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Finite Element Analyses of Ankylosaurid Dinosaur Tail Club Impacts.

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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 tomography 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 averagesized knobs were unlikely to fail during forceful impacts, but large clubs
may have been at risk of fracture cranial to the knob. The modified handle 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 supC 2009 Wiley-Liss,
port this hypothesis. Anat Rec, 292:1412–1426, 2009. V
Inc.
Key words: Ankylosauria; Euoplocephalus; biomechanics; finite
element analysis; functional morphology; palaeobiology
INTRODUCTION
Ankylosaurs were large, quadrupedal ornithischian
dinosaurs with extensive dermal ossifications on the
head, body, and tail (Vickaryous et al., 2004). Ankylosaurids had highly modified distal caudal vertebrae
forming a handle that, along with terminal osteoderms
(the knob), formed a club-like structure (Fig. 1; terminology after Coombs, 1995). Several authors (Maleev, 1952,
1954; Coombs, 1971, 1979, 1995) have suggested that
the tail was used as a defensive weapon. Tail club
impact forces vary depending on the size of the knob,
and large Euoplocephalus tutus (Lambe, 1910) knobs
could impact with a force sufficient to break bone in
shear (Arbour, 2008). Could Euoplocephalus tail clubs
withstand these impact forces without fracturing? How
were stress and strain dissipated throughout the club? If
the vertebrae or knob osteoderms fractured under normal impact forces, this would suggest that the primary
purpose of the knob was not for delivering forceful
blows.
C 2009 WILEY-LISS, INC.
V
These questions about ankylosaurid tail function are
testable through finite element analysis (FEA). FEA is a
powerful tool for understanding the biomechanics of
extant and extinct organisms through modeling of
stress, strain, and deformation in anatomical structures.
Grant sponsors: NSERC PGS-M, Alberta Ingenuity
Studentship, Alberta Ingenuity Postdoctoral Fellowship,
University of Alberta Graduate Students Association,
Department of Biological Sciences (University of Alberta),
Dinosaur Research Institute, Canada Foundation for Innovation,
Jurassic Foundation.
*Correspondence to: Victoria M. Arbour, Department of Biological Sciences CW 405 Biological Sciences Centre, University
of Alberta, Edmonton, Alberta, Canada T6G 2E9. E-mail:
arbour@ualberta.ca
Received 9 June 2009; Accepted 9 June 2009
DOI 10.1002/ar.20987
Published online in Wiley InterScience (www.interscience.wiley.
com).
1413
ANKYLOSAUR TAIL CLUB IMPACTS
TABLE 1. Material examined
Taxon
Specimens examined
Euoplocephalus
tutus
AMNH 5211, AMNH 5245, AMNH 5337,
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 catalogue information and previously published identifications.
Fig. 1. Diagram of tail club terminology used in this paper. Threedimensional digital reconstruction of UALVP 47273 in Mimics based
on computed tomography scans, in (A) dorsal, (B) ventral, and (C)
right lateral views. Scale bar equals 10 cm.
Rayfield (2007) provides an overview of the finite element method and its uses in palaeontology. Stress (force/
area) is simulated in a modeled structure when a force
(load) is applied; tensile stresses are, by convention, represented by positive values, and compressive stresses by
negative values. Strain is the change in length after a
load is applied divided by the original length of a
structure.
FEA of dinosaur fossils has predominantly dealt with
theropod skulls (Rayfield, 2001; Mazzetta et al., 2004;
Rayfield, 2004, 2005; Rayfield et al., 2007; Shychoski et
al., 2007), with fewer studies on ornithischian skull
mechanics (Farke et al., 2007; Maidment and Porro,
2007; Porro, 2007; Snively and Cox, 2008). Analyses of
the postcranial skeleton are rarer, and have included the
metatarsus of a tyrannosaurid (Snively and Russell,
2002), dromaeosaurid claws (Manning et al., 2007), and
ossified tendons (Organ, 2006) and pedal morphology
(Moreno et al., 2007) of ornithopods. This is the first
study to use FEA to investigate biomechanics in ankylosaurs. Four ankylosaurid tail clubs referred to Euoplocephalus tutus are examined to understand the
distribution and magnitude of stresses within the club
under simulated impact conditions. If stress magnitudes
within the modeled clubs are greater than necessary to
fracture bone, then tail clubs were not likely used as
weapons. Distributions of stresses provide information
on the function of the handle and knob.
MATERIALS AND METHODS
Computed Tomography
Four ankylosaurid tail clubs (Tables 1 and 2) were
scanned using computed tomography (CT), to derive
three-dimensional models for use in FEA (Fig. 2).
UALVP 47273 has a small knob and much of the handle
preserved. UALVP 16247 and a cast of TMP 83.36.120
are average-sized knobs; TMP 83.36.120 does not preserve much of the handle, and UALVP 16247 lacks a
handle completely. ROM 788 has the largest knob
TABLE 2. Institutional abbreviations
AMNH
CMN
ROM
TMP
UALVP
American Museum of Natural History,
New York, New York, USA
Canadian Museum of Nature, Ottawa,
Ontario, Canada
Royal Ontario Museum, Toronto,
Ontario, Canada
Royal Tyrrell Museum of Palaeontology,
Drumheller, Alberta, Canada
University of Alberta Laboratory for
Vertebrate Paleontology, Edmonton,
Alberta, Canada
referred to Euoplocephalus and also includes most of the
handle. UALVP 47273, UALVP 16247, and TMP
83.36.120 were scanned at the University of Alberta
Hospital Alberta Cardiovascular and Stroke Research
Centre (ABACUS), on a Siemens Somatom Sensation 64
CT scanner, at 1 mm increments. ROM 788 was scanned
at CML Healthcare Imaging in Mississauga, Ontario, at
2 mm increments, and as two separate scans (the knob
and the handle).
