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First published online October 31, 2008
Journal of Experimental Biology 211, 3619-3626 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.020586
Functional consequences of tooth design: effects of blade shape on energetics of cutting
1 Department of Geophysical Sciences, University of Chicago, 5734 S. Ellis
Avenue, Chicago, IL 60637, USA
2 Department of Organismal Biology and Anatomy, University of Chicago, 1027 E.
57th Street, Chicago, IL 60637, USA
* Author for correspondence at present address: Department of Earth Sciences, University of Bristol, Wills Memorial Building, Queen's Road, Bristol BS8 1RJ, UK (e-mail: phil.anderson{at}bristol.ac.uk)
Accepted 25 September 2008
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Summary |
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 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Key words: blades, cutting, dentition, fracture, toughness
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INTRODUCTION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Lucas et al. (Lucas et al.,
2002
) define prey items in terms of the stiffness and toughness of
their component materials. Brittle materials, such as bone or mollusk shell,
store strain energy well but fail catastrophically; energy is required to
initiate a crack but, after the crack reaches a certain critical size, it can
grow explosively, drawing on the stored strain energy to create new surfaces
and extend the fracture (Lucas et al.,
2002). Cracks in tough materials, such as muscle or leather,
usually requires less energy to initiate, but tough materials (by definition)
blunt cracks and arrest fracture growth, making it harder to completely
fragment the material. Because tough materials do not store strain energy
well, energy must be continuously supplied to the crack tip from outside the
system in order to extend the fracture
(Lucas, 2004).
One way to supply energy directly to the fracture is through the use of a
bladed edge. A blade, especially a sharp blade, greatly reduces the work to
fracture (a measure of the work done per unit area created) of tough materials
such as rubber (Lake and Yeoh,
1978) and animal tissue
(Purslow, 1983;
Pereira et al., 1997;
Lucas and Peters, 2000), but
less so in plant material (Lucas et al.,
1997). Evans and Sanson (Evans
and Sanson, 1998) tested the effects of cusp shape on penetration
of animal tissues. For brittle cuticle (from adult beetles), sharper tips and
more acute angled cones required less energy to produce fracture; only the
sharpest tip on the most narrow angled cones was able to penetrate the tough
cuticle of beetle larvae.
The effects of blade design on the work required to fracture tough
materials is biologically relevant. Modern examples of `bladed dentitions'
include the carnassials of carnivorous mammals, which possess teeth with both
straight and curved blades (Van
Valkenburgh, 1989; Evans and
Sanson, 2003), the triangular fangs with bladed edges of
insectivorous mammals (Evans and Sanson,
2003), and the bladed edges in a variety of shapes and patterns
found in sharks (Frazzetta,
1988). Although not actually teeth, many birds, and even some
turtle species (Davenport et al.,
1992), have irregularly shaped bladed beaks used for fragmenting
prey. Extensive bladed dentitions exist in fossil taxa as well, such as the
bladed jaws of some placoderms, a group of basal fishes.
Few studies have examined the effects of blade design on cutting
efficiency. Frazzetta's (Frazzetta,
1988) classification of shark teeth's cutting ability was largely
theoretical – experimentation was limited and observations were strictly
qualitative. Abler (Abler,
1992) attempted to test several aspects of serrated teeth focusing
on isolating different cutting styles. This is one of the few studies to
actually try to experimentally test aspects of tooth design and efficiency.
The canine teeth in bats (Freeman,
1992) and the molars of herbivorous mammals
(Popowics and Fortelius, 1997)
have been analyzed theoretically, but the hypotheses proposed were never
experimentally tested. Evans and Sanson's
(Evans and Sanson, 1998) work
was notable for testing the effects (in terms of force required and energy to
fracture) of tip and cusp sharpness. Their subsequent work
(Evans and Sanson, 2003;
Evans and Sanson, 2006)
defined several characteristics of bladed dentitions that should reduce the
work required to fracture tough materials but did not experimentally test the
theoretical models on actual materials. Numerous studies quantify aspects of
the functional design of human incisors (e.g.
