The Effect of Early Hominin Occlusal Morphology on the Fracturing of Hard Food Items.код для вставкиСкачать
THE ANATOMICAL RECORD 293:594–606 (2010) The Effect of Early Hominin Occlusal Morphology on the Fracturing of Hard Food Items MICHAEL BERTHAUME,1 IAN R. GROSSE,1* NIRDESH D. PATEL,1 DAVID S. STRAIT,2 SARAH WOOD,1 AND BRIAN G. RICHMOND3 1 Department of Mechanical & Industrial Engineering, University of Massachusetts, Amherst, Massachusetts 2 Department of Anthropology, University at Albany, Albany, New York 3 Center for the Advanced Study of Hominid Paleobiology, Department of Anthropology, The George Washington University, Washington, District of Columbia ABSTRACT Tooth proﬁle plays an important role in interpretations of the functional morphology of extinct species. We tested hypotheses that australopith occlusal morphology inﬂuences the fracture force required to crack large, hard food items using a combination of physical testing and ﬁnite element analysis (FEA). We performed mechanical experiments simulating both molar and premolar biting using metal replicas of four hominin specimens representing species that differ in occlusal relief (Praeanthropus afarensis, Australopithecus africanus, Paranthropus robustus, and P. boisei). The replicas were inserted into an Instron machine and used to fracture hollow acrylic hemispheres with known material properties. These hemispheres simulate a hard and brittle food item but exhibit far less variability in size and strength than actual nuts or seeds, thereby facilitating interpretations of tooth function. Fracture forces and fracture displacements were measured, and analysis of variance revealed signiﬁcant differences in fracture force and energy between specimens and tooth types. Complementing the physical testing, a nonlinear contact ﬁnite element model was developed to simulate each physical test. Experimental and FEA results showed good correspondence in most cases, and FEA identiﬁed stress concentrations consistent with mechanical models predicting that radial/median fractures are important factors in the failure of nut and seed shells. The fracture force data revealed functional similarities between relatively unworn Pr. afarensis and P. robustus teeth, and between relatively unworn A. africanus and heavily worn P. boisei teeth. These results are inconsistent with functional hypotheses, and raise the possibility that the tooth morphology of early hominins and other hard object feeders may not represent adaptations for inducing fractures in large, hard food items, but rather for resisting fractures in the C 2010 Wiley-Liss, Inc. tooth crown. Anat Rec, 293:594–606, 2010. V Key words: bite mechanics; feeding; diet; hominid; ﬁnite element analysis Grant sponsor: National Science Foundation (Physical Anthropology HOMINID program); Grant numbers: NSF BCS 0725078, 0725126, and 0725122. *Correspondence to: Ian R. Grosse, Department of Mechanical & Industrial Engineering, University of Massachusetts, 160 Governor’s Drive, Amherst, MA, 01003-2210. Fax: þ413-5451027. E-mail: firstname.lastname@example.org C 2010 WILEY-LISS, INC. V fracture force; Received 7 January 2010; Accepted 11 January 2010 DOI 10.1002/ar.21130 Published online in Wiley InterScience (www.interscience.wiley. com). EFFECT OF EARLY HOMININ OCCLUSAL MORPHOLOGY Occlusion force is one of the most important variables in analyses of feeding behavior. For example, occlusion force is needed to assess the biomechanical performance of skull structure (Jennings and Macmillan, 1986), and occlusion force can also provide insights into diet, which is often difﬁcult to infer for extinct species. In particular, the application of high occlusion forces are critical for species whose diets include stress-limited food items (those that fail under the application of high forces such as nuts or seeds) (Lucas, 2004), since the consumption of these foods is not possible until an outer, protective shell is fractured. These foods are often informally categorized as being ‘‘hard,’’ although this is not precise insofar as hardness refers speciﬁcally to an object’s resistance to indentation (the formal deﬁnition of hardness and other commonly used mechanical terms are provided in Appendix A). Occlusion force can be measured, with difﬁculty, in living primates (Hylander, 1979; Dechow and Carlson, 1990) but cannot be directly measured in extinct primates. However, fossils may provide information about how the species in question may have adapted to either maximize occlusion force production or minimize the occlusion force needed to initiate fractures in a given food item. These considerations are especially important for understanding human evolution, because it has been hypothesized (Peters, 1987; Strait et al., 2009) that some early humans possessed adaptations for feeding on large, stress-limited ‘‘fallback’’ foods (foods eaten during time periods when other, more preferred food items may not have been available) (Marshall and Wrangham, 2007). This study tests whether or not tooth morphology affects the occlusion force needed to fracture large, hard food items. There are two competing hypotheses that may explain how occlusal relief inﬂuences the fracturing of such foods. The Blunt Cusp Hypothesis is based on comparative biology. It has long been noted that primates that feed on hard objects have reduced occlusal relief, exhibiting blunter cusps and shorter shearing crests (e.g., Kay, 1981; Luke and Lucas, 1983). Among early hominins, it has been suggested that gracile australopiths exhibit less occlusal relief than extant African apes and that robust australopiths exhibit less relief than the gracile species (Grine, 1981, 1984; Teaford and Ungar, 2000; Ungar, 2004). These observations have led to inferences that blunt cusps are efﬁcient at fracturing hard foods (Ungar, 2004): ‘‘ : : : the species average SQ [shearing quotient] for ‘gracile’ australopith M2s was found to be higher than the ‘robust’ australopith average SQ value. This suggests that neither species was well suited to processing tough, deformable foods, and that P. robustus teeth would have been particularly adept at crushing brittle, inelastic items that are less resistant to crack propagation : : : . Results presented here for Australopithecus [Praeanthropus] afarensis indicate less crown relief and less sloping occlusal surfaces at given stages of wear than in either gorillas or chimpanzees. This implies more efﬁcient fracture of brittle, less deformable foods : : : ’’ The Blunt Cusp Hypothesis predicts, therefore, that teeth with reduced occlusal relief will be able to fracture 595 a given hard food item at a lower force or with lower energy than will teeth with higher relief. In contrast, the Pointed Cusp Hypothesis predicts that tall, pointed cusps will be more efﬁcient than blunt cusps at fracturing hard foods. A corollary of the hypothesis is that unworn teeth will be more efﬁcient than worn teeth at cracking such items. This hypothesis is based on mechanical principles. A tall, narrow cusp will apply force to a smaller area of contact on the food item, thereby concentrating stress and facilitating crack initiation. The aspects