Bolted connections are ubiquitous in mechanical designs and pose a significant challenge to understanding and predicting the vibration response of assembled structures. The present paper develops a physics-based rough contact model of the frictional interactions within a joint. This model sums over the probable interactions of asperities – defined as locally maximum surface features – to determine the contact forces. Here, the tangential contact forces vary smoothly between sticking and slipping and allow the model to better capture the qualitative trends of experimental amplitude dependent frequency and damping than previous studies. Furthermore, the novel model is generalized to allow for arbitrarily varying normal pressure including potential separation to better represent the interfacial dynamics. This includes developing a new, computationally tractable approximation to the analytical Mindlin partial slip solution for tangential loading of contacting spheres. The results highlight the importance of accurately characterizing the as-built topology of the interface, the plastic behavior of the contacting asperities, the relevant length scale of asperities, and the eccentricity of asperities. A predictive friction coefficient based on plasticity provides a poor match to experiments, so fitting the friction coefficient is also considered. Numerical results are compared to experiments on the Brake-Reuß Beam to assess the predictive potential of the models. While blind predictions over-predict the slip limit, the current model presents a significant improvement in physics-based modeling and highlights areas for ongoing research.