Machine learning-driven inverse design of functionally graded auxetic metamaterials including non-linear regimes

Auxetic metamaterials, characterized by their negative Poisson’s ratio and unique deformation behavior, offer remarkable potential for developing tunable and energy-absorbing structures. However, the vast geometric design space of auxetic unit cells and nonlinear deformation mechanisms that extend well beyond the linear elastic regime, present a major challenge for inverse design and optimization. This study addresses the inverse design of auxetic metamaterials by integrating efficient forward prediction with machine learning-driven inverse optimization. A deep neural network model is developed and trained on a comprehensive labeled dataset of numerically simulated auxetic unit cells within a printable design space across all deformation stages, with finite element analysis results validated through compression testing. The forward prediction model accurately estimates mechanical responses based on geometric parameters, while the inverse design framework determines optimal configurations to achieve target energy absorption levels. A detailed parametric study is conducted to explore the influence of geometric variations on mechanical behavior and identify optimized unit cell designs. These optimized cells are assembled into 3x3 metamaterial structures to ensure stable mechanical performance. Furthermore, functionally graded configurations are proposed to enhance tunability and energy absorption capacity. Among various graded designs, structures graded in thickness along the Y-direction exhibit superior stress distribution and performance. Numerical and experimental analyses of stress–strain behavior and Poisson’s ratio confirm the tunable mechanical response of the proposed graded structures. The findings demonstrate that the developed deep learning-based framework enables accurate inverse design of auxetic metamaterials and provides an effective pathway for engineering tunable, high-performance graded structures suitable for applications in impact mitigation, biomedical devices, and adaptive engineering systems.