of tooth morphology relevant to testing this hypothesis have been deﬁned in multiple ways (Evans and Sanson, 2003). ‘‘Tip sharpness’’ is deﬁned as the radius of curvature at the tip of a point, so a point with higher tip sharpness has a smaller radius of curvature (Evans and Sanson, 1998). A smaller radius of curvature will give a smaller area of contact (for a given elastic modulus of the food) and, therefore, will produce a higher stress in the food (Lucas, 1982). Freeman and Leman (2006) and Evans and Sanson (1998) demonstrated that increased tip sharpness signiﬁcantly decreased the force and energy required to penetrate foods. Moreover, Xie and Hawthorne (2002) analytically determined an equation which shows that induced stress in a thin surface indented by a spherical indenter is inversely proportional to indenter radius, which, in our case, refers to the tooth cusps. However, it must be noted that if an indenter is too sharp, then it may pierce through the surface instead of fracturing it. As an added effect, if a fracture were to form directly beneath the cusp tip, then the cusp could act as a wedge driving crack propagation (as when an axe head splits a log). Once a point has initiated a crack in a tough food, it must be continually driven into the food to sustain propagation of the crack. The force and energy required will in part depend on the volume of the tool and the amount of food displaced. This can be quantiﬁed as ‘‘cusp sharpness,’’ which is inversely proportional to the volume of the point at increasing distances from the tip (Evans and Sanson, 2003). A point with higher cusp sharpness has a smaller cusp volume for a given distance from the tip. Increased cusp sharpness reduces the force and energy required for the tooth to drive through a tough food as fewer bonds in the material need to be broken or strained (Evans and Sanson, 2003). In summary, the Pointed Cusp Hypothesis predicts that teeth with high occlusal relief will initiate fractures in hard foods at a lower force or with lower energy than teeth with low relief. The Pointed Cusp and Blunt Cusp Hypotheses make opposite predictions concerning the impact of occlusal morphology on hard-food fracturing, and thus they can be easily evaluated against each other. However, there is a third, alternative mechanical hypothesis, the Strong Cusp Hypothesis, that warrants consideration but is not as easy to test. This hypothesis notes that the fracture strength of a tooth cusp increases as does its radius of curvature (Lucas et al., 2008; Lawn and Lee, 2009). Thus, bunodont teeth with low relief may not be adaptations for increasing the efﬁciency of a tooth for fracturing a given food item, but rather for increasing the ability of the tooth to itself resist fracture under the application of high occlusion forces (Lucas, 2004; Vogel et al., 2008). Obviously, there should be strong positive selection favoring traits that enhance the structural integrity of teeth, because the functional utility of the tooth declines 596 BERTHAUME ET AL. dramatically once it breaks. This hypothesis makes no prediction concerning the efﬁciency of tooth form, so in principle it is compatible with both the Blunt Cusp and Pointed Cusp Hypotheses. However, recalling that comparative evidence indicates that hard-object feeders tend to have low, rounded tooth crowns (consider mammals as diverse as orangutans, peccaries, and sea otters), a ﬁnding that blunt cusps are less or equally efﬁcient as pointed cusps at inducing fractures would suggest that fracture efﬁciency was not driving the evolution of tooth form. In this context, the Strong Cusp Hypothesis would provide a plausible, alternative hypothesis. These hypotheses are tested here using a combination of physical testing and ﬁnite element analysis (FEA). FEA is a numeric method which has been employed widely in engineering and science for more than four decades to understand how objects of complex geometry and/or material properties respond to load. A brief historical review of the method can be found in Cook et al. (2001) and Rayﬁeld (2007). In this method, complex geometry is subdivided into a ﬁnite number of subdomains, called ﬁnite elements. These elements have simple geometrical shapes such as triangles and quadrilaterals for 2D analysis problems and tetrahedrons and hexahedrons for 3D problems. The elements are connected to each other at speciﬁc points, called nodes. Use of FEA was restricted to relatively small problems until the mid 1980s due to a lack of computing power and computer memory, but it has been widely used since then in the medical literature to study stress and strain distributions as a result of the combined inﬂuence of forces and residual stresses in teeth, bones, and even soft tissues. Following advances in computing power in the late 1990s, FEA has been used in a broad range of biomedical and engineering applications, such as ﬂuid mechanics, heat transfer, and the study of stress and strain in various complex biomechanical and mechanical problems. Patel et al. (2008) and Patel (2009) used a combination of FEA and physical testing to study the effect of primate tooth form on the fracturing of macadamia nuts (a representative hard food item). However, results were statistically inconclusive due to high variability in nut size, shape, and strength, resulting in standard deviations in fracture energy as high as 65% of the mean. The study presented here also involved physical testing and FEA, but an engineered object was selected as a substitute for a hard food item. The engineered objects were hollow hemispheres composed of a homogeneous material whose hardness, elastic modulus, diameter, and wall thickness resembled that of a typical macadamia nut. In this way, the effect of variability in the geometry and material properties of the hard food item can be minimized so that differences in fracture results, if any, due to tooth morphology can be observed. Obviously, macadamia nuts are not endemic to Africa, so early hominins were not consuming them. The hemispheres were chosen to resemble macadamias because the mechanical properties of these nuts are well understood (see later). MATERIALS AND METHODS Physical Testing Food source. The food source employed to represent a hard food item is the nut of the Australian evergreen tree (Macadamia ternifolia, Family: Proteaceae). Jen- nings and Macmillan (1986) studied the microstructure and mechanical properties of macadamia nutshells, and found using X-ray diffraction that green (22 wt% of water) and dry (1.5 wt%) shells possessed mechanical properties that resemble isotropic wood. Microstructure of the nut neither varies systematically with position within the shell nor exhibits any overall anisotropy. Investigations of the fracture surface suggest that cracks propagate approximately perpendicular to the load axis. Fractures generally propagate through rather than around the bundles of rods that make up the shell microstructure, and the fracture surface is generally smoother at its inner and outer edges than near its center (i.e., it is smoother in the regions of higher stress far from the neutral axis). Lucas et al. (1994) found