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: email@example.com 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. 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