The Sliding Hinge Joint (SHJ) is an Asymmetric Friction Connection (AFC) developed to create a repeatable, efficient means of dissipating seismic response energy and reducing structural damage without yielding of the structural frame elements. Testing has demonstrated stable efficient hysteretic behaviour. However, it is necessary to fully characterise their dynamic behaviour including any less stable aspects observed in the response of these devices for selected materials. This observed behaviour may reduce device force and energy dissipation, creating an influence on the overall structure that should be fully understood and accounted for in design. This research models the hysteretic behaviour of a SHJ with a zinc anti-corrosion coating that demonstrates less than fully stable experimental dynamic behaviour in contrast to many other SHJ material choices. The model developed uses a stick-slip mechanism based on a variable friction coefficient to capture the observed dynamics with an overall Menegotto-Pinto dynamic hysteretic model. The overall results show how the model may be realistically extended to a more general model that captures observed non-linear dynamics in these and similar friction devices, and yield new insight and design tools for use with these devices.