that the fracture load for the macadamia nutshell using semi-imitative tests varied from 1.68–2.08 kN, with standard deviations in the range of one-third to one-fourth of the mean value. Hollow acrylic hemispheres were chosen as a substitute for macadamia nuts in this experiment because of their similarity in mechanical properties. A hollow hemisphere was considered a suitable substitute for the nut, as the seed kernel in dry nuts is often loose and therefore does not contribute to its strength (note, however, that in fresh nuts the kernel tends not to be loose). Further, fracture of the macadamia nut by primate tooth forms was shown by Patel et al. (2008) to occur in the vicinity of indentation. Therefore, a properly supported half-spherical shell (i.e., a hollow hemisphere supported at its base by a smooth metal surface) indented by a single tooth form is expected to exhibit similar fracture behavior as a spherical shell loaded by upper and lower tooth forms. The hemispheres were made using a slow precision casting process, but speciﬁc elastic material properties or chemical composition data were not provided by the manufacturer (Kit Kraft, Studio City, Ca.) However, material properties such as modulus of elasticity (2–6 GPa for nut versus 1.5–6 GPa for acrylic), density, and tensile strength of the macadamia and common acrylic grades lie in similar ranges. Moreover, we chose acrylic hemispheres whose dimensions (external diameter ¼ 28.34 mm; wall thickness ¼ 2.54 mm) resembled those of the nuts. The hardness and brittleness of macadamia nuts is somewhat higher than acrylic (Shahdad et al., 2007; Patel, 2009) at room temperature. As noted by Patel (2009), the hemispheres often exhibited large degrees of plastic deformation before brittle failure occurred (if brittle failure occurred at all). In some of their trials, the primate metal tooth castings would displace the acrylic hemispheres up to 11 mm, nearly ﬂattening the hemisphere entirely. In contrast, macadamia nuts exhibited consistent brittle failure at much smaller displacements (Patel et al., 2008). As acrylic is an amorphous plastic, brittle failure can be induced by lowering its temperature below the glass transition temperature Tg. As Tg of acrylic varies widely from values as low as 210–378 K (Gupta, 1995), we ensured brittle failure in our acrylic hemispheres by chilling the hemispheres to 78 C using a methanol and dry ice bath. To keep the hemispheres from warming up signiﬁcantly during the test, the steel base on which the acrylic half spheres were placed was also submerged in a separate bath before every trial, EFFECT OF EARLY HOMININ OCCLUSAL MORPHOLOGY bringing it down to the same temperature as the acrylic hemisphere. The base and hemisphere were quickly removed from their baths, set in place (see later), and the test was conducted. The temperature of the base was monitored in preliminary trials, and it was determined that the base only warmed up 10 C in the time that it took for the trial to be conducted. This procedure resulted in the consistent brittle fracturing of the hemispheres (see Appendix B). 597 ful for further testing of nuts even harder than macadamia. A ﬂat bar at the base of the teeth was designed into the casting process to create a holding grip for the Instron jaws. Risers and gates were designed into the mold pattern to ensure proper material ﬂow. Casting was done by Bay State Casting LLC (Springﬁeld, MA). Figure 1 below shows the original plasticine and plaster casts of the fossil specimens and the resulting cast iron replicas. Hominin Teeth Cast iron replicas of the upper cheek teeth of four early hominin specimens (representing four different species) were fabricated from plastocene and plaster casts. Although the casts may differ from the actual fossil hominin specimens, it was assumed that these discrepancies would not profoundly affect the results of the physical tests or the FEA, because the scale of those differences is likely to be less than the scale of the differences between specimens (or, at a minimum, the scale of differences between robust and gracile australopiths). Praeanthropus afarensis (more commonly referred to as Australopithecus afarensis; see Strait et al., 1997) was represented by the left cheek teeth of specimen AL 200– 1a. Australopithecus africanus was represented by the right molars and premolars of Sts 52a. The right cheek teeth of SK 13/14 and the left teeth of OH 5 represented Paranthropus robustus and P. boisei, respectively. Specimens AL 200–1a, Sts 52a, and SK 13/14 preserve teeth ranging from relatively unworn to moderately worn, and thus all exhibit higher cusp relief than OH 5, which preserves heavily worn teeth. Interestingly, the teeth in OH 5 are not worn ﬂat, but rather preserve a blunt enamel ridge running mesio-distally along the tooth row. Thus, the teeth of OH 5 exhibit slight relief. AL 200–1a and Sts 52a represent gracile australopiths, while SK 13/14 and OH 5 represent robust australopiths. To assess the sharpness of the contacting cusps, we imported our digital *.stl teeth models into Geomagic Studio. The fracture displacement value and direction from the physical test for each experiment was used to identify the portion of each cusp in contact with the hemisphere. Using an automated tool within Geomagic, we ﬁtted a sphere to the cusp on each tooth that ﬁrst contacted the hemisphere using only that portion of the cusp surface in contact with the hemisphere to achieve the ﬁt. The radius of this sphere provided an estimate for the radius of curvature of the portion of cusp in contact with the hemisphere. As noted above, the radius of curvature is a direct measure of tip sharpness and, thus, is a measure directly relevant to testing the Pointed and Blunt Cusp Hypotheses. The cast fabrication process followed a procedure similar to that presented in Patel et al., (2008). ASTM -40 cast iron, which has a tensile strength of 293 MPa and a compressive strength of 965 MPa, was used as the material for the casts. Brinell hardness and density for this material are 235 Hb and 7,600 kg/m3, respectively. The elastic modulus of cast iron teeth is 158 GPa. Cast iron was used because it has a very high compressive strength, and during the biting tests, the teeth are subjected to vertical, compressive loads. In addition, cast iron has high surface hardness and, hence, may be use- Apparatus The testing equipment consisted of an Instron machine (model 4411) instrumented with a 5-kN load cell. A slow, controlled displacement rate of 5 mm/min was applied to the Instron machine, and NI Lab View 8.5 software was used to record force and displacement versus time. The displacement rate was chosen based on observations by Lucas et al., (1994) who studied orangutans while they ate hard food sources (Mezzettia parviﬂora and Macadamia ternifolia). The authors observed that the mandible remains stationary up until the point of fracture, indicating that the nuts experienced static loading. The testing procedure was similar to the method used by Patel et al. (2008). However, this time the hollow acrylic hemispheres and supporting metal base were chilled in separate methanol dry ice