Zoological Journal of the Linnean Society, 2005, 144, 309–316. With 2 figures © 2005 The Linnean Society of London, Zoological Journal of the Linnean Society, 2005, 144, 309–316 309 Blackwell Science, LtdOxford, UKZOJZoological Journal of the Linnean Society0024-4082The Lin- nean Society of London, 2005? 2005 1443 309316 Original Article THEROPOD CRANIAL MECHANICSE. J. RAYFIELD *Current address: Department of Palaeontology, The Natural History Museum, Cromwell Road, London, SW7 5BD, UK. E-mail: e.rayfield@nhm.ac.uk Aspects of comparative cranial mechanics in the theropod dinosaurs Coelophysis, Allosaurus and Tyrannosaurus E. J. RAYFIELD* Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ, UK Received June 2004; accepted for publication March 2005 The engineering analysis technique finite element analysis (FEA) is used here to investigate cranial stress and strain during biting and feeding in three phylogenetically disparate theropod taxa: Coelophysis bauri, Allosaurus fragilis and Tyrannosaurus rex. Stress patterns are generally similar in all taxa with the ventral region of the skull tensed whilst the dorsal aspect is compressed, although the skull is not purely behaving as a cantilever beam as there is no discernible neutral region of bending. Despite similarities, stress patterns are not wholly comparable: there are key differences in how certain regions of the skull contain stress, and it is possible to link such differences to cranial morphology. In particular, nasal morphology can be explained by the stress patterns revealed here. Tyr- annosaurus models shear and compress mainly in the nasal region, in keeping with the indistinguishably fused and expanded morphology of the nasal bones. Conversely Allosaurus and Coelophysis models experience peak shear and compression in the fronto-parietal region (which is tightly interdigitated and thickened in the case of Allosaurus) yet in contrast the nasal region is lightly stressed, corresponding to relatively gracile nasals and a frequently patent internasal suture evident in Allosaurus. Such differences represent alternate mechanical specializations between taxa that may be controlled by functional, phylogenetic or mechanical constraints. Creation of finite element models placed in a phylogenetic context permits the investigation of the role of such mechanical character complexes in the cranium of nonavian theropods and the lineage leading towards modern birds. © 2005 The Linnean Society of Lon- don, Zoological Journal of the Linnean Society, 2005, 144, 309–316. ADDITIONAL KEYWORDS: bite force – Dinosauria – feeding – finite element analysis – skull – strain – stress – Theropoda. INTRODUCTION Functional behaviours such as feeding, respiration and fighting impart loads upon the vertebrate cra- nium that stress and strain the bones and soft tissues of the head. Cranial bones possess a number of struc- tural features apparently associated with stress and strain resistance, transmission and dissipation, such as sutures, trabeculation, material property distribu- tion and bone thickenings or reduction (Oxnard, 1971; Buckland-Wright, 1978; Thomason & Russell, 1986; Jaslow, 1990; Jaslow & Biewener, 1995; Herring, 2000; Rayfield et al., 2001; Rafferty, Herring & Marshall, 2003). Such features modify the stress and strain envi- ronment of the skull and as a result may serve as indi- cators of loading patterns and functional behaviour (Rafferty & Herring, 1999; Rayfield et al., 2001; Jen- kins, Thomason & Norman, 2002). This paper investigates the mechanical behaviour of the crania of three taxonomically disparate theropod dinosaurs in response to feeding loads, in order to begin deciphering the evolution of structural mecha- nisms in place to contain cranial stress and strain in theropods and their avian descendants. Non-avian theropod dinosaurs are interesting test cases: their endocranium in all except maybe the most derived forms is proportionally much smaller relative to over- all skull size than it is in mammals or birds (Larsson, Sereno & Wilson, 2000; Domínguez Alonso et al., 2004) As such, functional constraints imposed by enclosure of the brain and sense organs (Demes, 1982; Thoma- son, 1991) may be lessened in theropods, resulting in