A deep learning based multi-objective optimization design of two-dimensional auxetic metamaterials

Metamaterials exhibit enhanced properties such as auxetic deformation and superior energy absorption, making them promising for applications in energy engineering, aerospace, and advanced manufacturing. Among the various types of metamaterials, two-dimensional (2D) auxetic metamaterials are composed of periodic arrays of negative Poisson’s ratio (NPR) cells, whose geometric structure and dimensions dictate their unique mechanical behaviors. However, quantifying the relationship between the geometric disorder (non-uniform dimensional distributions of cellular structures) and the macroscopic mechanical properties in 2D metamaterials remains a significant challenge. To address this, a machine learning (ML) model is developed based on the parameterized finite element method (PFEM) for multi-objective iterative optimization of 2D auxetic metamaterials. In this model we derive the optimal non-uniform dimensional distributions of cellular structures under specific design objectives. Firstly, a parameterized finite element model is established to comprehensively analyze the quantitative relationship between the non-uniform dimensional distributions of cellular structures and the macroscopic responses. Next, the deep neural network (DNN) prediction models are developed to forecast the macroscopic responses based on the non-uniform dimensional distributions of cellular structures. Additionally, an optimization model using the genetic algorithm (GA) is implemented to determine the optimal non-uniform dimensional distributions for given objectives. Finally, quasi-static uniaxial tensile tests on designed samples validate their macroscopic responses. This study provides a solid foundation for more complex designs of 2D auxetic metamaterials, enhancing their NPR characteristic and energy absorption capability.