baths, as previously described. The setup allowed the simulation of bites using either the premolars (P3 and P4) or the molars (M1 and M2) on identical acrylic balls. The tooth replicas were attached to the working end of the Instron machine by using a 5-kN wedge grip to hold the bar on the back of the tooth molds (Fig. 2). The teeth were placed in the grip in such a manner that the apex of the hemisphere was always directly below either P3/P4 or M1/M2. Thus, two teeth (either molars or premolars) were touching the acrylic hemisphere as the trials were run. The tooth form was lowered until contact was made with the hemisphere. The controlled displacement test was then conducted until the hemisphere fractured. Figure 2 shows the experimental setup with a hollow acrylic hemisphere placed on the ﬂat support at the bottom end of the Instron and the cast iron teeth ﬁxed at the upper jaw of the Instron. During static loading, the crosshead was stopped as soon as possible after fracture had occurred. To make this possible, the automatic ‘‘stop after fracture’’ option was activated on the Instron machine. To ensure maximum accuracy during the testing, Lab View collected data at 25 points per second. Eight experiments were carried out simulating premolar and molar biting using each of the four fossil specimens. Each experiment consisted of 10 fracturing trials. For each experiment, force and displacement versus time data was collected using Lab View. Because the forces employed in these tests were high, it was important to account for the compliance of the Instron machine. A load-deﬂection curve for a trial conducted without the hemisphere (i.e., as the jaws pressed directly into the support base) was obtained and a linear ﬁt yielded an R2 value of 0.99. This deﬂection for a given force was then subtracted from the test results to yield 598 BERTHAUME ET AL. Fig. 1. (Top) Fossil teeth replicas for A. africanus, A. boisei, Pr. afarensis, and P. robustus from left to right and corresponding cast iron replicas of teeth. (Bottom) Computer-generated models of teeth specimen. From upper right to lower left are AL 200–1a, OH 5, SK13/14, and Sts 52a. the net force-deﬂection curves for the teeth-hemisphere contact problem. Statistical Analysis Ten acrylic hemispheres were fractured in each of the eight experiments, for a total of 80 mechanical trials. Two-way analysis of variance was performed using the R statistical package to test the signiﬁcance of effects due to specimen (AL 200–1a, Sts 52a, SK 13/14, OH 5), tooth type (molar, premolar), and the interaction between them. When signiﬁcant differences were found, all relevant pairwise comparisons (equivalent to Student’s t tests) were performed. The Blunt Cusp Hypothesis predicts that specimens with lower occlusal relief (expected to be the robust australopiths OH 5 and SK 13/14) fracture the hemisphere at signiﬁcantly lower force and energy than those with higher relief (expected to be the gracile australopiths AL 200–1a and Sts 52a). The Pointed Cusp Hypothesis predicts the reverse. The Strong Cusp Hypothesis makes no speciﬁc prediction regarding fracture force or enegy, but is an alternative in the event that the data are inconsistent with the Blunt and Pointed Cusp Hypotheses. Finite Element Analysis Physical testing was complemented with FEA simulation of the indentation test. The simulation required development of geometry models for the teeth and the hemispheres, meshing, assignment of material properties, and proper speciﬁcation of constraints and loading conditions. Fig. 2. Indentation of hard food item substitute by hominin toothform casting. Model Construction The surface geometries of the teeth were scanned using a Roland Modela MDX 15/20 (Roland DG corporation) tactile type surface scanner with a resolution of 0.1 mm. Surface geometries were then imported into Strand 7 (Strand7 Pty.) using stereo lithographic ﬁle format (*.stl) and were processed to remove noise. Strand7 meshed data was exported to ANSYS Workbench 11.0 using the Nastran ﬁle transfer format (*.dat) and then EFFECT OF EARLY HOMININ OCCLUSAL MORPHOLOGY 599 subsequently transferred to ANSYS Classic 11.0 for contact analysis. Figure 1 shows the computer-generated models of the four teeth specimens. Pro/Engineer CAD System was used to develop a geometry model of a hollow acrylic hemisphere with a diameter of 28.3 mm and a wall thickness of 2.54 mm. Material Properties The acrylic hemispheres were modeled as linear isotropic materials with a Young’s modulus, E, of 3.2 GPa and Poisson’s ratio, m, of 0.4, based on values provided by several online material property databases1 and in the literature (Raptis et al., 1981; Patel et al., 2008). Lucas et al., (1994) suggest that during biting, teeth do not undergo macroscopic plastic deformation. Moreover, elastic deformation of the teeth is assumed to be small compared to deformation of the food item. This assumption is based on the fact that the Young’s modulus of cast iron is 50 times the Young’s modulus of the acrylic. Hence, the teeth were considered to be perfectly rigid. Meshing The tooth surface was initially meshed with shell elements (ANSYS element number 181) in ANSYS 11.0. The acrylic hemisphere was meshed with 10 noded quadratic tetrahedral elements (ANSYS element Type 186). A convergence study consisting of three separate analyses involving element sizes of 2, 1, and 0.5 mm using a ﬂat rigid plate to indent the acrylic hemisphere revealed only a 3.2% difference in stress results between the 1- and 0.5-mm element sizes. Hence, a 1 mm element size for the hemisphere was used for all toothhemisphere indentation simulations. Nonlinear surface-to-surface contact analysis in ANSYS requires that the meshed geometries of the two contacting surfaces be overlaid with special contact/target surface elements. Target elements (ANSYS element TARGET174) were surface meshed over the underlying shell elements representing the teeth, and contact elements (ANSYS CONTAC170) were surface meshed over the upper (i.e., contacting) portion of the hemisphere. To impose rigid body motion on the target surface (i.e., the teeth), a pilot element consisting of a single target element node was created on the target element surface. This constrains all target element nodes deﬁning the target surface to behave as a rigid body. As the target surface deﬁned by the target elements and nodes is now considered rigid, the underlying shell elements were no longer necessary and were deleted. Boundary Conditions Nodes on the bottom surface of the hemisphere were constrained against motion in the direction normal to its surface (i.e., the z direction). In addition, to prevent rigid body motion without overconstraining the hemisphere, a cylindrical coordinate system was used to prevent nodes on the bottom surface of the hemisphere from moving in the circumferential direction. Essentially, this prevented the hemisphere from rigid body rotation about the z axis 1 See http://www.engineeringtoolbox.com/young-modulus-d_417. html, http://www.3d-cam.com/materials/acrylic.asp. Fig. 3. SK13/14 tooth replica position for third and fourth premolar biting simulation. and rigid