Three-Dimensional Modeling and Meshing
CT scans were used to create 3D models for use in
FEA (Fig. 2). The computer program MimicsV (Materialise) was used to create a 3D model and mesh for each
specimen, and to apply material properties to each
mesh. A mask over the desired portion of the scan is created using the thresholding function. Each slice is manually edited using the ‘‘multiple slice edit’’ function to
both add and remove mask, to fill in cracks in the specimen and remove artifacts and unwanted parts of the
scan (including the scanning bed and specimen support
jackets). A 3D model was then calculated and inspected
for artifacts. A 3D mesh of hexahedral elements was created in Mimics and exported as a NASTRAN (.nas) file.
The default settings in Mimics produce a mesh with too
many elements, which will not work properly in the
FEA software Strand7V [Strand7 (Strand7 Pty) deals
well with meshes of 1 million elements or less]. The
mesh size is reduced by grouping voxels in the xy and z
R
R
1414
ARBOUR AND SNIVELY
Fig. 2. Models used in this study. UALVP 47273 in (A) oblique left
dorsolateral and (B) caudal view. UALVP 16247 in (C) dorsal, (D) caudal, and (E) left lateral view. TMP 83.36.120 in (F) oblique dorsal, (G)
left lateral, (H) ventral, and (I) caudal. ROM 788 in (J) oblique dorsal,
(K) ventral, (L) caudal, and (M) left lateral view. The lateral edges of
the knob were excluded from the scan; photos of the specimen are
overlain in (K) and (L) to show the missing portions. Ridges on the
knob in (J) and (K) are artifacts resulting from poor scan quality and
manual editing in this region. All images created in Mimics from computed tomography scans. Photograph in (L) by R. Sissons and used
with permission. Scale equals 10 cm.
1415
ANKYLOSAUR TAIL CLUB IMPACTS
TABLE 3. Material properties used in analyses
Density
(kg/m3)
Young’s
modulus (Pa)
Poisson’s
ratio
Compact bone
2000
20e9
0.4
Cancellous bone
1000
8e9
0.4
Keratin
1300
2.5e9
0.4
dimensions; this results in a loss of fine surface features,
such as the knob osteoderm texture, but the model is
still an accurate representation of specimen geometry.
Once a mesh has been created, material properties can
be assigned. Mimics calculates Hounsfield density values
of the CT images and displays these as a histogram.
Materials can be automatically specified from the density values, and material properties can be manually
entered (a better practice with matrix-filled fossils). The
mesh is then exported as a .nas file for use in Strand7.
ROM 788 was scanned in two pieces, and the data
from the two CT scans were combined to make a single
model for FEA. Both CT scans were cleaned in Mimics
as for the other models. Each model was exported as a
surface stereolithography (.stl) file and imported into a
Mimics project file. The .stl models were aligned appropriately and then joined using the Boolean Unite function in the Segmentation module. The united model was
then decimated using the reduce triangles, smooth, and
remesh functions in the Mimics Remesher. This
remeshed, united model was then imported into
Strand7. The missing lateral edges of each major osteoderm, which were outside of the field of view of the CT
scanner, could not be reconstructed. No additional meshing is needed for models in .nas format, but the model of
ROM 788 required additional automatic and manual
cleaning in Strand7 to remove triangles with free edges.
The surface mesh was then converted to a solid mesh.
The tail clubs subjected to FEA were variably complete
and taphonomically distorted, inevitable with most fossil
specimens. We therefore checked them against results
for an idealized replica of a club (UALVP 47273) based
on simple geometric forms. Deviations from the simplified model were evaluated as possible preservationinduced stress artifacts, versus those arising from anatomical details not captured in the simple FEM. UALVP
47273 was bent taphonomically into a dorsally concave
arc, but was otherwise undistorted dorsoventrally. As
the basis for a straightened model, we traced a dorsal
photograph of the club in Adobe IllustratorV (Rayfield,
R
Notes
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)
Density: Human 0.1-0.7 (Wirtz et al., 2000)
Young’s modulus: Human 774
(Peterson and Dechow, 2003)
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)
2004, 2005; Snively and Cox, 2008), and imported the
coordinates into RhinoV (McNeel North America, 2007).
We used this outline as the coronal perimeter of the
idealized model. The geometric model consisted of elliptical cylinders for the handle (centra plus neural arches,
and haemal arches), and ellipsoids for the flanking proximal and collective distal knob osteoderms. The shapes
were combined into one model and exported as a .stl file
into Mimics. We used the Mimics Remesher to reconstitute the .stl surface mesh into uniform triangles, and to
create a volumetric tetrahedral mesh.
This simplified mesh was imported as a .nas file into
Strand7, where we applied material properties, constraints, and forces for Analysis 1 described below. Analyses were successful on the model initially imported into
Strand7, but scaling it to accommodate unit variance
between Rhino and Strand7 resulted in mesh anomalies
and solution failure. This required scaling stress results
of the successful analysis. Stress is inversely proportional to the square of linear dimensions. We therefore
multiplied the simple model’s stress results by the
square of the ratio between maximum widths across the
osteoderms, in the simple Strand7 mesh and original
club. The dimensions of the geometrically modeled osteoderms were correct, and the calculated stresses were
similar in magnitude to those of the CT-based club
model. We are thus confident that stress scaling yields
accurate results.
