Data-driven design of topologically optimized auxetic metamaterials for tailored stress–strain and Poisson’s ratio-strain behaviors
Yueyou Tang, Anfu Zhang, Qi Zhou, Mu He, Liang Xia
Abstract
Conventional topology optimization methods often struggle to achieve simultaneous customization of stress–strain and Poisson’s ratio–strain curves in auxetic metamaterials, due to the complexity of nonlinear analysis, multi-objective coupling, and high computational costs. To overcome these limitations, present work proposes a physics–data collaborative design framework that integrates nonlinear topology optimization with neural networks. This framework first generates baseline configuration approximating the target mechanical behavior via nonlinear topology optimization, thereby establishing a physically reliable initial design space. High-precision neural networks are then trained using geometric features extracted through PCA (principal component analysis), enabling real-time, simultaneous prediction of stress–strain and Poisson’s ratio–strain responses. By combining evolutionary strategies with an adaptive learning factor, we construct an efficient global optimization model that enables high-accuracy coupled customization of both curves under finite deformation. Compression experiments on polyurethane specimens fabricated via precision milling validate the feasibility of the proposed method, showing an average curve-matching accuracy of 98.2% between the experimental and target curves. Compared to traditional topology optimization, our approach improves customization accuracy by 71.51% to 93.24%, achieves simultaneous coupling of both mechanical responses, and delivers an overall design accuracy exceeding 99%.