body translation in the x–y plane. However, the bottom surface of the hemisphere was still free to elastically deform in the radial direction. Load Conditions and Analysis Options For each simulation a displacement was applied to the pilot node on the tooth-surface mesh in the direction of the unit outward normal to the bottom surface of the hemisphere. Also, for each simulation the hemisphere was placed as close as possible to the appropriate contacting teeth on the tooth surface without interference based on what was observed in the physical test, as shown in Fig. 3. The value of displacement was set to a value larger than that observed in the test to account for initial clearance between the tooth surface and hemisphere. The ‘‘displacement load’’ was applied as a ramped load using up to 20 substeps. The nonlinear geometry option was enabled to account for possible large displacement effects, and analysis results were stored for all substeps. Eight FEA simulations were performed to compare the effect of premolar and molar biting in each of the four specimens. For each simulation the reaction force and displacement of the pilot node were extracted from the results ﬁle and a force-deﬂection plot created. Up until contact the force required to displace the pilot node of the rigid tooth surface is zero. Thus, this data enabled calculation of the displacement of the pilot node at which contact between the tooth surface and hemisphere ﬁrst occurred which represents the initial clearance between the tooth surface and the hemisphere in the FEA. We then subtracted this from the pilot node displacement to give the displacement that corresponds to the physical test displacement. Stress results and pilot node reaction force (i.e., FEA fracture force) for which this net displacement matched the experimental fracture displacement were extracted. RESULTS Failure modes for all physical test trials involved brittle failure of the hemisphere with the specimen breaking apart catastrophically into two or more pieces (see Fig. 4). Table 1 presents a comparison of experimental and 1.83 1.30 0.21 0.30 1.61 0.55 0.23 0.19 894 744 785 490 774 550 524 696 St. Dev. 3.444 2.969 1.130 1.500 3.965 1.925 1.290 1.136 0.525 0.451 0.170 0.174 0.426 0.261 0.138 0.138 0.899 0.834 0.292 0.254 0.693 0.479 0.237 0.253 Avg. St. Dev. 0.42 0.62 0.41 0.39 0.44 0.65 0.36 0.37 1.67 1.76 1.34 1.16 1.77 2.13 1.23 1.24 Avg. Al 200-1a Pr. afarensis Sts 52a A. africanus SK13/14 P. robustus 1.03 0.89 0.39 0.39 0.87 0.42 0.35 0.37 0.46 0.30 0.12 0.15 0.55 0.12 0.10 0.10 Avg. Bite Specimen Species OH 5 P. boisei P3/P4 M1/M2 P3/P4 M1/M2 P3/P4 M1/M2 P3/P4 M1/M2 St. Dev. 358 294 130 133 267 129 122 139 Energy to fracture (J) Max r3 (MPa) Max r1 (MPa) Force at fracture disp. (kN) Energy to Fracture (J) Fracture Force (kN) Displacement (mm) FEA results. For the most part, consistency was found between the measured fracture force and energy and the force and energy required to impose a corresponding fracture displacement on the indenting tooth surface form in the ﬁnite element simulations. However, for both OH 5 biting simulations and for Sts 52a premolar bite simulation, the FEA gave a much higher force and energy at the fracture displacement than found in the corresponding experiment. Experimental average fracture displacements for these three cases were approximately twice the average displacements required to fracture the specimen observed in the other ﬁve test cases. This is reﬂected in maximum principal stress values as well, with the three highest values corresponding to the three largest fracture displacements and somewhat reﬂected in the minimum principal stress values, with three of the four largest magnitudes corresponding to the three largest fracture displacements. Conversely, there is good consistency in the maximum tensile stresses (122–139 MPa) predicted at the fracture displacements for the same ﬁve simulations (SK 13/14 molar and premolar, Al 200–1a molar and premolar, and Sts 52a molar) in which the FEA predicted fracture force was consistent with the measured fracture force. Figures 5 and 6 show minimum and maximum principal stress distributions obtained from nonlinear contact FEA for the eight simulations. For comparative purposes, the same scale is used for each minimum principal stress contour plot and for each maximum principal stress plot. Deformed geometry is also shown in these ﬁgures, exaggerated by a factor of ﬁve to improve visualization of the deformation. At the point of contact between the teeth casting and the acrylic hemisphere, highly localized compressive stresses were observed, while on the inner surface of the acrylic hemisphere localized tensile stress reached its maximum value. For crack initiation to occur, tensile stress is a prerequisite. Thus, the tensile stress patterns support experimental observation that cracks initiate near the point of contact and imply that radial cracks initiate from the inner surface of the hemisphere. Two-way analysis of variance revealed that fracture force and fracture energy (i.e., the work required to fracture the specimen) differed signiﬁcantly according to Physical testing experiments Fig. 4. Examples of fractured hemispheres from physical test. Finite element analysis (FEA) BERTHAUME ET AL. TABLE 1. Comparison of experimental and FEA results (r1 and r3 are maximum and minimum principal stresses) 600 601 EFFECT OF EARLY HOMININ OCCLUSAL MORPHOLOGY Fig. 5. Minimum principal stress distribution in Pa (top) and maximum principal stress distributions (bottom) at the fracture displacement (deformation shown is 5 the true deformation) for premolar biting. From upper left to lower right: P. boisei (OH 5), P. robustus (SK 13/14), A. africanus (Sts 52a), and Pr. afarensis (AL 200–1a). Fig. 6. Minimum principal stress distribution in Pa (top) and maximum principal stress distributions (bottom) at the fracture displacement (deformation shown is 5 the true deformation) for molar biting. From upper left to lower right: P. boisei (OH 5), P. robustus (SK 13/14), A. africanus (Sts 52a), and Pr. afarensis (AL 200–1a). specimen, but not according to the type of bite being simulated (i.e., molar versus premolar) or according to the interaction between specimen and tooth type (Tables 2 and 3). Consequently, all pairwise comparisons were performed between specimens while pooling the premolar and molar data (Tables 2 and 3). These revealed signiﬁcant differences between, on the one hand, AL 200– 1a and SK 13/14, and, on the other, OH 5 and Sts 52a. Both fracture force and fracture energy were lower in the former two specimens than in the latter. Thus, there is good evidence that AL 200–1a and SK 13/14 are more efﬁcient at fracturing large, hard objects than OH 5 and Sts 52a during both molar and premolar biting. In Table 4, we present the radius of curvature calculated for the ﬁrst contacting cusps of the hominin teeth. Note that these measures have direct functional signiﬁcance insofar as they capture only that aspect of tooth form that participated in the physical tests. As expected, the heavily worn OH 5 exhibited, on average, the highest radius of curvature (i.e., least relief) in the