R
Analysis-Specific Models, Boundary Conditions,
and Material Properties
We applied material properties, a constraint, and a
load to finite element meshes in Strand7, and then analyzed for both stress and strain results using the linear
solver. Table 3 lists the material properties used in the
different analyses, and Table 4 lists the forces, constraints, and other variables used for each mesh of each
analysis. Estimates of tail club strike forces are from
Arbour (2008), and follow a method for estimating tail
1416
ARBOUR AND SNIVELY
TABLE 4. Summary of forces (N) used in analyses
Analysis
1
2
3
4
5
ROM
788
TMP
83.36.120
UALVP
16247
UALVP
47273
UALVP 47273
knob þ vertebrae
UALVP 47273
isolated vertebra
10,160
–
10,160
–
–
1,029
–
–
960
–
960
–
960
–
–
–
–
960
570
1,127
570
570
39
126
1,029
570
–
–
–
570
39
–
–
–
–
–
–
200
–
–
–
200
–
–
–
–
–
tip angular velocity from Carpenter et al. (2005). Von
Mises stress results were displayed both as 3D surface
plots, and as 2D cross-sections at various locations
within the specimen. Strand7 can produce colored contour and vector plots; tensile stresses are positive values,
and compressive stresses are negative values.
Each specimen provides different benefits and limitations for analysis. UALVP 47273 is a relatively complete
specimen, and allows for analysis of the knob and handle together. However, a mesh of less than 5 million elements does not show the details of the individual neural
and haemal arches. To better reveal stress distribution
in these structures, a smaller model was created by
removing all but the last two of the visible handle vertebrae and the knob. The original scan of UALVP 47273
was edited slice by slice in Mimics to model details of
the penultimate visible vertebra, and to remove the
proximal elements. In this manner, an impact force
could be applied to the knob, and details of stress distribution observed in the handle vertebrae. Appropriate
forces could then be applied to a single vertebra isolated
from the handle in the same manner. Additionally,
UALVP 47273 represents a small knob morphology
which is not representative of most ankylosaurid knobs.
ROM 788 is the largest specimen in this study, but the
handle and knob are separate elements, and the lateral
sides of the knob osteoderms were not included in the
CT scan. UALVP 16247 is an isolated knob, but represents the average knob size in Euoplocephalus, and the
CT scan of this specimen had few artifacts. As such, the
effects of differing bone densities and material properties
were best analyzed in this specimen. The cast of TMP
83.36.120 cannot be used to examine material properties, but can be compared with the similarly-sized
UALVP 16247. To examine different aspects of club mechanical response to impacts, we conducted five analyses
with varying boundary conditions.
Analysis 1. Three specimens with different knob
sizes were used to examine the effect of knob size and
impact force on tail clubs. For each model, the cranial
face of the centrum of the most cranially located part of
the handle was constrained. A force was applied to both
a small and large area at approximately the midheight
and midlength of the left major osteoderm of each knob.
This force was oriented at right angles into the osteoderm. The impact force for each knob was applied to
each node in both the small and large impact area analyses. This is reasonable because impact velocity and
force would not vary greatly over the larger area of con-
tact. For this analysis, the knobs were assigned uniform
material properties of cancellous bone. We applied the
same material properties and constraints to the simplified model as those for the CT-based FE model.
Analysis 2. Impacts did not necessarily always occur
at the same location on the tail club. Impacts were simulated on the handle just cranial to the knob, and on the
distal end of the knob, to understand how stress distribution changes as impact site changes. The most realistic force was used for both ROM 788 and UALVP 47273,
and the meshes were given the material properties of
cancellous bone.
Analysis 3. As explained earlier, two models were
constructed from the CT scan of UALVP 47273 to examine stress details on individual handle vertebrae. First,
the knob and two preceding handle vertebrae were isolated and meshed as the ‘‘knob þ vertebrae’’ model. In
Strand 7, a force was applied at the midlength and midheight of the left lateral osteoderm, as for Analysis 1.
The model was constrained at the cranialmost vertebra,
on the medial faces of the prezygapophyses, the cranial
face of the centrum, and the medial sides of the cranial
projection of the haemal spine. Results of the stress distribution in these models were then applied to a second
model of a single handle vertebra (‘‘single vertebra’’
model), which was also manually isolated and meshed in
Mimics. Properties of cancellous bone were applied to
the model. To simulate a tail club with unfused centra,
an additional analysis, where the centrum was not constrained, was conducted for both the knob þ vertebrae
and isolated vertebra models.
Analysis 4. The unusually robust haemal arches of
ankylosaurid tail clubs may play a role in postural support of the large knob. Impact forces are assumed to be
directed in the horizontal plane, but gravity would also
act to pull downward on the tail club. Coombs (1995)
noted that ankylosaurids probably did not drag their
tails on the ground, although the tail may not have been
held very high off of the ground. The weight (Table 5) of
each knob is calculated using the volumes and masses in
Arbour (2008), multiplied by gravitational acceleration
(9.81 m/s2). UALVP 47273 is the only specimen in this
study that preserves the knob and handle together. Handle vertebrae become moderately larger as knob size
increases, but the two are not linearly correlated
(Arbour et al., in press). As such, it is reasonable to
apply the forces and torques derived for each knob
ANKYLOSAUR TAIL CLUB IMPACTS
TABLE 5. Weights of specimens used in
Analysis 4 (volumes and masses from Arbour, 2008)
Specimen
ROM 788
UALVP 16247
UALVP 47273
Knob
volume (cm3)
Knob
mass (kg)
Force
(N)
53007.00
6,486.17
2,008.32
104.95
12.84
3.98
1,029.56
126.00
39.01
(UALVP 47273, UALVP 16247, and ROM 788) to the
model of UALVP 47273, for the purposes of comparing
large and small knob weights. UALVP 47273 was constrained at the cranial face of the cranialmost vertebra,
and the force was applied to a single node at a point ventral to the estimated centre of mass of the knob. To investigate the distribution of stress within a single vertebra,
this force was also applied to the knob þ vertebrae model.
Analysis 5. Knob osteoderms have regions of high,
medium, and low density, which may affect the distribution of stress and strain throughout the club. Strait et
al. (2005) found that elastic properties affect quantitative strain data in finite element analyses, although
overall strain patterns are similar using different elastic
properties. Precise material properties for ankylosaur
bone cannot be known. However, a range of different
properties from various taxa were used to estimate material properties in tail clubs (Table 3).
