The mammalian postorbital bar as a torsion‐resisting helical strut

The mammalian skull is asymmetrically loaded during mastication because most of these animals chew on only one side at a time. This loading regime tends to twist the braincase relative to the rostral, tooth bearing part of the skull at the zone of potential weakness between the orbits. This torsional effect is exaggerated, and a postorbital bar is present, in those animals with very large masseter and pterygoid muscles. The lines of action of these muscles are oriented at large angles to the long axis of the skull in lateral view, providing large components of force that twist the skull segments relative to one another. When the temporalis is the dominant muscle, the torsional effect is usually less important, and the bar is absent, because this muscle acts at a smaller angle to the skull axis. The postorbital bar exhibits the predicted three dimensional spatial orientation required to resist torsional forces: it is a segment of an imaginary 45° helix that is wound around the skull, if the skull is idealized as a cylinder. This orientation is significant because, in general, maximum compressive and tensile shear stresses lie along 45° helices on a cylinder loaded in torsion; to resist torsion, material should be placed far from the axis of torsion and along a helix oriented at 45° to the deforming forces. Each half of a supraorbital ridge is also a segment of a 45° helix that is perpendicular to the helix passing through the postorbital bar. This model suggests that the postorbital bar is loaded in compression on the chewing side and in tension on the non‐chewing side; the supraorbital ridge is loaded in tension on the chewing side and in compression on the non‐chewing side.