Analysis of the Quasistatic Nonlinear Mechanical Model of Hemispherical Shell Metal Rubber

The hemispherical shell metal rubber (HSMR) exhibits high elasticity and large damping properties. Compared with a traditional metal hemispherical shell, this structure can elastically recover to its original shape after undergoing a certain degree of large deformation. However, its nonlinear mechanical properties cannot be accurately characterized, limiting its extensive application in vibration damping and impact resistance. To address this issue, this article develops a multiscale quasistatic nonlinear mechanical model, deriving nonlinear mechanical models for two deformation stages: the flattening stage and the denting stage. The influence of relative density and shape parameters on the generation of negative stiffness is analyzed. Experimental validation confirms the accuracy of the restoring force, nonlinear elastic force, and viscous damping force models for HSMR at different relative densities. The results show that relative density primarily affects the peak restoring force during the flattening stage, while thickness significantly influences the range of negative stiffness and the minimum negative stiffness during the denting stage. Furthermore, for three different relative densities, the residuals between the theoretical model's restoring force‐displacement curves exceed 98.82%, and the maximum relative error between the theoretical model's static loss factor and the experimental results is 9.80%.