Regions of differing density were calculated using
Mimics for the knob of UALVP 16247 and an isolated
handle vertebra of UALVP 47273. UALVP 16247 was
loaded over a small area on the left lateral osteoderm, as
for Analysis 1, and UALVP 47273 was loaded on the
neural spine as for Analysis 3.
Knob osteoderms were likely covered by a keratinous
sheath in life. Snively and Cox (2008) showed that the relative thickness of a horny covering on pachycephalosaur
domes would have greatly influenced the distribution and
magnitude of stresses within the osseous dome. To simulate the effects of a keratinous sheath, a new mask was
created for UALVP 47273 in Mimics. The outline of a thin
keratinous sheath was traced for each slice of the knob
osteoderms and added to the overall mask, and the grayscale values in the resulting model were assigned material properties for cancellous bone and keratin.
Additional analyses were conducted using two-dimenR . The outline of a transsional models in MultiphysicsV
verse section through the knob of both UALVP 16247
was traced, as well as areas of low density in each osteoderm, and hypothetical keratinous coverings on each
osteoderm. These coordinate outlines were exported as
CAD .dxf files, imported into Multiphysics, coerced to
solid, and assigned material properties as per the 3D
models. The section models were constrained at the dorsal and ventral borders of the centrum (equivalent to
the midline of the knob) and loaded as for the 3D
models.
RESULTS
Analysis 1: Effect of Knob Size and
Impact Force
In all of the models, stresses were greatest at the constraint and at the impact site (Figs 3–5; Table 6). Stress
1417
was also concentrated in some locations that correspond
to breaks in the specimens, and is not biologically meaningful. Peak stress was over 1,000 MPa in all models,
and was greater in larger knobs and when impact force
was applied to a larger area. Stress values decreased
rapidly away from the peak stress, sometimes by several
orders of magnitude. Peak stress was always oriented
craniocaudally, not mediolaterally or dorsoventrally. In
all specimens, the maximum stress values always represented tensile, rather than compressive, stress.
In UALVP 47273 (Fig. 3, Table 6), tensile stress was
found from the impact site to the distal terminus of the
left half of the knob. Tensile stress was also particularly
high between the cranial terminus of the left major knob
osteoderms and the handle, whereas compressive stress
was found in the same location on the right side of the
tail club. Maximum stress was found within the constrained area of the handle, and minimum stress was
found distal to the impact site on the knob. The magnitude of the impact force did not change the distribution
of stress within the club, but did change the absolute
values of the peak stress. Varying the size of the impact
area also changed the absolute values of the maximum
stress. In lateral view, stress vectors were oriented radially from the impact site and lengthwise along the handle. In dorsal view, stress vectors were oriented
transversely across the handle and formed a complex
swirling pattern on the knob around the impact site.
In the idealized model of UALVP 47273 (Fig. 3, Table
6), general stress distribution was nearly identical to
that of the CT based model, yet varied in some details.
Peak stresses occurred in the proximal handle near the
constraint, yet were not particularly high near the
cranial junctures between the lateral osteoderms and
the handle. Stresses along the lateral surfaces of the
proximal handle were somewhat higher than in the CTbased model.
In both TMP 83.36.120 and UALVP 16247 (Fig. 4,
Table 6), compression was found on the left osteoderms
and was greatest at the site of impact, whereas tension
was found on the right osteoderms and near the constraints. Tensile stress was also concentrated at the
boundaries between the major and minor plates. Stress
vectors were oriented radially from the impact sites on
the lateral faces of the osteoderms, craniocaudally on
the left major osteoderms in dorsal view, and mediolaterally on the right major osteoderms in dorsal view. In
cranial view, the stress vectors converged towards the
constraints, forming clockwise swirls.
In ROM 788 (Fig. 5, Table 6), compressive stress was
found at the impact site, with tensile stress immediately
adjacent to the impact site rapidly changing to approximately neutral stress throughout the rest of the osteoderm. Tensile stress was found at the boundary of the
knob osteoderms and handle, with compressive stress concentrated along the midline of the knob dorsally and tensile stress ventrally. Stress vectors radiated from the
impact site and formed a complex, swirling pattern in dorsal view at the knob and cranial view at the constraint.
Stress vectors were oriented craniocaudally along the
handle in lateral view, and mediolaterally in dorsal view.
The cranial face of the handle centrum of ROM 788
experienced tensile stress on the right half and compressive stress on the left half, similar to that observed
in UALVP 47273. The medial face of the right
1418
ARBOUR AND SNIVELY
Fig. 3. Impact stresses in TMP 83.36.120 and UALVP 16247.
Arrows summarize stress vector orientations, and arrowheads indicate
direction and location of load. Positive values are compression, negative values are tension. TMP 83.36.120, (A) stress vector plot (75 to
75 MPa), dorsal view, and (B) stress contour plot (50 to 50 MPa),
oblique caudosorsal view. UALVP 16247, (C) stress vector plot (75 to
75 MPa), dorsal view, and (D) stress contour plot (30 to 30 MPa),
oblique caudosorsal view.
ANKYLOSAUR TAIL CLUB IMPACTS
1419
Fig. 4. Results from a simplified model of UALVP 47273 match
closely with the CT-based model. Positive values are compression,
negative values are tension. UALVP 47273 in oblique left dorsolateral
view, showing that differences in impact location affect stress distributions. Stress range in A is 155 to 155 MPa, in B is 300 to 300
MPa, in C, E, and G is 75 to 75 MPa, and in D, F, and H is 500 to
500 MPa. Impact at midlength of knob, in (A) simplified model, stress
contour plot, (B) simplified model, stress vector plot, (C) CT model
stress vector plot, and (D) CT model, stress vector plot. Impact on
handle cranial to knob, (E) stress contour plot, and (F) stress vector
plot. Impact on distal tip of knob, (G) stress contour plot, and (H)
stress vector plot.
prezygapophysis experienced tension, and the lateral
face experienced compression; the reverse was found in
the left prezygapophysis. Tensile stress was also found
within bone surrounding the neural canal. Along the
handle, tensile stress was found at the cranial edges of
the prezygapophyses on the right side. An area of concentrated tensile stress (600 MPa) was present on the
right side of the handle 5 cm cranial to the knob (Fig.
