A boundary-coupled unified frictional hysteresis model for metal rubber under quasi-static and dynamic loading

Abstract

Metal rubber (MR) contains numerous internal contact, sliding, and frictional interfaces among metallic wires, which leads to pronounced nonlinear and hysteretic characteristics under quasi-static and dynamic loading conditions. Existing hysteresis models are mostly developed for specific loading conditions and are therefore unable to uniformly describe the transition from quasi-static compressive behavior to dynamic hysteretic response in MR materials. Moreover, their capability to characterize asymmetric hysteretic behavior and equilibrium-position shifts remains limited under variations in biased mass, pre-compression, and support configuration. To address these issues, a boundary-coupled unified frictional hysteresis model (BC-UFH) is proposed in this study. Within this framework, the quasi-static frictional hysteresis (QFH) form is adopted as the baseline to identify the nonlinear elastic and frictional hysteresis parameters of MR under quasi-static compression, thereby providing the parameter basis for the subsequent dynamic extension and boundary-coupled mapping. On this basis, a dynamic frictional hysteresis (DFH) extension form is further developed by introducing a dynamic slip-softening term and a pore-gas pumping viscous damping term. By incorporating the boundary conditions of unilateral and symmetric support configurations, the BC-UFH model provides a unified description of quasi-static and dynamic responses. The proposed model enables the quasi-static compressive properties of MR materials to be consistently transformed into dynamic hysteretic responses under different support configurations. The model is validated through quasi-static compression tests and dynamic loading experiments under different support configurations. The results show that the unified model can not only accurately describe the quasi-static hysteretic response of MR materials, but also effectively characterize the dynamic hysteretic behavior under different support configurations. In addition, it can explain the asymmetric hysteresis loops and equilibrium-position shifts induced by biased loading conditions. The proposed method provides an effective reference for parameter identification, structural design, and engineering application of MR isolators.