Finite Element Analyses of Ankylosaurid Dinosaur Tail Club Impacts
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
THE ANATOMICAL RECORD 292:1412–1426 (2009)
Finite Element Analyses of Ankylosaurid
Dinosaur Tail Club Impacts
VICTORIA M. ARBOUR* AND ERIC SNIVELY
Department of Biological Sciences, Biological Sciences Centre, University of Alberta,
Edmonton, Alberta, Canada
ABSTRACT
Ankylosaurid dinosaurs have modified distal caudal vertebrae (the
handle) and large terminal caudal osteoderms (the knob) that together
form a tail club. Three-dimensional digital models of four tail clubs
referred to Euoplocephalus tutus were created from computed tomogra-
phy scans of fossil specimens. We propose to use finite element modeling
to examine the distribution of stress in simulated tail club impacts in
order to determine the biological feasibility of hypothesized tail clubbing
behavior. Results show that peak stresses were artificially high at the
rigid constraint. The data suggest that tail clubs with small and average-
sized knobs were unlikely to fail during forceful impacts, but large clubs
may have been at risk of fracture cranial to the knob. The modified han-
dle vertebrae were capable of supporting the weight of even very large
knobs. Long prezygapophyses and neural spines in the handle vertebrae
helped distribute stress evenly along the handle. We conclude that tail
swinging-behavior may have been possible in Euoplocephalus, but more
sophisticated models incorporating flexible constraints are needed to sup-
port this hypothesis. Anat Rec, 292:1412–1426, 2009. V C 2009 Wiley-Liss,
Inc.
Key words: Ankylosauria; Euoplocephalus; biomechanics; finite
element analysis; functional morphology; palaeo-
biology
INTRODUCTION These questions about ankylosaurid tail function are
testable through finite element analysis (FEA). FEA is a
Ankylosaurs were large, quadrupedal ornithischian
powerful tool for understanding the biomechanics of
dinosaurs with extensive dermal ossifications on the
extant and extinct organisms through modeling of
head, body, and tail (Vickaryous et al., 2004). Ankylo-
stress, strain, and deformation in anatomical structures.
saurids had highly modified distal caudal vertebrae
forming a handle that, along with terminal osteoderms
(the knob), formed a club-like structure (Fig. 1; terminol-
ogy after Coombs, 1995). Several authors (Maleev, 1952, Grant sponsors: NSERC PGS-M, Alberta Ingenuity
1954; Coombs, 1971, 1979, 1995) have suggested that Studentship, Alberta Ingenuity Postdoctoral Fellowship,
University of Alberta Graduate Students Association,
the tail was used as a defensive weapon. Tail club Department of Biological Sciences (University of Alberta),
impact forces vary depending on the size of the knob, Dinosaur Research Institute, Canada Foundation for Innovation,
and large Euoplocephalus tutus (Lambe, 1910) knobs Jurassic Foundation.
could impact with a force sufficient to break bone in *Correspondence to: Victoria M. Arbour, Department of Bio-
shear (Arbour, 2008). Could Euoplocephalus tail clubs logical Sciences CW 405 Biological Sciences Centre, University
withstand these impact forces without fracturing? How of Alberta, Edmonton, Alberta, Canada T6G 2E9. E-mail:
were stress and strain dissipated throughout the club? If arbour@ualberta.ca
the vertebrae or knob osteoderms fractured under nor- Received 9 June 2009; Accepted 9 June 2009
mal impact forces, this would suggest that the primary DOI 10.1002/ar.20987
purpose of the knob was not for delivering forceful Published online in Wiley InterScience (www.interscience.wiley.
blows. com).
C 2009 WILEY-LISS, INC.
V
ANKYLOSAUR TAIL CLUB IMPACTS 1413
TABLE 1. Material examined
Taxon Specimens examined
Euoplocephalus AMNH 5211, AMNH 5245, AMNH 5337,
tutus AMNH 5403, AMNH 5404,
AMNH 5405, AMNH 5406,
AMNH 5409, AMNH 5470,
CMN 0210 (holotype), CMN 349,
CMN 2234, CMN 2251, CMN 2252,
CMN 2253, CMN 8530, CMN 40605,
ROM 784, ROM 788, ROM 1930,
ROM 7761, TMP 82.9.3, TMP 53.36.120,
TMP 85.36.70, TMP 1992.36.334,
TMP 2000.57.3, UALVP 16247,
UALVP 47273
Ankylosauridae TMP 2007.020.0100,
indeterminate TMP 2007.020.0080, TMP 84.121.33,
TMP 2005.09.75
Taxonomic assignment of specimens is based on museum cata-
logue information and previously published identifications.
Fig. 1. Diagram of tail club terminology used in this paper. Three-
dimensional digital reconstruction of UALVP 47273 in Mimics based
on computed tomography scans, in (A) dorsal, (B) ventral, and (C) TABLE 2. Institutional abbreviations
right lateral views. Scale bar equals 10 cm. AMNH American Museum of Natural History,
New York, New York, USA
CMN Canadian Museum of Nature, Ottawa,
Rayfield (2007) provides an overview of the finite ele- Ontario, Canada
ment method and its uses in palaeontology. Stress (force/ ROM Royal Ontario Museum, Toronto,
area) is simulated in a modeled structure when a force Ontario, Canada
(load) is applied; tensile stresses are, by convention, rep- TMP Royal Tyrrell Museum of Palaeontology,
resented by positive values, and compressive stresses by Drumheller, Alberta, Canada
negative values. Strain is the change in length after a UALVP University of Alberta Laboratory for
Vertebrate Paleontology, Edmonton,
load is applied divided by the original length of a Alberta, Canada
structure.
FEA of dinosaur fossils has predominantly dealt with
theropod skulls (Rayfield, 2001; Mazzetta et al., 2004;
referred to Euoplocephalus and also includes most of the
Rayfield, 2004, 2005; Rayfield et al., 2007; Shychoski et
handle. UALVP 47273, UALVP 16247, and TMP
al., 2007), with fewer studies on ornithischian skull
83.36.120 were scanned at the University of Alberta
mechanics (Farke et al., 2007; Maidment and Porro,
Hospital Alberta Cardiovascular and Stroke Research
2007; Porro, 2007; Snively and Cox, 2008). Analyses of
Centre (ABACUS), on a Siemens Somatom Sensation 64
the postcranial skeleton are rarer, and have included the
CT scanner, at 1 mm increments. ROM 788 was scanned
metatarsus of a tyrannosaurid (Snively and Russell,
at CML Healthcare Imaging in Mississauga, Ontario, at
2002), dromaeosaurid claws (Manning et al., 2007), and
2 mm increments, and as two separate scans (the knob
ossified tendons (Organ, 2006) and pedal morphology
and the handle).
