An apparatus and system is disclosed for dental modeling. The apparatus includes a first tray positioned opposite a second tray and a dearticulating hinge coupling the first tray to the second tray. The dearticulating hinge includes a first hinging element coupled to one of the first tray and the second tray and a second hinging element coupled to the other of the first tray and the second tray. At least one of the first hinging element and the second hinging element includes a disengaging element configured to engage a spur to uncouple the first hinging element from the second hinging element upon extending the first tray and the second tray beyond a predefined angle relative to one another.