four teeth considered here. Contrary to expectations, the other robust australopith, SK 13/14, had similar tooth sharpness as the two gracile australopiths, AL 200–1a and Sts 52a. The radius of curvature is heavily inﬂuenced by variation in vertical displacements, so one must be cautious in interpreting these data too ﬁnely, but, on balance, the indices do not appear to be consistent with predictions regarding cusp tip sharpness in these specimens (at TABLE 2. Results of two-way analysis of variance based on physical testing Variable: effect Fracture force Specimen Tooth type Interaction Residual Fracture energy Specimen Tooth type Interaction Residual Degrees of freedom F-statistic P value 3 1 3 72 18.79 4.36 2.75 0.0000* 0.5111 0.3542 3 1 3 72 18.79 4.36 2.75 0.0000* 0.3193 0.7082 *Signiﬁcant at the P < 0.0001 level. least among those that are relatively unworn). However, the small number of individuals examined here (one specimen per species) does not preclude the possibility that increased sampling would allow the identiﬁcation of species-level differences among these taxa. DISCUSSION Functional Hypotheses The results obtained here are inconsistent with both the Blunt Cusp and Pointed Cusp Hypotheses. We observed 602 BERTHAUME ET AL. TABLE 3. Results of pairwise comparisons (P values) when comparing fracture force and fracture energy based on physical testing Fracture Force OH 5 Sts 52a SK 13/14 AL 200-1a Fracture Energy OH 5 Sts 52a SK 13/14 AL 200-1a OH 5 Sts 52a – 0.2035 0.0040* 0.0012* – 0.0001* 0.0000* SK 13/14 – 0.8800 AL 200-1a TABLE 4. Cusp functional radius of curvature for hominin teeth Specimen Tooth Vertical displacement (mm) Radius of curvature (mm) AL 200-1a P3 P4 M1 M2 P3 P4 M1 M2 P3 P4 M1 M2 P3 P4 M1 M2 0.35 0.35 0.37 0.37 0.89 0.89 1.03 1.03 0.39 0.39 0.39 0.39 0.87 0.87 0.42 0.42 2.37 2.61 3.36 1.94 7.41 6.98 8.08 10.50 2.45 2.06 3.14 3.75 2.15 1.96 3.09 2.17 – OH 5 – 0.0514 0.0000* 0.0000* – 0.0015* 0.0002* – 0.5500 – SK 13/14 *Signiﬁcant using an adjusted Bonferroni protected probability of P ¼ 0.0167. Sts 52a signiﬁcant differences in fracture force or energy between specimens with broadly similar degrees of functional cusp radii of curvature (Sts 52a versus AL 200–1a and SK 13/ 14), and we failed to observe differences between specimens with worn (OH 5) and relatively unworn (Sts 52a) teeth. Although the signiﬁcant differences between OH 5 and either AL 200–1a or SK 13/14 appear to be consistent with the Pointed Cusp Hypothesis, the data derived from Sts 52a are less obviously explained. On balance, the results of this study cannot be accommodated by these two hypotheses. Moreover, considering that the standard deviations of fracture force and fracture energy are high (illustrating that fracture is inherently a stochastic phenomenon, even in reference to a precision manufactured, engineered object of uniform size, shape, and material), it would not be surprising if the distinctions between the species blurred once intraspeciﬁc variability is taken into account. Although it was not practical in the current study to perform physical testing on multiple fossil specimens for each species, the reasonable correspondence between the FEA and physical testing results suggest that FEA could provide the means for assessing intraspeciﬁc variation in the fracture efﬁciency of teeth. One explanation for the poor correspondence between the results and the hypotheses may be that the hypotheses fail to account for the effect of multiple cusps simultaneously contacting the food item. The surprisingly large fracture force required by Sts 52a could be due to the fact that its pattern of cusp contact differs from those of the other two relatively unworn specimens. FEA results show that Sts 52a molar and premolar biting resulted in four-point contact, while biting in AL 200–1a and SK 13/14 resulted in two- and three-point contact, respectively. As more cusps come into contact with the item, the overall contact area increases and consequently localized stresses are reduced for a given total occlusal force. Further, the size of highly stressed areas is relatively small, which could explain the high fracture force in some trials, given the probabilistic nature of fracture being initiated at randomly distributed material ﬂaw points. Alternatively, multiple contact points that are close to each other may result in interacting localized stress ﬁelds that increase the probability of fracture, although this was not observed here. Obviously, the size and shape of the occlusal surface affect the number and proximity of contact points between the teeth and the item, but, unfortunately, we were unable in our experimental trials to ﬁnely manipulate the posi- tion of the hemispheres on the teeth (as might happen when a hominin or other primate cracks a nut in vivo), and thus we cannot rule out the possibility that AL 200– 1a and SK 13/14 might have employed four-point contact when alive. Further study on the role of cusp contact in food fracture mechanics is clearly warranted, but we suspect that this variable has a greater impact on fracture efﬁciency than cusp morphology per se, at least with respect to large, hard food items. An alternative but not mutually exclusive explanation of the results is that the initiating of fractures in food is not the primary selective force driving the evolution of early hominin tooth morphology. Rather, if large, hard food items were selectively important components of the early hominin diet, then tooth form may instead be driven by the need for the tooth crowns to resist being fractured themselves (i.e., the Strong Cusp Hypothesis). A recent study (Chai et al., 2009) has documented that numerous, preexisting radial cracks exist near the enamel-dentine junction (EDJ) of mammalian teeth. These cracks may play a stress-shielding function protecting the EDJ but, conversely, a key objective in prolonging tooth life is the prevention of the propagation of these cracks to the surface. Mechanical models (Lawn and Lee, 2009) predict that the force needed to propagate a radial fracture is, in part, a product of the effective radius of curvature of a tooth cusp (as the radius increases, so will the critical force value needed to propagate a crack). Furthermore, the theory of elasticity predicts that sharper indenters themselves will experience higher stresses for a given indentation force. Certainly, even if a pointed cusp were more efﬁcient at fracturing hard food items, the usefulness of that cusp will end once it breaks. Thus, the evolution of blunt cusps in hard object feeders may represent a trade-off in which the efﬁciency of food fracturing is sacriﬁced in return for an enhanced safety factor for the tooth. Diet and the Evolution of Craniodental Form and Function in Australopiths For more than half a century (e.g., Robinson, 1954, 1963; Jolly, 1970; Rak, 1983; Teaford and Ungar, 2000; EFFECT OF EARLY HOMININ OCCLUSAL MORPHOLOGY Strait et al., 2009), it has been recognized that the craniodental morphology of the australopiths is distinctive, phylogenetically derived, and almost certainly functionally related to diet. Interestingly, although there is nearly universal