(Moreno et al., 2007) of ornithopods. This is the first
study to use FEA to investigate biomechanics in ankylo-
saurs. Four ankylosaurid tail clubs referred to Euoploce-
Three-Dimensional Modeling and Meshing
phalus tutus are examined to understand the
distribution and magnitude of stresses within the club CT scans were used to create 3D models for use in
R
under simulated impact conditions. If stress magnitudes FEA (Fig. 2). The computer program MimicsV (Material-
within the modeled clubs are greater than necessary to ise) was used to create a 3D model and mesh for each
fracture bone, then tail clubs were not likely used as specimen, and to apply material properties to each
weapons. Distributions of stresses provide information mesh. A mask over the desired portion of the scan is cre-
on the function of the handle and knob. ated using the thresholding function. Each slice is man-
ually edited using the ‘‘multiple slice edit’’ function to
MATERIALS AND METHODS both add and remove mask, to fill in cracks in the speci-
men and remove artifacts and unwanted parts of the
Computed Tomography
scan (including the scanning bed and specimen support
Four ankylosaurid tail clubs (Tables 1 and 2) were jackets). A 3D model was then calculated and inspected
scanned using computed tomography (CT), to derive for artifacts. A 3D mesh of hexahedral elements was cre-
three-dimensional models for use in FEA (Fig. 2). ated in Mimics and exported as a NASTRAN (.nas) file.
UALVP 47273 has a small knob and much of the handle The default settings in Mimics produce a mesh with too
preserved. UALVP 16247 and a cast of TMP 83.36.120 many elements, which will not work properly in the
R
are average-sized knobs; TMP 83.36.120 does not pre- FEA software Strand7V [Strand7 (Strand7 Pty) deals
serve much of the handle, and UALVP 16247 lacks a well with meshes of 1 million elements or less]. The
handle completely. ROM 788 has the largest knob mesh size is reduced by grouping voxels in the xy and z
1414 ARBOUR AND SNIVELY Fig. 2. Models used in this study. UALVP 47273 in (A) oblique left overlain in (K) and (L) to show the missing portions. Ridges on the dorsolateral and (B) caudal view. UALVP 16247 in (C) dorsal, (D) cau- knob in (J) and (K) are artifacts resulting from poor scan quality and dal, and (E) left lateral view. TMP 83.36.120 in (F) oblique dorsal, (G) manual editing in this region. All images created in Mimics from com- left lateral, (H) ventral, and (I) caudal. ROM 788 in (J) oblique dorsal, puted tomography scans. Photograph in (L) by R. Sissons and used (K) ventral, (L) caudal, and (M) left lateral view. The lateral edges of with permission. Scale equals 10 cm. the knob were excluded from the scan; photos of the specimen are
ANKYLOSAUR TAIL CLUB IMPACTS 1415
TABLE 3. Material properties used in analyses
Density Young’s Poisson’s
(kg/m3) modulus (Pa) ratio Notes
Compact bone 2000 20e9 0.4 Density: Human 1.5-2.0 (Wirtz et al., 2000)
Young’s modulus: Alligator mississippiensis
cortical 12 020, Crocodylus sp. cortical 5630,
Geochelone niger 13780 (Currey, 1988);
Varanus exanthematicus cortical 22 800
(Erickson et al., 2002)
Poisson’s ratio: Human cortical 0.22 to 0.47
(Peterson and Dechow, 2003)
Cancellous bone 1000 8e9 0.4 Density: Human 0.1-0.7 (Wirtz et al., 2000)
Young’s modulus: Human 774
(Peterson and Dechow, 2003)
Keratin 1300 2.5e9 0.4 Young’s modulus: Ramphastos toco beak 6.7 GPa
(Seki et al., 2006); Struthio camelus claw 1.84,
1.33 GPa (Bonser, 2000); avian feather 2.5 GPa
(Bonser and Purslow, 1995), bovine hoof
261-418 MPa (Franck et al., 2006); Gekko gekko
setae 1.6 GPa, Ptyodactylus hasselquistii setae
1.4 GPa (Peattie et al., 2007)
Poisson’s ratio: bovine hoof 0.38 (Franck et al., 2006)
dimensions; this results in a loss of fine surface features, 2004, 2005; Snively and Cox, 2008), and imported the
R
such as the knob osteoderm texture, but the model is coordinates into RhinoV (McNeel North America, 2007).
still an accurate representation of specimen geometry. We used this outline as the coronal perimeter of the
Once a mesh has been created, material properties can idealized model. The geometric model consisted of ellipti-
be assigned. Mimics calculates Hounsfield density values cal cylinders for the handle (centra plus neural arches,
of the CT images and displays these as a histogram. and haemal arches), and ellipsoids for the flanking prox-
Materials can be automatically specified from the den- imal and collective distal knob osteoderms. The shapes
sity values, and material properties can be manually were combined into one model and exported as a .stl file
entered (a better practice with matrix-filled fossils). The into Mimics. We used the Mimics Remesher to reconsti-
mesh is then exported as a .nas file for use in Strand7. tute the .stl surface mesh into uniform triangles, and to
ROM 788 was scanned in two pieces, and the data create a volumetric tetrahedral mesh.
from the two CT scans were combined to make a single This simplified mesh was imported as a .nas file into
model for FEA. Both CT scans were cleaned in Mimics Strand7, where we applied material properties, con-
as for the other models. Each model was exported as a straints, and forces for Analysis 1 described below. Anal-
surface stereolithography (.stl) file and imported into a yses were successful on the model initially imported into
Mimics project file. The .stl models were aligned appro- Strand7, but scaling it to accommodate unit variance
priately and then joined using the Boolean Unite func- between Rhino and Strand7 resulted in mesh anomalies
tion in the Segmentation module. The united model was and solution failure. This required scaling stress results
then decimated using the reduce triangles, smooth, and of the successful analysis. Stress is inversely propor-
remesh functions in the Mimics Remesher. This tional to the square of linear dimensions. We therefore
remeshed, united model was then imported into multiplied the simple model’s stress results by the
Strand7. The missing lateral edges of each major osteo- square of the ratio between maximum widths across the
derm, which were outside of the field of view of the CT osteoderms, in the simple Strand7 mesh and original
scanner, could not be reconstructed. No additional mesh- club. The dimensions of the geometrically modeled osteo-
ing is needed for models in .nas format, but the model of derms were correct, and the calculated stresses were
ROM 788 required additional automatic and manual similar in magnitude to those of the CT-based club
cleaning in Strand7 to remove triangles with free edges. model. We are thus confident that stress scaling yields
The surface mesh was then converted to a solid mesh. accurate results.
