Topology Optimization Based on Micropolar Elasticity and Enhanced by Machine Learning: Structure Generation and Material Design

This work presents a novel topology optimization (TO) framework that integrates the micropolar elasticity theory with machine learning (ML) techniques to design high-performance structures and metamaterials. Traditional TO approaches rooted in classical elasticity neglect microstructural effects such as size-dependent behaviors and microrotations, which limits their accuracy for advanced materials (e.g., composites and metamaterials). To address this limitation, a new TO model based on micropolar (Cosserat) elasticity is developed, which introduces the rotational degrees of freedom and the associated couple stresses to more accurately capture microstructure-dependent mechanical responses. The framework is further enhanced with ML algorithms – including feedforward neural networks (FFNN), convolutional neural networks (CNN), and generative adversarial networks (GAN) – to accelerate the optimization process. By training these models on intermediate designs from iterative TO, the ML-assisted approach can predict near-optimal material layouts with greatly reduced computational effort. Compared to conventional methods, the integrated approach achieves an 80–85% reduction in iteration count, about 80% faster convergence, and approximately 70% lower computational energy consumption, while maintaining a high level of accuracy (with a root-mean-square error ≤ 0.007). The proposed methodology is validated through both 2D and 3D structural examples under diverse loading conditions. Results show that incorporating micropolar parameters (such as a coupling coefficient and a characteristic length) into the TO significantly enhances structural stiffness – improvements of up to 18.5% are observed – by enabling better load distribution and increased bending resistance. For mechanical metamaterials, the framework optimizes periodic structures for target properties (e.g., bulk or shear modulus and micropolar coupling effects), with the ML models effectively capturing design trends under periodic boundary conditions. In case studies, the deep learning-based predictors (CNN and GAN) outperformed the FFNN in accurately generating spatially complex optimal topologies. Overall, this work bridges advanced continuum mechanics with data-driven optimization techniques, offering a robust tool for designing next-generation materials and lightweight structures in fields such as aerospace, automotive, and biomedical engineering. The findings demonstrate the potential of combining physics-based modeling with machine learning to efficiently solve high-resolution topology optimization problems that were previously computationally prohibitive.