Comparison of beam theory and finite‐element analysis with in vivo bone strain data from the alligator cranium

Abstract

The mechanical behavior of the vertebrate skull is often modeled using free-body analysis of simple geometric structures and, more recently, finiteelement (FE) analysis. In this study, we compare experimentally collected in vivo bone strain orientations and magnitudes from the cranium of the American alligator with those extrapolated from a beam model and extracted from an FE model. The strain magnitudes predicted from beam and FE skull models bear little similarity to relative and absolute strain magnitudes recorded during in vivo biting experiments. However, quantitative differences between principal strain orientations extracted from the FE skull model and recorded during the in vivo experiments were smaller, and both generally matched expectations from the beam model. The differences in strain magnitude between the data sets may be attributable to the level of resolution of the models, the material properties used in the FE model, and the loading conditions (i.e., external forces and constraints). This study indicates that FE models and modeling of skulls as simple engineering structures may give a preliminary idea of how these structures are loaded, but whenever possible, modeling results should be verified with either in vitro or preferably in vivo testing, especially if precise knowledge of strain magnitudes is desired.

Biomechanics of the rostrum in crocodilians: A comparative analysis using finite‐element modeling

“…We included specimens representing intermediate stages of platyrostry, Melanosuchus niger, an adult Caiman crocodilus, and a juvenile C. crocodilus, as well as a longirostrine taxon (Crocodylus johnstoni). Mechanically, the rostrum can be thought of as a cantilevered beam (Rafferty et al, 2003;Metzger et al, 2005), and as such the proximal sections are of particular importance in determining its structural characteristics. Ultimately, we compared results from beam and finite-element models of each specimen to test for variation due to modeling technique and formulated two specific hypotheses: A. the most platyrostral taxon will give the best mechanical performance under loads simulating twist feeding behaviors; B. qualitatively, the mechanical performance of the six rostral finite-element models should match the predictions of simple beam theory models based on the dimensions of the proximal end of the rostral beam.…”

“…As we were modeling the rostrum as a cantilevered beam (Rafferty et al, 2003;Metzger et al, 2005), we assigned the posterior part of the rostrum the greater importance in determining the shape of the simple beam model: the dimensions of each beam were set as the average of the rostral dimensions at the front of the orbits and at the largest maxillary tooth (i.e., the fourth maxillary tooth in alligatorids, the fifth in crocodylids) for each respective specimen (Appendix A). Each beam model was then subjected to loads equivalent to the 10 load cases used on the 6 finite-element models.…”

“…It is thus possible that the broad rostra of forms such as Alligator only helps in resisting torsional loads given the low profile of the snout enforced by hydrodynamic factors (Busbey, 1995;Metzger et al, 2005). The mechanical consequences of platyrostry were emphasized by Busbey (1995): compared to an oreinirostral skull, a platyrostral skull will be exposed to higher bending loads as a result of jaw adduction.…”

Functional shape of the skull in vertebrates: Which forces determine skull morphology in lower primates and ancestral synapsids?

“…The ultimate question is: What are the reasons for the development of skull shape in evolution and ontogeny? This research program does not seek to find out how the existing skull of a crocodile, a galago, or a macaque behaves under load (see, e.g., Metzger et al, 2005, this issue; Strait et al, 2005, this issue;and Ross et al, 2005, this issue), but rather why the various skull shapes have evolved. In terms of evolutionary theory, the question is:…”

The Anatomical Record Inside the Head: A History of Reporting Findings on the Skull, Paranasal Sinuses, and Nose

“…An enticing sample includes the following: Frost's et al (2003) insightful study of factors influencing cranial diversity in baboons, and the equally thoughtful Commentary accompanying it by world-renown baboon biologist Clifford Jolly (2003); Brauer and collegues' 3D CT virtual reconstruction of the endocranial cavity of the fossil hominid cranium from Eliye Springs, Kenya (2004); the CT study of the cranium of the fossil anthropoid primate, Parapithecus grangeri, with insights into the evolution of our sensory systems by Bush and his most eminent colleagues Elwyn Simons and John Allman (2004); outstanding studies using finite-element modeling and analysis on the crania of alligators by Metzger et al (2005), and on meat-eating dinosaurs by Rayfield (2005) Bastir et al (2008) using 3D CT reconstructions of fossil humans to assess how the middle cranial fossa has morphed and changed during hominid evolution.…”