Korioth et al., 1997; Agrawal
and Lucas, 2002).
Blade sharpness, measured as the radius of curvature of the cutting edge
(Arcona and Dow, 1996;
Popowics and Fortelius, 1997),
has been examined in a number of papers comparing various toughness testing
methods (Darvell et al., 1996;
Aranwela et al., 1999;
Doran et al., 2004). All these
paper show that blunt blades require more energy to cut than sharp ones. The
forensic literature includes experimental work on sharp implements and their
effect on human tissue, especially puncture wounds from needles
(O'Callaghan et al., 1999;
Frick et al., 2001;
Shergold and Fleck, 2004). The
fracture properties of animal tissue are an issue in the food science
literature, but the tissue itself is typically highly processed beforehand
(e.g. Fernandez-Martin et al.,
1998; Skjervold et al.,
2001). Atkins and Xu (Atkins
and Xu, 2005) offered a detailed theoretical framework for
examining the effects of curved blades, such as on a commercial meat slicer,
on the cutting of tough materials. They compared their predictions with data
from Pereira et al. (Pereira et al.,
1997), but did not perform any experiments of their own.
In this study, we focused on a small set of blade designs, comparing
straight blades to `notched' blades or triangular fangs in which the cutting
edges are set at select angles. One of the challenges of cutting tough, low
shear modulus materials like animal muscle between bladed teeth, is that such
material can deform and slide out from between the dental structures when
compressed. It has been suggested that the recesses of a notched blade can act
as a trap for the muscle, holding it in place and preventing deformation
(Lucas, 2004). Less
deformation means less energy dissipated during cutting, which should lead to
decreased work required to fragment the material
(Lucas, 2004).
We tested the effects of different notched blade configurations on the measured work to fracture (energy) and maximum force required to fully fragment unprocessed biological materials. We tested the following null hypotheses. (1) There are no significant differences in energetic cost to fragment the biological materials using notched blades or straight blades. (2) The measured work to fracture is independent of the angle of the notched blade used. (3) A notched blade with a matching fang does not reduce the work to fracture relative to a notch–straight blade pair. (4) The configuration of the blade shapes will have no effect on the maximum force required to create and propagate fractures in biological materials.
Testing apparatus
Work to fracture (sometime called fracture toughness) is defined as the
work required to create a surface of unit area on a material
(Atkins and Mai, 1985). It is
the work done on the specimen (the energy input) divided by the area cut. Two
basic methods have been used to measure work to fracture: the guillotine test
and the scissors test. Guillotine tests involve a single blade, which is
forced through a test specimen lying on a flat surface
(Atkins and Mai, 1979); it is
frequently used on non-biological materials such as rubbers
(Lake and Yeoh, 1978) and
metal (Atkins and Mai, 1979).
The guillotine blade is often set at an angle to the surface of the test
material and the direction of travel of the blade. The Warner–Bratzler
shear test uses a variation on the guillotine design in which the blade
incorporates a 73 deg. notch; it has been used to measure fracture properties
in commercial fish (Veland and Torrissen,
1999). The rationale for including this notch is never
clarified.
The scissors test is extensively used on biological materials (e.g.
Pereira et al., 1997;
Lucas, 2004). A pair of
scissors is mounted within a universal testing machine, a sample of thin
material (such as animal skin, plant leaves, or sheet metal) is suspended
between the blades, and the forces required to close the handles (and thereby
the blades) are registered by a force transducer
(Pereira et al., 1997). The
guillotine test and scissors test share the common feature of keeping a sharp
blade pressed against the tip of the advancing fracture, preventing crack
blunting (Lucas, 2004).
The scissors test is a reasonable approximation of the double bladed dentition (opposing bladed teeth on both the upper and lower jaws) found in many carnivorous animals. However, the difficulty of substituting blades in a pair of scissors makes it hard to test differences in blade design. A guillotine design permits blade substitution and allows considerable variation in blade design. Although the standard implementation of the guillotine involves only a single blade, there is no fundamental barrier to mounting two opposing blades to determine how two blades interact.
