This study establishes a finite element model based on the Iwan model to accurately characterize the force–displacement relationship and energy dissipation in bolted joints under small-amplitude tangential displacement. The force–displacement behavior of the Iwan model is transformed into a stress–strain relationship using a hybrid hardened intrinsic model. A subroutine developed with UMAT and UHARD is used to simulate the elastic–plastic behavior of the Iwan model during surface contact in the finite element model. Three-dimensional modeling and joint simulation are conducted using ABAQUS software. Experimental data verify the model's validity, and the effects of multiple factors on the bolted bonding surface are analyzed. The influence of friction coefficient, cyclic displacement amplitude, and preload on the force–displacement relationship of the bolted bonding surface is explored. Polynomial interpolation of the loading and unloading curves is applied to investigate the energy dissipation phenomenon. Results show that the finite element method can effectively reflect the hysteresis and energy dissipation behavior of the bonding surface. Increased friction coefficient and preload improve residual stiffness and energy dissipation capacity, while larger cyclic displacement amplitudes increase energy dissipation but have a minimal effect on residual stiffness.