The tail clubs subjected to FEA were variably complete
and taphonomically distorted, inevitable with most fossil Analysis-Specific Models, Boundary Conditions,
specimens. We therefore checked them against results
and Material Properties
for an idealized replica of a club (UALVP 47273) based
on simple geometric forms. Deviations from the simpli- We applied material properties, a constraint, and a
fied model were evaluated as possible preservation- load to finite element meshes in Strand7, and then ana-
induced stress artifacts, versus those arising from ana- lyzed for both stress and strain results using the linear
tomical details not captured in the simple FEM. UALVP solver. Table 3 lists the material properties used in the
47273 was bent taphonomically into a dorsally concave different analyses, and Table 4 lists the forces, con-
arc, but was otherwise undistorted dorsoventrally. As straints, and other variables used for each mesh of each
the basis for a straightened model, we traced a dorsal analysis. Estimates of tail club strike forces are from
R
photograph of the club in Adobe IllustratorV (Rayfield, Arbour (2008), and follow a method for estimating tail
1416 ARBOUR AND SNIVELY
TABLE 4. Summary of forces (N) used in analyses
ROM TMP UALVP UALVP UALVP 47273 UALVP 47273
Analysis 788 83.36.120 16247 47273 knob þ vertebrae isolated vertebra
1 10,160 960 960 570 – –
– – – 1,127 – –
2 10,160 960 570 – –
3 – – – 570 570 200
4 – – – 39 39 –
1,029 – – 126 – –
– – – 1,029 – –
5 – – 960 570 – 200
tip angular velocity from Carpenter et al. (2005). Von tact. For this analysis, the knobs were assigned uniform
Mises stress results were displayed both as 3D surface material properties of cancellous bone. We applied the
plots, and as 2D cross-sections at various locations same material properties and constraints to the simpli-
within the specimen. Strand7 can produce colored con- fied model as those for the CT-based FE model.
tour and vector plots; tensile stresses are positive values,
and compressive stresses are negative values. Analysis 2. Impacts did not necessarily always occur
Each specimen provides different benefits and limita- at the same location on the tail club. Impacts were simu-
tions for analysis. UALVP 47273 is a relatively complete lated on the handle just cranial to the knob, and on the
specimen, and allows for analysis of the knob and han- distal end of the knob, to understand how stress distri-
dle together. However, a mesh of less than 5 million ele- bution changes as impact site changes. The most realis-
ments does not show the details of the individual neural tic force was used for both ROM 788 and UALVP 47273,
and haemal arches. To better reveal stress distribution and the meshes were given the material properties of
in these structures, a smaller model was created by cancellous bone.
removing all but the last two of the visible handle verte-
brae and the knob. The original scan of UALVP 47273
was edited slice by slice in Mimics to model details of Analysis 3. As explained earlier, two models were
the penultimate visible vertebra, and to remove the constructed from the CT scan of UALVP 47273 to exam-
proximal elements. In this manner, an impact force ine stress details on individual handle vertebrae. First,
could be applied to the knob, and details of stress distri- the knob and two preceding handle vertebrae were iso-
bution observed in the handle vertebrae. Appropriate lated and meshed as the ‘‘knob þ vertebrae’’ model. In
forces could then be applied to a single vertebra isolated Strand 7, a force was applied at the midlength and mid-
from the handle in the same manner. Additionally, height of the left lateral osteoderm, as for Analysis 1.
UALVP 47273 represents a small knob morphology The model was constrained at the cranialmost vertebra,
which is not representative of most ankylosaurid knobs. on the medial faces of the prezygapophyses, the cranial
ROM 788 is the largest specimen in this study, but the face of the centrum, and the medial sides of the cranial
handle and knob are separate elements, and the lateral projection of the haemal spine. Results of the stress dis-
sides of the knob osteoderms were not included in the tribution in these models were then applied to a second
CT scan. UALVP 16247 is an isolated knob, but repre- model of a single handle vertebra (‘‘single vertebra’’
sents the average knob size in Euoplocephalus, and the model), which was also manually isolated and meshed in
CT scan of this specimen had few artifacts. As such, the Mimics. Properties of cancellous bone were applied to
effects of differing bone densities and material properties the model. To simulate a tail club with unfused centra,
were best analyzed in this specimen. The cast of TMP an additional analysis, where the centrum was not con-
83.36.120 cannot be used to examine material proper- strained, was conducted for both the knob þ vertebrae
ties, but can be compared with the similarly-sized and isolated vertebra models.
UALVP 16247. To examine different aspects of club me-
chanical response to impacts, we conducted five analyses Analysis 4. The unusually robust haemal arches of
with varying boundary conditions. ankylosaurid tail clubs may play a role in postural sup-
port of the large knob. Impact forces are assumed to be
directed in the horizontal plane, but gravity would also
Analysis 1. Three specimens with different knob act to pull downward on the tail club. Coombs (1995)
sizes were used to examine the effect of knob size and noted that ankylosaurids probably did not drag their
impact force on tail clubs. For each model, the cranial tails on the ground, although the tail may not have been
face of the centrum of the most cranially located part of held very high off of the ground. The weight (Table 5) of
the handle was constrained. A force was applied to both each knob is calculated using the volumes and masses in
a small and large area at approximately the midheight Arbour (2008), multiplied by gravitational acceleration
and midlength of the left major osteoderm of each knob. (9.81 m/s2). UALVP 47273 is the only specimen in this
This force was oriented at right angles into the osteo- study that preserves the knob and handle together. Han-
derm. The impact force for each knob was applied to dle vertebrae become moderately larger as knob size
each node in both the small and large impact area anal- increases, but the two are not linearly correlated
yses. This is reasonable because impact velocity and (Arbour et al., in press). As such, it is reasonable to
force would not vary greatly over the larger area of con- apply the forces and torques derived for each knobANKYLOSAUR TAIL CLUB IMPACTS 1417
TABLE 5. Weights of specimens used in was also concentrated in some locations that correspond
Analysis 4 (volumes and masses from Arbour, 2008) to breaks in the specimens, and is not biologically mean-
ingful. Peak stress was over 1,000 MPa in all models,
Knob Knob Force
Specimen volume (cm3) mass (kg) (N) and was greater in larger knobs and when impact force
was applied to a larger area. Stress values decreased
ROM 788 53007.00 104.95 1,029.56 rapidly away from the peak stress, sometimes by several
UALVP 16247 6,486.17 12.84 126.00 orders of magnitude. Peak stress was always oriented
UALVP 47273 2,008.32 3.98 39.01 craniocaudally, not mediolaterally or dorsoventrally. In
all specimens, the maximum stress values always repre-
sented tensile, rather than compressive, stress.