5). The haemal arch experienced neutral stress for much
of its length, with increasing tensile stress near the
constraint.
are oriented mediolaterally, and in lateral view they are
oriented dorsoventrally.
An impact near the distal tip of the knob results in
stress vectors oriented craniocaudally in lateral view of
the knob and handle, and mediolaterally in dorsal view.
The distribution of stress along the handle did not
change, and shifted distally in the knob. Tensile stress
radiated cranially through the left half of the minor
plates, and compressive stress did the same on the right
half.
Analysis 2: Impact Site Analysis
Analysis 3: Stress Distributions in the
Handle Vertebrae
Altering the location of the impact site did not change
the distribution of stresses near the constraint in
UALVP 47273 (Fig. 3, Table 7). Impacts to the handle
resulted in almost zero stress within the knob. Peak
stress did not greatly increase or decrease based on
impact location, and was always found within the constraint. Stress vectors radiate from the impact site on
the handle. In dorsal view, stress vectors on the knob
Peak stress values were higher in the UALVP 47273
knob þ vertebrae model with only the prezygapophyses
and haemal arch constrained, in comparison to the
model with the centrum, prezygapophyses and haemal
arch constrained (Fig. 6, Table 8). However, in the constrained prezygapophyses and haemal arch model, the
decrease in stress adjacent to the peak stress (to less
than 100 MPa) was greater than in the constrained
1420
ARBOUR AND SNIVELY
Fig. 5. Stress is concentrated cranial to the knob and at the cranial
borders of the prezygapophyses in ROM 788. (A) Stress contour plot
(150 to 150 MPa), oblique right lateral view, with stress concentration
indicated by open-headed arrow. (B) Stress contour plot (60 to
60 MPa), left lateral view, three examples of high tensile stress at
prezygapophyses indicated by open-headed arrows. (C) Stress vector
plot (1500 to 1500), cranial view, stress orientations summarized by
closed-headed arrows, load indicated by arrowhead. Positive values
are compression, negative values are tension.
TABLE 6. Peak stresses in Analysis 1, examining large and small impact areas
Model
ROM 788
TMP 83.36.120
UALVP 16247
UALVP 47273
UALVP 47273
simple model
Maximum stress (MPa)
Impact
force (N)
Impact
area
XX
YY
ZZ
XY
YZ
ZX
10,160
10,160
1,000
960
960
1,420
1,420
570
570
1,127
1,127
570
Small
Large
Small
Small
Large
Small
Large
Small
Large
Small
Large
Small
9,150
103,426
587
1,073
11,547
1,668
16,841
1,368
21,295
2,127
40,750
641
8,264
93,388
383
837
9,126
1,316
13,310
1,215
18,893
1,874
36,151
416
16,351
184,760
695
1,308
14,238
2,055
20,767
2,758
42,961
4,307
82,216
425
385
4,342
49
74
728
106
1,061
115
1,806
186
3,459
100
3,313
37,389
46
180
1,748
256
2,548
748
11,656
1,166
22,308
19.4
1,142
12,979
221
298
3,148
456
4,591
168
2,620
265
5,015
24.5
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
(where stress decreased to around 100 MPa).
Compressive stress was found at the impact site on
the left major osteoderm, dorsally between the left major
osteoderm and handle, and on the right half of the cranial face of the centrum, where the model was constrained (Fig. 6). The midline of the centrum had stress
near zero, approximating a neutral axis. Tensile stress
1421
ANKYLOSAUR TAIL CLUB IMPACTS
TABLE 7. Peak stresses in Analysis 2, examining impact location
Maximum stress (MPa)
Model
ROM 788
UALVP 47273
Impact force (N)
Impact location
XX
YY
ZZ
XY
YZ
ZX
10,160
10,160
10,160
570
570
570
Handle
Midlength of knob
Knob distal tip
Handle
Midlength of knob
Knob distal tip
77,776
9,150
39,730
3,569
1,368
2,546
57,925
8,264
35,732
2,914
1,215
2,291
121,921
16,351
70,743
7,463
2,758
5,102
2,587
385
1,566
412
115
201
25,412
3,313
13,887
1,982
748
1,389
13,189
1,142
5,467
487
168
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
major osteoderm and the handle, and on the left half of
the cranial face of the centrum. Within the prezygapophyses, stresses were greater caudally and decreased to
nearly zero at the cranial termini. Changing the constrained area of the model changed the distribution of
stresses within the vertebrae. When only the prezygapophyses were constrained, peak stress occurred on the
caudal part of the right prezygapophysis, within the constrained area. Tensile stress was concentrated below the
right prezygapophysis on the cranial face of the centrum, but dissipated abruptly away from the
prezygapophysis.
Stress vectors in the unconstrained centrum model
were complex (Fig. 6). In dorsal view of the knob, stress
vectors are oriented mediolaterally in the right osteoderm, and in the left osteoderm collectively form a swirling pattern, inclined craniocaudally. In left lateral view,
vectors were oriented caudolaterally along the neural
spine, but became undulate along the prezygapophyses.
Along the centrum, vectors were oriented approximately
craniocaudally, looping ventrally onto the haemal spine.