A recent paper by Ang et al. (Ang et
al., 2008) criticizes the use of double blade systems for
measuring work to fracture. Ang et al. (Ang
et al., 2008) illustrate several difficulties with cutting
materials cleanly and getting accurate measurements of material properties
using double blade systems and propose a new testing system: the razor slicing
test (RST). This system comprises a single blade guillotine at an angle, used
to cut the test material. Although this testing system has many advantages for
comparing work to fracture between various materials, we are specifically
interested in the effect of various blade configurations, which mimic real
biological dentitions, on fracture properties of the same material.
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MATERIALS AND METHODS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Test materials
We tested four commercially purchased biological materials: (1) salmon
muscle, cut into small rectangular pieces (20–50 mm2 in cross
section) which usually included a portion of one or more myosepta; (2) shrimp
flesh (abdominal muscle), removed from the exoskeleton (elliptical cross
section, on the order of 1–1.5 cm2); (3) whole shrimp tails
with exoskeleton intact (same size and shape as the shrimp abdomens); and (4)
whole smelt (Osmerus mordax), 5–6 cm in length, 50–80
mm2 in cross section, sold locally for human consumption. All test
materials were purchased raw and frozen but thawed prior to testing. All
experiments done on any given material were performed on the same day to
eliminate differences in the history of the materials (and thus possibly
material properties) as a variable in the response of the tissues to different
blade configurations. We placed the specimens between the two blades of the
guillotine, centered under the middle of the notch when a notch was present
(Fig. 3A–C). The smelt
were oriented on their side with the dorsoventral axis horizontal such that
the blades made contact at the thickest portion of the body. We started
measuring displacement and force when the top blade made contact with the test
material and stopped when the material was fully separated into two pieces.
The area cut was calculated as the measured cross sectional area of a cut
surface.
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KnoxTM unflavored gelatin, prepared as per Harris
(Harris, 1978) was cut into
small squares (on the order of 75 mm2 in cross section) and tested
using the double guillotine with the same array of blade morphologies. Gelatin
is a photoelastic material, which allows patterns of strain to be visualized
under polarized light illumination
(Harris, 1978;
Full et al., 1995;
Dorgan et al., 2005). When
undeformed, the collagen molecules within the gelatin are randomly oriented.
When gelatin is deformed, the collagen molecules reorient and align relative
to the resulting strain, which makes the gelatin birefringent. Interference
colors (Bloss, 1961) are a
function of the thickness of the material (constant in this study) and the
magnitude of the strain. For a full review of how polarized light and
photoelastic materials interact, see Harris
(Harris, 1978), Full et al.
(Full et al., 1995) and Dorgan
et al. (Dorgan et al.,
2005).
We placed a linear polarizing filter on either side of the double guillotine and oriented them perpendicular to each other; a fiber optic illuminator was used as a light source. We photographed the interference color patterns (Nikon D100 with a 60 mm macro lens) seen through the second polarizing filter during the cutting of the gelatin. We compared the strain patterns observed with different configurations (paired straight blades, straight and notched blades, notched and triangular blades), restricting the analysis to qualitative comparisons of color patterns between different test conditions.
Analyses
Voltage outputs from the force transducer and LVDT were converted into
force and displacement based on calibration curves constructed using known
masses and distances. We calculated the area under force-displacement curves
generated from each experiment (=work in joules) and divided the result by the
cross sectional area of the cut specimen to determine work to fracture (J
m–2). Maximum force required for fracture was taken as the
peak force measurement seen during each experiment.
All five materials (four biological tissues and the gelatin) were tested under the following conditions: two opposing straight blades, 120 deg. notched blade vs a straight blade, 90 deg. notched blade vs a straight blade, 60 deg. notched blade vs. a straight blade. The shrimp tails with cuticle were also tested using matching fang and notched blades at notch angles of 120 deg. and 90 deg. We repeated each test ten to 12 times, yielding a total of 220 individual measurements. Some results were removed from analysis because the tissues had been damaged prior to testing.
We calculated average work to fracture and maximum force required for each material and blade configuration. We used ANOVA to compare these values between treatments and performed post-hoc tests to identify significant differences between specific conditions (SPSS for Mac OS X).