(UALVP 47273, UALVP 16247, and ROM 788) to the In UALVP 47273 (Fig. 3, Table 6), tensile stress was
model of UALVP 47273, for the purposes of comparing found from the impact site to the distal terminus of the
large and small knob weights. UALVP 47273 was con- left half of the knob. Tensile stress was also particularly
strained at the cranial face of the cranialmost vertebra, high between the cranial terminus of the left major knob
and the force was applied to a single node at a point ven- osteoderms and the handle, whereas compressive stress
tral to the estimated centre of mass of the knob. To inves- was found in the same location on the right side of the
tigate the distribution of stress within a single vertebra, tail club. Maximum stress was found within the con-
this force was also applied to the knob þ vertebrae model. strained area of the handle, and minimum stress was
found distal to the impact site on the knob. The magni-
Analysis 5. Knob osteoderms have regions of high, tude of the impact force did not change the distribution
medium, and low density, which may affect the distribu- of stress within the club, but did change the absolute
tion of stress and strain throughout the club. Strait et values of the peak stress. Varying the size of the impact
al. (2005) found that elastic properties affect quantita- area also changed the absolute values of the maximum
tive strain data in finite element analyses, although stress. In lateral view, stress vectors were oriented radi-
overall strain patterns are similar using different elastic ally from the impact site and lengthwise along the han-
properties. Precise material properties for ankylosaur dle. In dorsal view, stress vectors were oriented
bone cannot be known. However, a range of different transversely across the handle and formed a complex
properties from various taxa were used to estimate ma- swirling pattern on the knob around the impact site.
terial properties in tail clubs (Table 3). In the idealized model of UALVP 47273 (Fig. 3, Table
Regions of differing density were calculated using 6), general stress distribution was nearly identical to
Mimics for the knob of UALVP 16247 and an isolated that of the CT based model, yet varied in some details.
handle vertebra of UALVP 47273. UALVP 16247 was Peak stresses occurred in the proximal handle near the
loaded over a small area on the left lateral osteoderm, as constraint, yet were not particularly high near the
for Analysis 1, and UALVP 47273 was loaded on the cranial junctures between the lateral osteoderms and
neural spine as for Analysis 3. the handle. Stresses along the lateral surfaces of the
Knob osteoderms were likely covered by a keratinous proximal handle were somewhat higher than in the CT-
sheath in life. Snively and Cox (2008) showed that the rel- based model.
ative thickness of a horny covering on pachycephalosaur In both TMP 83.36.120 and UALVP 16247 (Fig. 4,
domes would have greatly influenced the distribution and Table 6), compression was found on the left osteoderms
magnitude of stresses within the osseous dome. To simu- and was greatest at the site of impact, whereas tension
late the effects of a keratinous sheath, a new mask was was found on the right osteoderms and near the con-
created for UALVP 47273 in Mimics. The outline of a thin straints. Tensile stress was also concentrated at the
keratinous sheath was traced for each slice of the knob boundaries between the major and minor plates. Stress
osteoderms and added to the overall mask, and the gray- vectors were oriented radially from the impact sites on
scale values in the resulting model were assigned mate- the lateral faces of the osteoderms, craniocaudally on
rial properties for cancellous bone and keratin. the left major osteoderms in dorsal view, and mediolater-
Additional analyses were conducted using two-dimen- ally on the right major osteoderms in dorsal view. In
sional models in MultiphysicsV R . The outline of a trans- cranial view, the stress vectors converged towards the
verse section through the knob of both UALVP 16247 constraints, forming clockwise swirls.
was traced, as well as areas of low density in each osteo- In ROM 788 (Fig. 5, Table 6), compressive stress was
derm, and hypothetical keratinous coverings on each found at the impact site, with tensile stress immediately
osteoderm. These coordinate outlines were exported as adjacent to the impact site rapidly changing to approxi-
CAD .dxf files, imported into Multiphysics, coerced to mately neutral stress throughout the rest of the osteo-
solid, and assigned material properties as per the 3D derm. Tensile stress was found at the boundary of the
models. The section models were constrained at the dor- knob osteoderms and handle, with compressive stress con-
sal and ventral borders of the centrum (equivalent to centrated along the midline of the knob dorsally and ten-
the midline of the knob) and loaded as for the 3D sile stress ventrally. Stress vectors radiated from the
models. impact site and formed a complex, swirling pattern in dor-
sal view at the knob and cranial view at the constraint.
RESULTS Stress vectors were oriented craniocaudally along the
Analysis 1: Effect of Knob Size and handle in lateral view, and mediolaterally in dorsal view.
The cranial face of the handle centrum of ROM 788
Impact Force
experienced tensile stress on the right half and compres-
In all of the models, stresses were greatest at the con- sive stress on the left half, similar to that observed
straint and at the impact site (Figs 3–5; Table 6). Stress in UALVP 47273. The medial face of the right1418 ARBOUR AND SNIVELY Fig. 3. Impact stresses in TMP 83.36.120 and UALVP 16247. 75 MPa), dorsal view, and (B) stress contour plot (50 to 50 MPa), Arrows summarize stress vector orientations, and arrowheads indicate oblique caudosorsal view. UALVP 16247, (C) stress vector plot (75 to direction and location of load. Positive values are compression, nega- 75 MPa), dorsal view, and (D) stress contour plot (30 to 30 MPa), tive values are tension. TMP 83.36.120, (A) stress vector plot (75 to oblique caudosorsal view.
ANKYLOSAUR TAIL CLUB IMPACTS 1419
Fig. 4. Results from a simplified model of UALVP 47273 match 500 MPa. Impact at midlength of knob, in (A) simplified model, stress
closely with the CT-based model. Positive values are compression, contour plot, (B) simplified model, stress vector plot, (C) CT model
negative values are tension. UALVP 47273 in oblique left dorsolateral stress vector plot, and (D) CT model, stress vector plot. Impact on
view, showing that differences in impact location affect stress distribu- handle cranial to knob, (E) stress contour plot, and (F) stress vector
tions. Stress range in A is 155 to 155 MPa, in B is 300 to 300 plot. Impact on distal tip of knob, (G) stress contour plot, and (H)
MPa, in C, E, and G is 75 to 75 MPa, and in D, F, and H is 500 to stress vector plot.
prezygapophysis experienced tension, and the lateral are oriented mediolaterally, and in lateral view they are
face experienced compression; the reverse was found in oriented dorsoventrally.
the left prezygapophysis. Tensile stress was also found An impact near the distal tip of the knob results in
within bone surrounding the neural canal. Along the stress vectors oriented craniocaudally in lateral view of
handle, tensile stress was found at the cranial edges of the knob and handle, and mediolaterally in dorsal view.
the prezygapophyses on the right side. An area of con- The distribution of stress along the handle did not
centrated tensile stress (600 MPa) was present on the change, and shifted distally in the knob. Tensile stress
right side of the handle 5 cm cranial to the knob (Fig. radiated cranially through the left half of the minor
5). The haemal arch experienced neutral stress for much plates, and compressive stress did the same on the right
of its length, with increasing tensile stress near the half.
constraint.