consensus regarding these broad strokes, there is not yet agreement concerning how, precisely, diet inﬂuenced the evolution of these traits. Robinson (1954, 1963) proposed that A. africanus was an omnivore while P. robustus was a specialized herbivore, and that the morphological differences between them reﬂected these different dietary strategies. Jolly (1970), drawing an analogy with modern baboons, suggested that many derived australopith features represented adaptations to feeding on small, hard objects. Rak (1983) suggested that the facial skeletons of Pr. afarensis, A. africanus, P. robustus, and P. boisei preserved, respectively, progressively enhanced adaptations to absorbing elevated masticatory loads, with premolar loading being a particularly important selective force. Peters (1987) noted that nuts and seeds could have been, at the best, only a seasonally available resource for australopiths, and that such foods should, in most cases, be considered large (rather than small), hard objects. Thus, although large, hard objects may have been selectively important components of their diet, australopiths may have been generalized rather than specialized feeders. Walker (1981) suggested than an alternative to any hard-object hypothesis was the possibility that enlarged postcanine tooth crown area in australopiths was an adaptation to consuming large volumes of low quality foods. Early quantitative dental microwear analyses (Grine, 1986; Grine and Kay, 1988) found, however, that P. robustus, preserved highly pitted microwear surfaces consistent with hard-object feeding, and that A. africanus exhibited pitting frequencies that were slightly elevated relative to extant primate follivores and soft-food frugivores. Pioneering stable carbon isotope analyses (e.g., Lee-Thorp et al., 1994; Sponheimer and Lee-Thorp, 1999) demonstrated convincingly that southern African hominins (A. africanus, P. robustus) had isotopically mixed diets, composed primarily of browse (or animals that eat browse, i.e., browsers) but with an important component consisting of graze (or grazers). Teaford and Ungar (2000) summarized a variety of data and concluded that gracile austraopiths (e.g., Pr. afarensis, A. africanus) were dietary generalists, while robust australopiths (P. robustus, P. boisei) were specialized to consume hard foods. Wood and Strait (2004: 149) likewise summarized a broad range of data, but concluded instead, in a manner fully consistent with Peters (1987), that robust australopiths were dietary generalists whose derived craniofacial traits allowed them to broaden their diet: ‘‘We suggest that although the masticatory features of Paranthropus are most likely adaptations for consuming hard or gritty foods, they had the effect of broadening, not narrowing the range of food items consumed. It is possible that these adaptations allowed Paranthropus to become a ‘seasonal specialist’ by exploiting previously unavailable fallback food items during periods of dietary stress.’’ Shortly thereafter, carbon isotope (Sponheimer et al., 2006) and microwear texture analyses (Scott et al., 603 2005) both corroborated this hypothesis with respect to P. robustus. Studies (e.g., Laden and Wrangham, 2005) have also focused attention on the potential importance of underground storage organs (USOs) like tubers, bulbs, corms, and rhizomes in the diets of australopiths. Dominy et al., (2008), in particular, examined the material properties of USOs, and concluded that bulbs and corms, in particular, may have been hard objects consumed by these hominins. Note, however, that these USOs are hard only in the sense that they are as stiff as many seed kernels but are orders of magnitude less stiff than seed shells. Within the last 5 years, a series of increasingly sophisticated microwear, isotopic, and biomechanical studies have yielded seemingly contradictory results regarding early hominin diets and dietary adaptations. A series of quantitative microwear studies (Scott et al., 2005; Grine et al., 2006a,b; Ungar et al., 2006; Suwa et al., 2009) found that most australopiths (including P. boisei, A. africanus, and Pr. afarensis) lack evidence of hard object feeding and that some show evidence of variation in microwear anisotropy consistent with a periodic reliance on tough vegetation. Possible corroboration of this hypothesis may derive from a recent carbon isotope analysis (van der Merwe et al., 2008) demonstrating that two P. boisei specimens preserve an isotopic signal consistent with the intense consumption of sedges, which are tough and ﬁbrous. In contrast, recent biomechanical studies have suggested that derived features in A. africanus (and, possibly, other early hominins) may have been adaptations to structurally reinforce the facial skeleton against loads applied to the premolars (Strait et al., 2008, 2009). Based on considerations of gape and occlusal morphology, it has been suggested that such premolar bites would have been associated with feeding on large, hard objects. Biomechanical evidence, therefore, appears to be at odds with, particularly, dental microwear evidence. Our view is that these disparate lines of evidence are not, in fact, contradictory, but rather that reconstructing the diets of these early hominins may be more complicated than previously thought. Moreover, it is worth keeping in mind that reconstructing the diet of an extinct species is an endeavor that is in many ways different from explaining why the dietary adaptations of a species may have evolved. The reason for this discrepancy is that the food items that exert the strongest selective pressure on a species may not necessarily be the items that are consumed most regularly (e.g., Marshall and Wrangham, 2007; Dominy et al., 2008). Dental microwear and isotopic analysis may provide the clearest indication of the foods most frequently consumed by early hominins, but when functional anatomy seems to be inconsistent with those types of diets, then a reasonable alternative hypothesis may be that the foods driving the evolution of the anatomy may either be infrequently consumed or difﬁcult to detect using microwear and isotopes (e.g., Lucas et al., 2008; Lawn and Lee, 2009; Strait et al., 2009). As a case in point, the fact that shearing crests are reduced in gracile australopiths relative to extant African apes (Ungar, 2004) indicates to us that tough, ﬁbrous or leafy vegetation could not have been an important selective factor in the evolution of hominin craniodental form regardless of how frequently those foods may have been consumed. Comparative 604 BERTHAUME ET AL. evidence of occlusal morphology is consistent with the hypothesis that hard objects were selectively important, and biomechanical evidence suggests that large, hard objects were of particular evolutionary importance. The possibility that blunt cusps evolved to reinforce the tooth crowns of hard object feeders is fully consistent with this hypothesis. This interpretation of australopith adaptation is, in our view, also consistent with dietary reconstructions in which australopiths ate tough or soft foods during most of their time spent foraging. Future Directions The ﬁndings