A novel penalty contact constitution was developed to replicate the hysteresis memory effect observed in contact interfaces. On this basis, a refined finite element analysis (FEA) was performed to study the stick–slip friction contact behavior of bolted joint interfaces. The analysis was validated by comparing it with the experimental hysteresis loops in the literature. The simulated hysteresis loops were subsequently used to identify four parameters of the Iwan model. Additionally, the effects of bolt clamping, friction coefficient, and excitation amplitude were individually examined. It was found that the deterioration in bolt clamping performance resulted in a decrease in both the equivalent joint stiffness and energy dissipation. Similarly, the reduction in the friction coefficient yielded a comparable impact. Furthermore, the identified model parameters of critical stick–slip force and displacement exhibited a quasi-linear relationship to the bolt preload and friction coefficient.