Analysis 3: Stress Distributions in the
Analysis 2: Impact Site Analysis Handle Vertebrae
Altering the location of the impact site did not change Peak stress values were higher in the UALVP 47273
the distribution of stresses near the constraint in knob þ vertebrae model with only the prezygapophyses
UALVP 47273 (Fig. 3, Table 7). Impacts to the handle and haemal arch constrained, in comparison to the
resulted in almost zero stress within the knob. Peak model with the centrum, prezygapophyses and haemal
stress did not greatly increase or decrease based on arch constrained (Fig. 6, Table 8). However, in the con-
impact location, and was always found within the con- strained prezygapophyses and haemal arch model, the
straint. Stress vectors radiate from the impact site on decrease in stress adjacent to the peak stress (to less
the handle. In dorsal view, stress vectors on the knob than 100 MPa) was greater than in the constrained1420 ARBOUR AND SNIVELY
Fig. 5. Stress is concentrated cranial to the knob and at the cranial prezygapophyses indicated by open-headed arrows. (C) Stress vector
borders of the prezygapophyses in ROM 788. (A) Stress contour plot plot (1500 to 1500), cranial view, stress orientations summarized by
(150 to 150 MPa), oblique right lateral view, with stress concentration closed-headed arrows, load indicated by arrowhead. Positive values
indicated by open-headed arrow. (B) Stress contour plot (60 to are compression, negative values are tension.
60 MPa), left lateral view, three examples of high tensile stress at
TABLE 6. Peak stresses in Analysis 1, examining large and small impact areas
Maximum stress (MPa)
Impact Impact
Model force (N) area XX YY ZZ XY YZ ZX
ROM 788 10,160 Small 9,150 8,264 16,351 385 3,313 1,142
10,160 Large 103,426 93,388 184,760 4,342 37,389 12,979
TMP 83.36.120 1,000 Small 587 383 695 49 46 221
UALVP 16247 960 Small 1,073 837 1,308 74 180 298
960 Large 11,547 9,126 14,238 728 1,748 3,148
1,420 Small 1,668 1,316 2,055 106 256 456
1,420 Large 16,841 13,310 20,767 1,061 2,548 4,591
UALVP 47273 570 Small 1,368 1,215 2,758 115 748 168
570 Large 21,295 18,893 42,961 1,806 11,656 2,620
1,127 Small 2,127 1,874 4,307 186 1,166 265
1,127 Large 40,750 36,151 82,216 3,459 22,308 5,015
UALVP 47273 570 Small 641 416 425 100 19.4 24.5
simple model
Tensile stress is positive, and compressive stress is negative. X is mediolateral, Y is dorsoventral, and Z is craniocaudal.
centrum, prezygapophyses and haemal arch model osteoderm and handle, and on the right half of the cra-
(where stress decreased to around 100 MPa). nial face of the centrum, where the model was con-
Compressive stress was found at the impact site on strained (Fig. 6). The midline of the centrum had stress
the left major osteoderm, dorsally between the left major near zero, approximating a neutral axis. Tensile stressANKYLOSAUR TAIL CLUB IMPACTS 1421
TABLE 7. Peak stresses in Analysis 2, examining impact location
Maximum stress (MPa)
Model Impact force (N) Impact location XX YY ZZ XY YZ ZX
ROM 788 10,160 Handle 77,776 57,925 121,921 2,587 25,412 13,189
10,160 Midlength of knob 9,150 8,264 16,351 385 3,313 1,142
10,160 Knob distal tip 39,730 35,732 70,743 1,566 13,887 5,467
UALVP 47273 570 Handle 3,569 2,914 7,463 412 1,982 487
570 Midlength of knob 1,368 1,215 2,758 115 748 168
570 Knob distal tip 2,546 2,291 5,102 201 1,389 307
Tensile stress is positive, and compressive stress is negative. X is mediolateral, Y is dorsoventral, and Z is craniocaudal.
was found dorsally and cranially between the right GPa, and located at the point of bifurcation of the prezy-
major osteoderm and the handle, and on the left half of gapophyses. Immediately away from this point, stress
the cranial face of the centrum. Within the prezygapoph- dissipated to 100–200 MPa.
yses, stresses were greater caudally and decreased to
nearly zero at the cranial termini. Changing the con-
Analysis 4: Postural Role of the Haemal Arches
strained area of the model changed the distribution of
stresses within the vertebrae. When only the prezyga- Tensile stress was found at the junction of the prezy-
pophyses were constrained, peak stress occurred on the gapophyses, but not along their medial faces (Fig. 6,
caudal part of the right prezygapophysis, within the con- Table 9). Low tensile stresses were observed on the
strained area. Tensile stress was concentrated below the cranial face of the centrum dorsal to the haemal canal.
right prezygapophysis on the cranial face of the cen- Ventrally, tensile stress is found irregularly along the
trum, but dissipated abruptly away from the haemal arches. In lateral view, the knob experienced low
prezygapophysis. tensile stress ventrally, and low compressive stress dor-
Stress vectors in the unconstrained centrum model sally. In lateral view, the pattern of vectors within the
were complex (Fig. 6). In dorsal view of the knob, stress handle was similar to that in Analysis 4. In dorsal view,
vectors are oriented mediolaterally in the right osteo- the vectors are oriented craniocaudally along the knob
derm, and in the left osteoderm collectively form a swirl- osteoderms, the neural spines, and both right and left
ing pattern, inclined craniocaudally. In left lateral view, prezygapophyses.
vectors were oriented caudolaterally along the neural
spine, but became undulate along the prezygapophyses.
Analysis 5: Material Properties
Along the centrum, vectors were oriented approximately
craniocaudally, looping ventrally onto the haemal spine. In the keratinous sheath UALVP 47273 model (Fig. 7,
The cranial projection of the haemal spine had approxi- Table 10), the distribution of stresses within the handle
mately dorsoventrally directed stress vectors. In right and knob did not change noticeably compared to the nor-
lateral view, stress vectors were oriented dorsoventrally mal UALVP 47273 model. Compressive stress at the
on the neural spine, right prezygapophysis, centrum, impact site was surrounded by a halo of tensile stress,
and caudal portion of the haemal spine. The cranial pro- which was not observed in the bone model. The kerati-
jection of the haemal spine had approximately laterally nous sheath slightly reduced the peak stress at the con-
oriented vectors. Dorsally, craniocaudally directed vec- straint. The overall distribution of stresses in the
tors from the left side of the neural spine and haemal UALVP 47273 isolated vertebra model (Fig. 7, Table 10)
spine arced across the neural arch and haemal arches, did not change when the material properties were
becoming mediolaterally oriented on the right side of changed, although the stresses appeared more diffuse
each spine. Stress vectors looped mediolaterally around compared to the single material property model. Mate-
the right prezygapophysis. rial properties affected the external distribution of stress
The location and value of the peak stresses were used in UALVP 16247 slightly; there was an increase in ten-
to estimate a force for an analysis of a single vertebra sile stress at the cranial of the right major osteoderm.