presented here should be viewed as preliminary. Some future work should be directed towards increasing the sample size of hominin species so as to better facilitate investigation of both intraspeciﬁc and interspeciﬁc variation. This could be accomplished using mechanical testing, FEA, or both. Other work should investigate the impact of single versus multiple point tooth-food contact on fracturing, interactions between upper and lower teeth, the angle of incidence of the teeth with respect to the food item, and the impact, if any, of extraoral manipulation of foods items on the fracturing of large foods. Some of this can be easily accomplished using FEA but may be more difﬁcult to achieve using mechanical testing. Finally, an understanding of the Strong Cusp Hypothesis would be enhanced by further analyses investigating the relationship between tooth crown morphology and structural strength. CONCLUSION The use of FEA has been shown to be a valuable tool to simulate complex biting behavior. Results in terms of fracture force prediction were generally in good agreement with experimental data derived from physical testing, although more work is needed to fully establish intra- and interspeciﬁc patterns of variation among early hominin species. Results were broadly inconsistent with functional hypotheses relating the evolution of tooth shape to the fracturing of hard food items, suggesting that the relationship between occlusal morphology and fracturing ability may be complex. It is proposed, instead, that the evolution of tooth form in hard object feeders may be strongly inﬂuenced by the need to prevent the tooth crown from failing. This possibility is consistent with hypotheses explaining the evolution of australopith diets and dietary adaptations. ACKNOWLEDGMENTS The authors thank Adam Gordon for assistance with statistics, and Peter Lucas for advice regarding functional anatomy. LITERATURE CITED Chai H, Lee JJW, Constantino PJ, Lucas PW, Lawn BR. 2009. Remarkable resilience of teeth. Proc Natl Acad Sci USA 106: 7289–7293. Chekunaev I, Kaplan AM. 2008. Limiting velocity of crack propagation in elastic materials with effects of small viscosity and thermal conductivity. Theor Appl Fracture Mech 50:207–213. 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Surf Coatings Technol 155:121–129. APPENDIX A: DEFINITIONS OF COMMONLY USED MECHANICAL TERMS Hardness is the resistance to permanent deformation due to indentation, penetration, or scratching. Toughness is the amount of energy per volume that a material can absorb without fracture. Stiffness is the resistance of an elastic body to deformation by an applied force. Fracture is the local separation of a material under the action of stress that results in a crack. Fracture force is the minimum amount of force applied to an object that causes fracture to occur. Fracture energy is the minimum amount of work done by a force on an object that causes fracture to occur. Strength is the ability of a material to withstand an applied stress without failure. Displacement is the change in position of a point in reference to a previous position. Energy is the amount of work that can be performed by a force. Work is the amount of energy transferred by a force, given by the line integral of the force vector ~ F dotted ~ that locates the point with differential position vector ds of application of the force: Z W¼ ! ~ F ds c where C designates the force path. If the force acts along a straight line and is constant, then W¼~ F ~ d where ~ d is the displacement vector. If the force is linearly proportional to the displacement and acts in a straight line, then the total work done by the force to elastically deform the body is 1~ ~ W¼ F max dmax 2 where ~ Fmax and ~ dmax are the maximum force and displacement vectors. APPENDIX B: SUITABILITY OF THE HARD FOOD SUBSTITUTE The frozen acrylic hemispheres were a good substitute for the macadamia nuts. Results revealed that the acrylic hemispheres have a similar fracture force as macadamia nuts, a similar displacement before failure, and a similar failure mode. When they are frozen to -70 degrees Celsius, the hemispheres break in a brittle fashion as do the nuts. Note that when comparing the displacement to failure of the nuts and hemispheres, it is important to realize that the acrylic hemispheres represent half of a macadamia nut. Therefore, the elastic displacement of the hemispheres at a given load must be 606 BERTHAUME ET AL. doubled to obtain a comparative displacement value for the macadamia nuts. Another advantage of using an engineered object as a substitute for a hard food item is the ability to control its size, shape, and material properties. This enables one to isolate and test various hypotheses with regard to tooth morphology, food size, and bite mechanics. Further, the use of a clear acrylic hemisphere in this study enabled observations of crack formation. High-speed video of 10,000 frames per second revealed that the time for a crack to propagate from the top of the hemisphere to the bottom surface was <0.0001 sec. This corresponds to a crack propagation velocity exceeding 220 m/sec. Interestingly, Chekunaev and Kaplan (2008) derived a theoretical pﬃﬃﬃﬃﬃﬃﬃﬃﬃ limiting crack propagation velocity given by f ðvÞ E=q, where f(v) is an analytical function of Poisson’s ratio, and q is the mass density of the material. For the acrylic hemispheres with v ¼ 0.4, their equation yields f(v) ¼ 0.40. For E ¼ 3.2 GPa and density q ¼ 1.1 g/cm3, this yields a limiting crack propagation velocity of 677 m/s. Thus, high-speed video of up to 40,000 frames per second would be needed to observe the crack propagation over multiple frames. An observation worth noting is that the maximum tensile strength of acrylic is reported to be in the range of 19–90 MPa. However, FEA predicts stresses at the fracture displacement that are well beyond that found in the published literature. One reason for this difference might be the 70 C temperature of the hemisphere. No data could be found on the tensile strength of acrylic at this temperature. However, the FEA results that were consistent with physical testing indicate a maximum tensile stress, r1, of the chilled acrylic hemispheres in the range of 122–139 MPa. Also, it should be noted that the extremely high values of minimum principal stress, r3, are highly localized at the small regions of cusp contact and may be a result of modeling simpliﬁcations, namely the teeth modeled as rigid and faceted surfaces. Fracture Types All of the hemispheres in FEA showed highly tensile stresses on the inner surface of the hollow acrylic hemisphere. This corresponds well with predictions made by Lawn and Lee (2009) and Lee et al., (2009). They calculate that when teeth bite on bilayered ‘‘hard’’ foods such as seeds, in which an inedible shell protects a nutritious core, both median and radial cracks in the seed shell can be generated. Radial cracks initiate from the inner surface of the shell due to concentrations of tensile stress, while median cracks initiate at the contact between the shell surface and the indenter. Our FEA and physical test results are consistent with both of these predictions.