The cranial projection of the haemal spine had approximately dorsoventrally directed stress vectors. In right
lateral view, stress vectors were oriented dorsoventrally
on the neural spine, right prezygapophysis, centrum,
and caudal portion of the haemal spine. The cranial projection of the haemal spine had approximately laterally
oriented vectors. Dorsally, craniocaudally directed vectors from the left side of the neural spine and haemal
spine arced across the neural arch and haemal arches,
becoming mediolaterally oriented on the right side of
each spine. Stress vectors looped mediolaterally around
the right prezygapophysis.
The location and value of the peak stresses were used
to estimate a force for an analysis of a single vertebra
from the UALVP 47273 knob þ vertebrae model (Fig. 6,
Table 8). A 200 N force was applied to several nodes on
the left lateral side of the neural spine, with the force
directed medially at approximately right angles to the
neural spine. This is consistent with the orientation of
the stress vectors in the knob þ vertebrae model, where
the craniocaudally-oriented stress vectors in the right
prezygapophyses arc mediolaterally at the location
where the preceding neural spine would have interlocked with the prezygapophyses. Stress vector orientation in the isolated vertebra model was consistent with
that seen in the knob þ vertebrae model, confirming an
appropriate force direction. Compressive stress was concentrated where the model was loaded, but became tensile abruptly, cranial to the load. Peak stress was 2.389
GPa, and located at the point of bifurcation of the prezygapophyses. Immediately away from this point, stress
dissipated to 100–200 MPa.
Analysis 4: Postural Role of the Haemal Arches
Tensile stress was found at the junction of the prezygapophyses, but not along their medial faces (Fig. 6,
Table 9). Low tensile stresses were observed on the
cranial face of the centrum dorsal to the haemal canal.
Ventrally, tensile stress is found irregularly along the
haemal arches. In lateral view, the knob experienced low
tensile stress ventrally, and low compressive stress dorsally. In lateral view, the pattern of vectors within the
handle was similar to that in Analysis 4. In dorsal view,
the vectors are oriented craniocaudally along the knob
osteoderms, the neural spines, and both right and left
prezygapophyses.
Analysis 5: Material Properties
In the keratinous sheath UALVP 47273 model (Fig. 7,
Table 10), the distribution of stresses within the handle
and knob did not change noticeably compared to the normal UALVP 47273 model. Compressive stress at the
impact site was surrounded by a halo of tensile stress,
which was not observed in the bone model. The keratinous sheath slightly reduced the peak stress at the constraint. The overall distribution of stresses in the
UALVP 47273 isolated vertebra model (Fig. 7, Table 10)
did not change when the material properties were
changed, although the stresses appeared more diffuse
compared to the single material property model. Material properties affected the external distribution of stress
in UALVP 16247 slightly; there was an increase in tensile stress at the cranial of the right major osteoderm.
Two-dimensional models of UALVP 16247 (Fig. 7, Table
10) had higher strain values in the inner low density
areas of the osteoderms, compared to the outer cortex, in
models lacking a keratinous sheath. When a keratinous
sheath was modeled, strain was localized to the keratinous layer at the site of impact and strain values were
reduced in the bone.
DISCUSSION
Bone is most likely to fail as a result of shear stress.
Human femoral cortical bone can withstand shear stress
of 50 MPa longitudinally (with the grain) and 65 MPa
(across the grain), although bone actually appears to fail
in tension when subjected to transverse shear (Turner
1422
ARBOUR AND SNIVELY
Fig. 6. Results from Analyses 4 and 5 show that varying the constraint and direction of load affects stress distributions. Arrows summarize stress vectors, and arrowheads indicate the direction and
location of load. Positive values are tension, and negative values are
compression. UALVP 47273 knob þ vertebrae, impact force, centrum
constrained, stress contour plots in oblique left craniolateral view (A)
100 to 100 MPa, (B) 25 to 25 MPa; (C) cranial view, 100 to 100
MPa; and oblique left dorsolateral view (E) 100 to 100 MPa, (F) 25
to 25 MPa. UALVP 47273 knob þ vertebrae, impact force, centrum
unconstrained, stress contour plots in (D) cranial view, 125 to
125 MPa; and oblique left dorsolateral view (G) 50 to 50 MPa, (H)
25 to 25 MPa; stress vector plot in oblique left dorsolateral view,
125 to 125 MPa. UALVP 47273 knob þ vertebrae, knob weight,
stress contour plot in (I) dorsal view, 15 to 15 MPa, (L) cranial view,
15 to 15 MPa; (O) stress vector plot in left lateral view, 125 to
125 MPa. UALVP single vertebra, impact force, centrum unconstrained, 250 to 250 MPa, in (J) dorsal view, (K) oblique left dorsolateral view, and (M) 250 to 250 MPa, cranial view.
1423
ANKYLOSAUR TAIL CLUB IMPACTS
TABLE 8. Peak stresses in Analysis 3, examining the effects of different constraints
Impact
force (N)
Model
UALVP 47273
knob þ vertebrae
UALVP 47273
knob þ vertebrae
UALVP 47273
single vertebra
570
570
200
Maximum stress (MPa)
Constraint
XX
YY
ZZ
XY
YZ
ZX
Centrum, prezygapophyses,
haemal spine
Prezygapophyses,
haemal spine
Prezygapophyses,
haemal spine
175
64
39
13
15
8
216
103
50
21
15
129
2,389
1,297
1,443
754
110
247
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
Model
ROM 788
UALVP 47273
UALVP 47273
knob þ vertebrae
Maximum stress (MPa)
Impact
force (N)
Constraint
XX
YY
ZZ
XY
YZ
ZX
1,029
39
39
Centrum, Prezygapophyses
Cranial handle
Prezygapophyses, haemal spine
269
22
5
249
25
12
505
35
4
7
1
3
48
9
1
2
1
<1
Tensile stress is positive, and compressive stress is negative. X is mediolateral, Y is dorsoventral, and Z is craniocaudal.
et al., 2001). Currey (2002) summarizes several papers
which give values between 64 and 84 MPa for shear
strength of vertebrate bone. Bone is strongest in compression, and human femoral cortical bone fails at 193
MPa longitudinally and 133 transversely in compression
(Reilly and Burstein, 1975). Human femoral cortical
bone fails in tension at 133 MPa longitudinally and 51
MPa transversely (Reilly and Burstein, 1975). Although
material property distribution in ankylosaur tails differed from that in these mammalian examples these values can provide a baseline for estimating the potential
for tail clubs to fail during impacts. Material properties
for osteoderms in extant animals are poorly documented,
and ankylosaurid osteoderms have an unusual ‘‘chipboard-like’’ histological structure with a large amount
of structural fibers, which may have strengthened
these bones (Scheyer and Sander, 2004). Ankylosaurid
osteoderms may have had very different material
properties from the cancellous bone properties used in
this study, which may affect stress distributions and
values.