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RESULTS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Smelt exhibited a single, consistent fracture pattern with all blade configurations. The flesh was pinched and deformed before the fracture initiated and measured forces increased markedly when the blades engaged the bony vertebral column. The skin slid between the blades without being cut, but sometimes tore as the blades passed each other. Notched–straight blade pairs often yielded subjectively cleaner cuts than paired straight blades (Fig. 4A).
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In tests involving paired straight blades, cutting and crack growth occurred at both blades, but the top (mobile) blade induced the first fracture followed by the bottom (immobile) blade. When a notched blade was paired with a straight blade, all of the fractures initiated where the notched blade contacted the specimen regardless of which blade was mobile. When the fang and notch combination was used on the shrimp tails with cuticle, all fracture propagation occurred at the fang, either at the tip or along the sides. The notched blade held the specimen, but did not initiate any cracks.
The strain patterns seen in gelatin were consistent with the fracture patterns observed for biological tissues (Fig. 5). When paired straight blades were used, strain occurred at both blades (Fig. 5B,C). However, the other two blade configurations showed initial strain only occurring along blades creating cracks, whether that blade was notched (Fig. 5F) or a fang (Fig. 5J,K). After cutting had begun, some strain did occur at the straight blade in the notch–straight blade test (Fig. 5G) but strains appeared smaller than at the notched blade.
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Since all gelatin pieces were the same thickness, the colors seen in the three tests are directly comparable in terms of the magnitude of strain they represent, although absolute values of strain were not determined. Fig. 5G shows a spectrum from the lowest strain (bright white) up into first order (retardation <550µm) and even some possible second order interference colors (retardation 550–1100µm: lighter, almost pastel colors). The fang and matching notch test shows only white interference colors (retardation <250µm), indicating smaller overall strains during cutting than in the other two tests (Fig. 5J–L). The black line running vertically along the midline of the gelatin blocks in the notch–straight blade (e.g. Fig. 5F–H) and fang–notch tests (e.g. Fig. 5J–L) is an artifact of the orientation of the polarizing filters and disappears when the filters are rotated 45 deg.
Statistical results
The presence of a notched blade had different effects depending on the
material tested (Table 1).
Blade configuration had no significant effect on the measured work to fracture
of salmon muscle (ANOVA: F3,33=0.278; P=0.841)
nor the maximum force measured (ANOVA: F3,33=1.763;
P=0.173). The average work to fracture values and peak force values
measured for salmon were similar for all blade configurations
(Table 1). There were
significant differences in the work to fracture values measured under
different blade configurations for the other three materials: shrimp muscle
(ANOVA: F3,32=13.715; P<0.001), shrimp with
cuticle (ANOVA: F3,31=24.919; P<0.001) and
whole smelt (ANOVA: F3,34=8.494; P<0.001). The
same patterns were seen in values of maximum force: shrimp muscle (ANOVA:
F3,32=26.658; P<0.001), shrimp with cuticle
(ANOVA: F3,31=16.116; P<0.001) and whole smelt
(ANOVA: F3,34=12.475; P<0.001).
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For shrimp (with and without cuticle) and smelt, the angle of the notched blade significantly affected work to fracture measures (Table 1). For shrimp abdominal muscle without cuticle, using a 60 deg. notch–straight blade configuration reduced work to fracture by 40% in comparison with other configurations (Bonferroni post-hoc test: mean difference >188, P<0.01). When shrimp muscle with intact cuticle was tested, the use of 120 deg. and 90 deg. notch configurations resulted in 20–40% reductions in work to fracture compared with paired straight blades (Bonferroni post-hoc test: mean difference >268, P=0.01). Using a 60 deg. notch further reduced the work to 55% (Bonferroni post-hoc test: mean differences >207, P<0.05). Results from tests on smelt showed 30–40% lower work to fracture values when 90 deg. and 60 deg. notches were used (Bonferroni post-hoc tests: mean difference >260, P<0.01). Maximum force measurements showed the same pattern amongst different notch angles as indicated by Bonferroni post-hoc tests for the work to fracture.