from the UALVP 47273 knob þ vertebrae model (Fig. 6, Two-dimensional models of UALVP 16247 (Fig. 7, Table
Table 8). A 200 N force was applied to several nodes on 10) had higher strain values in the inner low density
the left lateral side of the neural spine, with the force areas of the osteoderms, compared to the outer cortex, in
directed medially at approximately right angles to the models lacking a keratinous sheath. When a keratinous
neural spine. This is consistent with the orientation of sheath was modeled, strain was localized to the kerati-
the stress vectors in the knob þ vertebrae model, where nous layer at the site of impact and strain values were
the craniocaudally-oriented stress vectors in the right reduced in the bone.
prezygapophyses arc mediolaterally at the location
where the preceding neural spine would have inter-
locked with the prezygapophyses. Stress vector orienta-
DISCUSSION
tion in the isolated vertebra model was consistent with Bone is most likely to fail as a result of shear stress.
that seen in the knob þ vertebrae model, confirming an Human femoral cortical bone can withstand shear stress
appropriate force direction. Compressive stress was con- of 50 MPa longitudinally (with the grain) and 65 MPa
centrated where the model was loaded, but became ten- (across the grain), although bone actually appears to fail
sile abruptly, cranial to the load. Peak stress was 2.389 in tension when subjected to transverse shear (Turner1422 ARBOUR AND SNIVELY Fig. 6. Results from Analyses 4 and 5 show that varying the con- unconstrained, stress contour plots in (D) cranial view, 125 to straint and direction of load affects stress distributions. Arrows sum- 125 MPa; and oblique left dorsolateral view (G) 50 to 50 MPa, (H) marize stress vectors, and arrowheads indicate the direction and 25 to 25 MPa; stress vector plot in oblique left dorsolateral view, location of load. Positive values are tension, and negative values are 125 to 125 MPa. UALVP 47273 knob þ vertebrae, knob weight, compression. UALVP 47273 knob þ vertebrae, impact force, centrum stress contour plot in (I) dorsal view, 15 to 15 MPa, (L) cranial view, constrained, stress contour plots in oblique left craniolateral view (A) 15 to 15 MPa; (O) stress vector plot in left lateral view, 125 to 100 to 100 MPa, (B) 25 to 25 MPa; (C) cranial view, 100 to 100 125 MPa. UALVP single vertebra, impact force, centrum uncon- MPa; and oblique left dorsolateral view (E) 100 to 100 MPa, (F) 25 strained, 250 to 250 MPa, in (J) dorsal view, (K) oblique left dorsolat- to 25 MPa. UALVP 47273 knob þ vertebrae, impact force, centrum eral view, and (M) 250 to 250 MPa, cranial view.
ANKYLOSAUR TAIL CLUB IMPACTS 1423
TABLE 8. Peak stresses in Analysis 3, examining the effects of different constraints
Maximum stress (MPa)
Impact
Model force (N) Constraint XX YY ZZ XY YZ ZX
UALVP 47273 570 Centrum, prezygapophyses, 175 64 39 13 15 8
knob þ vertebrae haemal spine
UALVP 47273 570 Prezygapophyses, 216 103 50 21 15 129
knob þ vertebrae haemal spine
UALVP 47273 200 Prezygapophyses, 2,389 1,297 1,443 754 110 247
single vertebra haemal spine
Tensile stress is positive, and compressive stress is negative. X is mediolateral, Y is dorsoventral, and Z is craniocaudal.
TABLE 9. Peak stresses in Analysis 4, comparing the effects of weight and differing constraints in
ROM 788 and UALVP 47273
Maximum stress (MPa)
Impact
Model force (N) Constraint XX YY ZZ XY YZ ZX
ROM 788 1,029 Centrum, Prezygapophyses 269 249 505 7 48 2
UALVP 47273 39 Cranial handle 22 25 35 1 9 1
UALVP 47273 39 Prezygapophyses, haemal spine 5 12 4 3 11424 ARBOUR AND SNIVELY
Fig. 7. Differing material properties slightly change the distribution properties of cancellous bone. UALVP 47273 isolated vertebra with
of stresses within the models, and a hypothetical keratinous covering two material properties, oblique left craniolateral view: (E) stress con-
reduces strain within the knob. UALVP 47273 with simulated kerati- tour plot (600 to 600 Pa) of results of mesh (F) with neural and hae-
nous covering, oblique left lateral view: (A) stress contour plot of mal arches assigned properties of compact bone and the centrum
results (150 to 150 MPa) of (B) mesh resulting from material property assigned properties of cancellous bone. (G) UALVP 16247, transverse
assignment in Mimics, where dark blue is assigned the material prop- section at approximately the midlength of the knob, first principal
erties of keratin and all other colors are assigned the properties of strain results using COMSOL Multiphysics, with an outer compact
cancellous bones. UALVP 16247 with two material properties, oblique zone, inner cancellous zone, and simulated keratinous covering over
left craniolateral view: (C) stress contour plot of results (50 to 50 the left osteoderm. Arrowhead indicates location and direction of load.
MPa) of (D) mesh where greens and blues are assigned the properties Tensile stresses are positive, compressive stresses are negative.
of compact bone and reds, yellows and oranges are assigned the
TABLE 10. Peak stresses in Analysis 5, examining the effects of different material properties
Maximum stress (MPa)
Model Impact force (N) Materials XX YY ZZ XY YZ ZX
UALVP 16247 960 All cancellous 1,073 837 1,308 74 180 298
960 Compact and cancellous 206 175 233 7 7 44
UALVP 47273 570 All cancellous 1,368 1,215 2,758 115 748 168
570 Compact, cancellous, with 809 833 1,220 227 230 238
keratinous sheath
UALVP 47273 200 Compact and cancellous 688 110 292 468 272 474
single vertebra
Tensile stress is positive, and compressive stress is negative. X is mediolateral, Y is dorsoventral, and Z is craniocaudal.
the junction of the prezygapophyses. Even though the The idealized model of UALVP 47273 was valuable for
medial faces of the prezygapophyses were constrained, cross-validation with analyses of the fossil-based origi-
stress values were generally lower than the 100 MPa nal. The similarity of their overall stress distributions
required to break bone in shear. suggests that distortion in UALVP 47273 did notANKYLOSAUR TAIL CLUB IMPACTS 1425
preclude interpretation of such results from this model, material properties, magnitude of force, and area of impact
and that simplified models can be informative even in size in the 3D analyses only changed the peak stress mag-
the case of complex analyses (Snively et al., 2006). Varia- nitude. Changes in the location of impact altered the dis-
tion between their results was also instructive. The sim- tribution of stress, and loading the models for impact force
plified model smoothed out breaks in the original versus weight altered the distribution of stress as well.
