Inverse design and experimental verification of a lateral variable-stiffness metamaterial for multilevel bridge seismic fortification

Bridge bearings connect the superstructure and substructure, carrying vertical loads and mitigating seismic forces. However, conventional unbonded laminated rubber bearings (ULRBs) provide limited energy dissipation and may undergo excessive displacement under strong ground motions. Although controlled sliding can dissipate energy, unrestrained sliding may cause girder dislodgment or collapse. To address this issue, a machine learning enabled inverse design framework is proposed for mechanical metamaterial energy dissipation components. Unlike most data driven studies that focus on uniaxial vertical loading, the proposed method directly generates topologies from prescribed lateral shear force displacement curves. The framework integrates a Denoising Diffusion Probabilistic Model (DDPM) and a Residual Neural Network (ResNet) to generate and efficiently screen metamaterial unit cells with tailored lateral shear responses. The selected designs not only reproduce the target response but also establish rational load transfer paths during plastic dissipation, promoting more uniform plastic strain distribution and favorable fracture modes. Parametric numerical analyses show that the hardening factor depends on geometric dimensions and can reach 19.75. Based on the inversely designed metamaterial components, a lateral variable stiffness metamaterial energy dissipation device (MEDD) is further developed using a function separated concept, in which conventional rubber bearings carry vertical loads and metamaterial units provide tunable lateral resistance. Quasi-static cyclic tests were conducted on 12 specimens under two interface conditions, namely with and without washers. The results indicate that the washer-free configuration exhibits a clearer staged energy-dissipation response, characterized by a 11.98% reduction in equivalent viscous damping ratio and a 106.26% increase in hardening factor. These results suggest that a moderate reduction in equivalent damping can significantly enhance hardening, peak load, and cumulative plastic dissipation within a variable-stiffness design framework. These results indicate that a moderate reduction in equivalent damping can significantly enhance hardening, peak load, and cumulative plastic dissipation in a variable stiffness design framework, thereby improving staged energy dissipation and displacement restraint. The proposed MEDD therefore shows strong potential for bridge seismic protection.