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.

中文翻译：

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使用遗传算法在大应变上用规定的负泊松比对缺失的肋骨拉胀进行等几何形状优化

摘要 本文提出了一个等几何形状优化框架，使用遗传算法来设计具有规定泊松比的二维拉胀结构，该结构在非线性变形状态下具有大的拉伸或压缩应变。使用 NURBS 对设计域进行参数化，以实现更平滑的结构形状变化，并实现优化结构的精确制造。通过在不同负载条件下优化具有四根韧带的缺失肋骨结构来说明该框架的多功能性。还展示了使用 NURBS 和 PolyJet 3D 打印技术的样品的可制造性。第一个示例侧重于在平面应力条件下在 50% 的外加拉伸应变内实现高达 -0.7 的恒定负泊松比。由于在大压缩应变下的拉胀实验很少进行和发表，第二个例子展示了压缩载荷的优化。由实验确定的泊松比与数值结果非常吻合。实验强调，对于非常灵活的材料，自重下的变形和相邻单元电池之间的接触是压缩的重要因素，需要进一步研究。