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The Effect of Early Hominin Occlusal Morphology on the Fracturing of Hard Food Items.

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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: grosse@ecs.umass.edu
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.
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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.
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