specimen, which eliminated some uninformative concen- Keeled knob osteoderms can reduce the impact area
trations of stress. However, the simple model was less during a tail club impact, which both reduces overall
realistically informative about effects of anatomical stress within the tail club and increases the stress on
details. We had not incorporated ossified tendons into the impacted object. A keratinous sheath over the keel
the coronal template, which resulted in a narrower han- may have helped to reduce strain within the knob, as
dle and higher compressive and tensile stresses from lat- keratin is tougher and more resistant to cracking than
eral bending. Also, the simple model missed stress bone (Ashby et al., 1995) Two-dimensional models of
concentrations, and potential adaptations for resilience, UALVP 16247 confirmed that even a thin layer of kera-
at articulations like those of the neural arch. tin could have greatly reduced strain within the cancel-
The components of the neural arch are arranged to lous bone of the knob. A keratinous sheath may have
resist lateral bending. The prezygapophyses are long been important for preventing damage to the underlying
and tall, and do not dorsally overlap the neural spine of bone during impacts.
the preceding vertebra. In ROM 788, tensile stress was Although peak stress values suggest that tail clubs
concentrated at the cranial edges of the prezygapophyses may have failed during impacts, a closer inspection of
on the impact side. In the model, these edges are fused several models indicates that most were probably able
to the handle. In reality, there is some space between to withstand forceful impacts. Stress values below
the prezygapophyses and neural spine of successive ver- 100 MPa immediately adjacent to the peak stress in the
tebrae, which would have allowed for a small amount of most accurate models (UALVP 16247, UALVP 47273
flexibility, and tensile stress may not have concentrated knob þ vertebrae, and UALVP 47273 isolated vertebra)
in this location. However, stress at this location in the provide further support that at least small and average-
model suggests that soft tissues in this area (possibly sized tail clubs were unlikely to fail from the impact
associated with Mm. interarticulares superiores), may forces calculated in Arbour (2008). Large tail clubs may
have experienced greater tensile stress than elsewhere have been at risk of failure during impacts. This suggests
between the prezygapophyses and neural spines. that 1) Euoplocephalus did not engage in hypothesized
Peak stresses in ROM 788 are very large, and stresses tail-swinging behavior, 2) Euoplocephalus did engage in
adjacent to the element with peak stress are still greater this behavior, but did not impact with as much force as
than that required to break bone in shear. Additionally, suggested in Arbour (2008), or 3) flexibility in the crania-
an area of concentrated stress (650 MPa) was observed lend part of the tail and within the handle may have
near the knob. A similar concentration of stress was not played an important role in preventing fracture of the tail
observed in the smaller tail clubs, and this stress may club, which is not modeled easily in the FEA used in this
be a result of the size difference between the knobs and study. In the future, more sophisticated finite element
calculated impact forces. Very large tail clubs, if impact- modeling, incorporating flexible constraints at the cranial
ing with the maximum force, may have been in danger end of the handle, and flexibility within the handle, could
of fracture. If the tail club was used for forceful impacts, provide additional insight into the mechanics of ankylo-
then individual animals with very large knobs may not saurid tail club strikes, and additional evidence for or
have attempted to achieve maximum impact forces dur- against this hypothesized behavior.
ing tail swings.
FEA simulating the weight of the club resulted in
ACKNOWLEDGEMENTS
peak stresses lower than that required to break bone in
UALVP 47273 (which has a small knob), and TMP The authors thank P. Currie (UALVP) for the opportu-
83.36.120 and UALVP 16247 (which have average-sized nity to conduct this research and for his supervision and
knobs). Tail clubs with small and average-sized knobs advice. M. Caldwell, A. Murray, A. Wolfe, and E. Koppel-
would not have been in danger of failure from weight hus (UALVP) also provided advice and support during
alone. However, peak stress values in ROM 788 were the course of this project. The authors wish to thank the
somewhat more than is required to break bone. As in following for access to and assistance at their respective
the other analyses, peak stresses were located within institutions: C. Mehling (AMNH), K. Shepherd and M.
the constraint, and stress values decreased greatly im- Feuerstack (CMN), D. Evans and B. Iwama (ROM), and
mediately adjacent to the peak stress, to under 50 MPa. J. Gardner and B. Strilisky (TMP). M. James, G. Pinto,
Tensile stress along the dorsal surface of the handle, P. Bell and A. Lindoe prepared specimens at UALVP. CT
and compressive stress along the ventral surface, was no scanning at the University of Alberta ABACUS facility
more than 15–17 MPa, which is far lower than that was made possible by R. Lambert and G. Schaffler. CT
required to break bone in tension or compression. None scanning of ROM 788 at CML Healthcare was made pos-
of the tail clubs were likely to fracture under their own sible by T. Ladd, and VMA thanks D. Evans and B.
weight, including ROM 788. Iwama (ROM) for their assistance and permission to
Porro (2008) found that material properties and force scan the specimen. The authors also thank J. Li and M.
did not change the distribution of stress within the skull of Lawrenchuck (Materialise) for technical assistance with
Heterodontosaurus, and only changed the magnitude of Mimics, and to Anne Delvaux (Beaufort Analysis, Inc.)
the maximum stress. However, the direction of force for assistance with Strand7. H. Mallison (Museum für
changed the distribution of stress within the skull. This is Naturkunde, Berlin) provided advice on digital imaging
also true for the ankylosaurid tail clubs: changes to the of fossils. VMA thanks M. Burns and R. Sissons1426 ARBOUR AND SNIVELY
(UALVP) for many excellent discussions on ankylosaur McNeelNorth America. 2007. Rhino 4.0. Seattle, Washington, USA.
biology. Comments from P. Dodson, K. Carpenter and Moreno K, Carrano MT, Snyder R. 2007. Morphological changes in
two anonymous reviewers greatly improved the pedal phalanges through ornithopod dinosaur evolution: a biome-
chanical approach. J Morphol 268:50–63.
manuscript.
Organ CL. 2006. Biomechanics of ossified tendons in ornithopod
dinosaurs. Paleobiology 32:652–665.
Peattie AM, Majidi C, Corder A, Jull RJ. 2007. Ancestrally high
LITERATURE CITED elastic modulus of gecko setal b-keratin. J R Soc Interface 4:
Arbour VM. 2008. Evolution, biomechanics, and function of the tail 1071–1076.
club of ankylosaurid dinosaurs (Ornithischia: Thyreophora). M.Sc. Peterson J, Dechow PC. 2003. Material properties of the human
thesis, University of Alberta, Edmonton, Alberta, Canada. cranial vault and zygoma. Anat Rec 274:785–797.
