Data-driven design of topologically optimized auxetic metamaterials for tailored stress–strain and Poisson’s ratio-strain behaviors

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%.