factors in compression, and further investigations are needed.