For both fang and notch angles (Table 2), the use of fang and matching notched blades significantly reduced (by 20–60%) the measured work to fracture of shrimp with cuticle compared with the same notch angle blade paired with a straight blade (independent t-test: 120 deg., t=2.528, d.f.=16, P=0.02; 90 deg., t=9.558, d.f.=18, P<0.001). By contrast, the maximum force values measured show the opposite trend, with the 120 deg. fang–notch conditions resulting in significantly higher peak forces during testing (independent t-test: t=2.980, d.f.=16, P<0.01) as shown in Table 2. The 90 deg. fang–notch combination also showed higher forces than the notch and straight blade, but this difference was not significant (Table 2).
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DISCUSSION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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A notched blade produced markedly less deformation in all the materials
tested. During the experiments on shrimp with cuticle, the cuticle fractured
at the points of contact with the notched blade, preventing the cuticle from
bending as seen with paired straight blades. For both smelt and shrimp with
cuticle, the use of notched blades led to much cleaner overall cuts, with
little shear deformation along the blade
(Fig. 4). These results support
the hypothesis that a notched blade acts to capture and restrain tough,
malleable materials, allowing fracture to occur with minimal deformation
(Lucas, 2004).
Further support for a reduction of deformation in materials cut with notched blades comes from the gelatin experiments. The colors seen in the gelatin during cutting (Fig. 5) showed that different blade configurations produced different levels of overall strain and deformation within test materials during cutting. The use of notched–straight blade or fang–notch blade pairs reduced the overall strains seen with a paired straight blade configuration. Lower internal strains indicate that less of the energy supplied by the blades is dissipated through deformation and should lead to a reduction in the overall work necessary to create fractures. However, the use of notched and fang configurations has a second effect on cutting properties. Not only is there less overall strain, but also the strain is localized around the points of contact with notched and fang blades, whereas paired straight blades resulted in higher strains throughout the material (Fig. 5A–D). By localizing strain around the points of contact, these alternative configurations cause the material to fail at lower overall strain levels. The dual effects of reduction and localization of strain mean that the prey material will fracture and fragment with less wasted energy caused by large scale deformation.
Effects of blade morphology
Results from the tests performed on the shrimp muscle, shrimp with intact
cuticle, and smelt bodies permit us to reject the null hypothesis 1 –
for all three biological materials, the use of a notched blade configuration
significantly reduced the work to fracture during cutting. Test results for
the shrimp with and without cuticle and smelt also permit us to reject null
hypothesis 2 – notched blades with more acute angles (60 deg. and/or 90
deg.) produced significantly lower work to fracture values in test materials
than the more obtuse angled notches (120 deg.). The third null hypothesis can
be rejected on the basis of the results from tests on shrimp with cuticle
using a fang–notch configuration; the fang–notch configuration
resulted in significantly lower measured work to fracture values than the
notch with straight blade configuration. Test results for salmon muscle failed
to show significant differences among measured work to fracture between
different blade configurations.
Null hypothesis 4 can be rejected based on experiments using shrimp muscle
(with and without cuticle) and smelt. The maximum forces measured show the
same patterns of variation with respect to notch angle as the work to fracture
values. However, maximum force shows the opposite trend when comparing
notch–fang configurations with notched–straight blade
configurations; a notch and matching fang lowers work to fracture, but
increases the maximum force required to initiate fracture. These results show
that force measurements do not necessarily correlate with energy expenditure
or cutting efficacy in tooth design. Incongruence between force and energy
measured during cutting has previously been noted in studies of fracture
toughness in plant material (Lucas and
Pereira, 1990).
A major goal of this study was to test the effects of blade morphology on the ability to cut various biological materials. Tough, low shear modulus materials like animal muscle deform between dental structures when compressed, and can blunt fracture growth when using a simple paired straight blade configuration. As shown here, notched blade designs reduce this deformation and have significant effects on the realized work to fracture of biological tissues.