Arbour VM, Sissons RL, Burns ME. A redescription of the ankylo- Porro L. 2007. Feeding and jaw mechanism in Heterodontosaurus
saurid dinosaur Dyoplosaurus acutosquameus parks, 1924 (Orni- tucki using finite element analysis. J Vertebr Paleontol 27:131A.
thischia: Ankylosaur) and a revision of the genus. J Vertebr Porro L. 2008. Accuracy in finite element modeling of extinct taxa:
Paleontol (In Press). sensitivity analyses in Heterodontosaurus tucki. J Vertebr Paleon-
Ashby MF, Gibson LJ, Wegst U, Olive R. 1995. The mechanical tol 28:128A.
properties of natural materials. I. Material property charts. Proc Rayfield EJ. 2004. Cranial mechanics and feeding in Tyrannosaurus
Math Phys Sci 450:123–140. rex. Proc R Soc Lond B Biol Sci 271:1451–1459.
Bonser RHC. 2000. The Young’s modulus of ostrich claw keratin. Rayfield EJ. 2005. Aspects of comparative cranial mechanics in the
J Mater Sci Lett 19:1039–1040. theropod dinosaurs Coelophysis, Allosaurus, and Tyrannosaurus.
Bonser RHC, Purslow PP. 1995. The Young’s modulus of feather Zool J Linn Soc 144:309–316.
keratin. J Exp Biol 198:1029–1033. Rayfield EJ. 2007. Finite element analysis and understanding the
Carpenter K, Sanders F, McWhinney L, Wood L. 2005. Evidence for biomechanics and evolution of living and fossil organisms. Ann
predator-prey relationships: Example for Allosaurus and Stego- Rev Earth Planet Sci 35:541–576.
saurus. In: Carpenter K, editor. The Carnivorous Dinosaur. Bloo- Rayfield EJ, Norman DB, Horner CC, Horner JR, Smith PM, Tho-
minton, IN: Indiana University Press. p 49–71. mason JJ, Upchurch P. 2001. Cranial design and function in a
COMSOL,Inc. 2005. COMSOL Multiphysics. Los Angeles, Califor- large theropod dinosaur. Nature 409:1033–1037.
nia, USA. Reilly DT, Burstein AH. 1975. The elastic and ultimate properties
Coombs WP, Jr. 1971. The Ankylosauria. Ph.D. dissertation, Colum- of compact bone tissue. J Biomech 8:393–405.
bia University, New York, New York, USA. Seki Y, Kad B, Benson D, Meyers MA. 2006. The toucan beak:
Coombs WP, Jr., 1979. Osteology and myology of the hindlimb in structure and mechanical response. Mater Sci Eng 26:1412–1420.
the Ankylosauria (Reptilia, Ornithischia). J Paleontol 53:666–684. Scheyer TM, Sander PM. 2004. Histology of ankylosaur osteoderms:
Coombs WP, Jr., 1995. Ankylosaurian tail clubs of middle Campanian implications for systematics and function. J Vertebr Paleontol
to early Maastrichtian age from western North America, with 24:874–893.
description of a tiny tail club from Alberta and discussion of tail ori- Shychoski L. 2006. A geometric morphometric and finite element
entation and tail club function. Can J Earth Sci 32:902–912. analysis investigating tyrannosauroid phylogeny and ontogeny
Currey JD. 1988. The effect of porosity and mineral content on emphasizing the biomechanical implications of scale. M.Sc. thesis,
the Young’s modulus of elasticity of compact bone. J Biomech University of Bristol, Bristol, United Kingdom.
21:131–139. Shychoski L, Rayfield E, Sakamoto M. 2007. The biomechanics of
Currey JD. 2002. Bones: structure and mechanics. New Jersey: scale: a phylogenetic and ontogenetic investigation of tyranno-
Princeton University Press. saurid dinosaurs using geometric morphometrics and the finite
Erickson GM, Catanese J, Keaveny TM. 2002. Evolution of the biome- element method. J Vertebr Paleontol 27:146A.
chanical material properties of the femur. Anat Rec 268:115–124. Snively E, Cox A. 2008. Structural mechanics of pachycephalosaur
Farke AA, Chapman RE, Andersen A. 2007. Structural properties crania permitted head-butting behavior. Palaeontol Electron
of the frill of Triceratops. Royal Tyrrell Museum Ceratopsian 11(1): 3A:1–17.
Symposium, 22–23 September 2007; Short Papers, Abstracts, and Snively E, Henderson DM, Phillips DS. 2006. Fused and vaulted
Programs. Drumheller, Alberta: Royal Tyrrell Museum. p 44–47. nasals of tyrannosarid dionsaurs: implications for cranial strength
Franck A, Cocquyt G, Simoens P, De Belie N. 2006. Biomechanical and feeding mechanics. Acta Paleontol Pol 51:45–454.
properties of bovine claw horn. Biosyst Eng 93:459–467. Snively E, Russell A. 2002. The tyrannosaurid metatarsus: bone
Lambe LM. 1910. Note on the parietal crest of Centrosaurus aper- strain and inferred ligament function. Senckenbergiana Lethaea
tus and a proposed new generic name for Stereocephalus tutus. 82:35–42.
Ott Nat 14:149–151. Strait DS, Wang Q, Dechow PC, Ross CF, Richmond BG, Spencer
Maidment S, Porro L. 2007. Homology and function of the ornithi- MA, Patel BA. 2005. Modeling elastic properties in finite-element
schian dinosaur palpebral. J Vertebr Paleontol 27:111A. analysis: how much precision is needed to produce an accurate
Maleev EA. 1952. A new ankylosaur from the Upper Cretaceous of model? Anat Rec 283A:275–287.
Asia. Dokl Akad Nauk SSSR 87:273–276 [In Russian]. Strand7Pty Ltd. 2008. Strand7. Sydney, Australia.
Maleev EA. 1954. The armored dinosaurs of the Cretaceous Period Turner CH, Wang T, Burr DB. 2001. Shear strength and fatigue
in Mongolia (Family Syrmosauridae). Work Paleontol Inst Acad properties of human cortical bone determined from pure shear
Sci USSR 48:142–170 [In Russian; translation by Robert Welch]. tests. Calcif Tissue Int 69:373–378.
Manning P, Ali J, McDonald S, Mummery P, Sellers W. 2007. Vickaryous MK, Maryanska T, Weishampel DB. 2004. Ankylosauria.
Biomechanics of dromaeosaurid claws: application of X-ray In: Weishampel DB, Dodson P, Osmolska H, editors. The Dinosau-
microtomography, nanoindentation and finite element analysis. ria, 2nd ed. Berkeley, California: University of California Press.
J Vertebr Paleontol 27:111A. p 363–392.
Materialise.2008. Mimics Version 12. Leuven, Belgium. Wirtz DE, Schiffers N, Pandorf T, Radermacher K, Weichert D,
Mazzetta GV, Cisilino AP, Blanco RE. 2004. Mandible stress distriu- Forst R. 2000. Critical evaluation of known bone material proper-
bution during the bite in Carnotaurus sastrei Bonaparte, 1982 ties to realize anisotropic FE-simulation of the proximal femur.
(Theropoda, Abelisauridae). Amehiniana 41:605–617. J Biomech 33:1325–1330.You can also read