Peak stresses in almost all models were far greater
than that required to break bone in shear, and commonly in compression and tension as well. This would
suggest that tail clubs were destined to fail during tail
strikes, and would imply that tail clubs were not used
for delivering forceful impacts. However, artificially high
peak stresses occur in FE models where they are rigidly
constrained, and stresses distal to these constraints are
more realistically informative for biological interpretations (Shychoski, 2006). In the ankylosaur simulations,
peak stresses are always found at the constraint of the
model, and stress values generally decrease greatly in
elements adjacent to that with the peak stress, from
thousands to hundreds of megapascals. Additionally,
shear stresses (the XY, YZ, and ZX orientations) were
always much lower than stresses in the XX, YY, and ZZ
orientations. Although the tail clubs are modeled as
being rigidly constrained at the cranial face of the handle, this was not really the case, as the tail club would
be free to flex laterally at the joint between the penultimate and transitional free caudal vertebrae. In addition, several Euoplocephalus tail clubs appear to have
unfused centra (e.g., AMNH 5245), which, despite the
rigidity imposed by the interlocking neural and haemal
arches, would allow for a small amount of flexion
between successive handle vertebrae. The analyses in
this study ignore the role of soft tissues in controlling
and reducing stress within the tail club. Ligaments,
tendons, and muscles connecting successive vertebrae,
as well as intervertebral cartilage, may all have acted
to absorb forces along the handle; no part of the handle would have been completely constrained, and even
a small amount of flexibility between successive vertebrae may have sufficed to prevent tail clubs from
breaking during impacts. Small amounts of flexion
may have greatly reduced stress cranially through the
handle. Additionally, the analyses in this study do not
model the free caudal vertebrae, and the effects of tail
club impacts in this region of the tail are unknown.
Models that provide the most biologically realistic simulations are UALVP 16247, the UALVP 47273 knob þ
vertebrae model, and the UALVP 47273 isolated vertebra. In UALVP 16247, the knob would have been a rigid
body, and placing a rigid constraint at the cranial face of
the vertebra contained within the knob is biologically realistic. Peak stress within this constraint is over 1,000
MPa, but adjacent to this point the maximum stress is
closer to 100 MPa. In UALVP 47273 knob þ vertebrae,
shear stresses were lower than 100 MPa. The decrease
in stress away from the peak stress was greater in the
unconstrained centrum model than in the constrained
centrum model, which suggests that unfused centra may
have contributed to reducing stress cranially through
the handle. In the UALVP 47273 isolated vertebra,
stress dissipated rapidly away from the peak stress at
1424
ARBOUR AND SNIVELY
Fig. 7. Differing material properties slightly change the distribution
of stresses within the models, and a hypothetical keratinous covering
reduces strain within the knob. UALVP 47273 with simulated keratinous covering, oblique left lateral view: (A) stress contour plot of
results (150 to 150 MPa) of (B) mesh resulting from material property
assignment in Mimics, where dark blue is assigned the material properties of keratin and all other colors are assigned the properties of
cancellous bones. UALVP 16247 with two material properties, oblique
left craniolateral view: (C) stress contour plot of results (50 to 50
MPa) of (D) mesh where greens and blues are assigned the properties
of compact bone and reds, yellows and oranges are assigned the
properties of cancellous bone. UALVP 47273 isolated vertebra with
two material properties, oblique left craniolateral view: (E) stress contour plot (600 to 600 Pa) of results of mesh (F) with neural and haemal arches assigned properties of compact bone and the centrum
assigned properties of cancellous bone. (G) UALVP 16247, transverse
section at approximately the midlength of the knob, first principal
strain results using COMSOL Multiphysics, with an outer compact
zone, inner cancellous zone, and simulated keratinous covering over
the left osteoderm. Arrowhead indicates location and direction of load.
Tensile stresses are positive, compressive stresses are negative.
TABLE 10. Peak stresses in Analysis 5, examining the effects of different material properties
Maximum stress (MPa)
Model
UALVP 16247
UALVP 47273
UALVP 47273
single vertebra
Impact force (N)
Materials
XX
YY
ZZ
XY
YZ
ZX
960
960
570
570
All cancellous
Compact and cancellous
All cancellous
Compact, cancellous, with
keratinous sheath
Compact and cancellous
1,073
206
1,368
809
837
175
1,215
833
1,308
233
2,758
1,220
74
7
115
227
180
7
748
230
298
44
168
238
688
110
292
468
272
474
200
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
medial faces of the prezygapophyses were constrained,
stress values were generally lower than the 100 MPa
required to break bone in shear.
The idealized model of UALVP 47273 was valuable for
cross-validation with analyses of the fossil-based original. The similarity of their overall stress distributions
suggests that distortion in UALVP 47273 did not
ANKYLOSAUR TAIL CLUB IMPACTS
preclude interpretation of such results from this model,
and that simplified models can be informative even in
the case of complex analyses (Snively et al., 2006). Variation between their results was also instructive. The simplified model smoothed out breaks in the original
specimen, which eliminated some uninformative concentrations of stress. However, the simple model was less
realistically informative about effects of anatomical
details. We had not incorporated ossified tendons into
the coronal template, which resulted in a narrower handle and higher compressive and tensile stresses from lateral bending. Also, the simple model missed stress
concentrations, and potential adaptations for resilience,
at articulations like those of the neural arch.
The components of the neural arch are arranged to
resist lateral bending. The prezygapophyses are long
and tall, and do not dorsally overlap the neural spine of
the preceding vertebra. In ROM 788, tensile stress was
concentrated at the cranial edges of the prezygapophyses
on the impact side. In the model, these edges are fused
to the handle. In reality, there is some space between
the prezygapophyses and neural spine of successive vertebrae, which would have allowed for a small amount of
flexibility, and tensile stress may not have concentrated
in this location. However, stress at this location in the
model suggests that soft tissues in this area (possibly
associated with Mm. interarticulares superiores), may
have experienced greater tensile stress than elsewhere
between the prezygapophyses and neural spines.
Peak stresses in ROM 788 are very large, and stresses
adjacent to the element with peak stress are still greater
than that required to break bone in shear. Additionally,
an area of concentrated stress (650 MPa) was observed
near the knob. A similar concentration of stress was not
observed in the smaller tail clubs, and this stress may
be a result of the size difference between the knobs and
calculated impact forces. Very large tail clubs, if impacting with the maximum force, may have been in danger
of fracture. If the tail club was used for forceful impacts,
then individual animals with very large knobs may not
have attempted to achieve maximum impact forces during tail swings.
FEA simulating the weight of the club resulted in
peak stresses lower than that required to break bone in
UALVP 47273 (which has a small knob), and TMP
83.36.120 and UALVP 16247 (which have average-sized
knobs). Tail clubs with small and average-sized knobs
would not have been in danger of failure from weight
alone. However, peak stress values in ROM 788 were
somewhat more than is required to break bone. As in
the other analyses, peak stresses were located within
the constraint, and stress values decreased greatly immediately adjacent to the peak stress, to under 50 MPa.
Tensile stress along the dorsal surface of the handle,
and compressive stress along the ventral surface, was no
more than 15–17 MPa, which is far lower than that
required to break bone in tension or compression. None
of the tail clubs were likely to fracture under their own
weight, including ROM 788.
Porro (2008) found that material properties and force
did not change the distribution of stress within the skull of
Heterodontosaurus, and only changed the magnitude of
the maximum stress. However, the direction of force
changed the distribution of stress within the skull. This is
also true for the ankylosaurid tail clubs: changes to the
1425
material properties, magnitude of force, and area of impact
size in the 3D analyses only changed the peak stress magnitude. Changes in the location of impact altered the distribution of stress, and loading the models for impact force
versus weight altered the distribution of stress as well.
Keeled knob osteoderms can reduce the impact area
during a tail club impact, which both reduces overall
stress within the tail club and increases the stress on
the impacted object. A keratinous sheath over the keel
may have helped to reduce strain within the knob, as
keratin is tougher and more resistant to cracking than
bone (Ashby et al., 1995) Two-dimensional models of
UALVP 16247 confirmed that even a thin layer of keratin could have greatly reduced strain within the cancellous bone of the knob. A keratinous sheath may have
been important for preventing damage to the underlying
bone during impacts.
Although peak stress values suggest that tail clubs
may have failed during impacts, a closer inspection of
several models indicates that most were probably able
to withstand forceful impacts. Stress values below
100 MPa immediately adjacent to the peak stress in the
most accurate models (UALVP 16247, UALVP 47273
knob þ vertebrae, and UALVP 47273 isolated vertebra)
provide further support that at least small and averagesized tail clubs were unlikely to fail from the impact
forces calculated in Arbour (2008). Large tail clubs may
have been at risk of failure during impacts. This suggests
that 1) Euoplocephalus did not engage in hypothesized
tail-swinging behavior, 2) Euoplocephalus did engage in
this behavior, but did not impact with as much force as
suggested in Arbour (2008), or 3) flexibility in the cranialend part of the tail and within the handle may have
played an important role in preventing fracture of the tail
club, which is not modeled easily in the FEA used in this
study. In the future, more sophisticated finite element
modeling, incorporating flexible constraints at the cranial
end of the handle, and flexibility within the handle, could
provide additional insight into the mechanics of ankylosaurid tail club strikes, and additional evidence for or
against this hypothesized behavior.
ACKNOWLEDGEMENTS
The authors thank P. Currie (UALVP) for the opportunity to conduct this research and for his supervision and
advice. M. Caldwell, A. Murray, A. Wolfe, and E. Koppelhus (UALVP) also provided advice and support during
the course of this project. The authors wish to thank the
following for access to and assistance at their respective
institutions: C. Mehling (AMNH), K. Shepherd and M.
Feuerstack (CMN), D. Evans and B. Iwama (ROM), and
J. Gardner and B. Strilisky (TMP). M. James, G. Pinto,
P. Bell and A. Lindoe prepared specimens at UALVP. CT
scanning at the University of Alberta ABACUS facility
was made possible by R. Lambert and G. Schaffler. CT
scanning of ROM 788 at CML Healthcare was made possible by T. Ladd, and VMA thanks D. Evans and B.
Iwama (ROM) for their assistance and permission to
scan the specimen. The authors also thank J. Li and M.
Lawrenchuck (Materialise) for technical assistance with
Mimics, and to Anne Delvaux (Beaufort Analysis, Inc.)
for assistance with Strand7. H. Mallison (Museum für
Naturkunde, Berlin) provided advice on digital imaging
of fossils. VMA thanks M. Burns and R. Sissons
1426
ARBOUR AND SNIVELY
(UALVP) for many excellent discussions on ankylosaur
biology. Comments from P. Dodson, K. Carpenter and
two anonymous reviewers greatly improved the
manuscript.
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