However, our results also show that it is not just the `trapping' ability of the notched blade configuration which reduces the work measured. As noted above, while the notched blades do reduce overall strain and deformation within the material, they also localize the strain at the point of contact with the notched blade. Furthermore, although the presence of a notch should reduce shear deformation along the blade, the angle of the notch per se should not have any effect on trapping ability. However, our results show that the angle of the notch does have a significant effect on the work to fracture in the materials tested. The introduction of a fang should also have no effect on food retention; however, the fang and notch combination results in even lower work to fracture values.
When the notch angle is altered, so is the approach angle of the blade (the
angle between the perpendicular of the long axis of the blade and the
direction of motion). The approach angle has been proposed to be a key feature
in bladed tooth design (Evans and Sanson,
2003). The fact that configurations with high approach angles
(more acutely angled notches) resulted in significantly lower work required
for fracture, may indicate that the approach angle plays a major part in
energy reduction with notched blades. This suggestion is further supported by
the results from the gelatin experiments which show that the majority of
cutting occurs along the high angled notched blades as opposed to the
underlying straight blade in notched–straight blade pairs. Further work
is planned to try to tease apart the trapping ability of a notched blade from
the effect of the approach angle on cutting efficiency.
Through a combination of trapping ability and high approach angles, bladed notches and complementary fangs provide significant energetic advantages for fragmenting prey tissues. Perhaps just as significant ecologically, notched and notch and fang configurations cut thin brittle materials (e.g. calcified shrimp cuticle) and muscle tissues cleanly and on a single pass, potentially reducing a predator's prey handling time considerably.
Notched blades with high approach angles and related dental morphologies
have evolved convergently multiple times in both living and fossil
gnathostomes. The carnassials of mammalian carnivores show a wide range of
morphologies, but one consistent aspect is the presence of large notched
blades of varying angle (Evans and Sanson,
2003; Evans and Sanson,
2006). Various chondrichthyan taxa show many bladed, triangular
teeth which, when arranged in a row, create a series of high angled bladed
notches (Frazzetta, 1988) some
of which become quite pronounced as in the cookie-cutter shark (Isistius
brasiliensis) (Shirai and Nakaya,
1992). The omnivorous turtle Batagur baska has a V-shaped
notch at the front of its jaws that it uses to help cut tough plant materials
(Davenport et al., 1992). Even
in the earliest gnathostomes, examples of notched blade morphology can be
found. There are numerous placoderm taxa (such as the monstrous
Dunkleosteus terrelli) which have bladed dentitions punctuated by
notches and matching fangs (Miles,
1969; Anderson and Westneat,
2007). These examples show that a simple, yet effective, dental
design has evolved multiple times, in multiple different ways across disparate
taxa.
Difficulties with tough prey
The deformation patterns seen using the paired straight blade configuration
offer insights into the difficulties of cutting tough materials that
carnivorous animals must deal with. In the tests done on salmon muscle, the
blades were observed to bend or deflect, often with muscle wedged in between
(Fig. 6). The observed kinking
of the material resembled the `burring' seen in metal when cut by a guillotine
(Atkins and Mai, 1979). The
maximum forces measured were quite low during these experiments (2–5 N),
so it is unlikely that the deflection was due to the applied force inducing
buckling in the utility blades. It is more likely that the tough ductile
nature of the material allowed it to deform and slide between the blades
creating lateral forces, which pushed the opposed blades apart. Researchers
design most guillotine and scissors tests to ensure the test material is
completely bisected regardless of how little the testing machine actually
resembles a carnivore's jaw morphology
(Purslow, 1983;
Pereira et al., 1997). The
lateral stiffness of these machines is great enough to make the lack of shear
stiffness in tough materials irrelevant. The double guillotine design better
resembles the dentition of a carnivore's jaw: two opposed blades with varied
morphologies. However, the design comes closer to reality at the expense of
stability. There is much lower lateral stiffness in the double guillotine than
other testing machines, so shear deformation in the biological tissues results
in the blades being pushed out of alignment
(Fig. 6).
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).
Recent work on mammals has suggested that the intricate dental morphology seen
in the rows of teeth of these carnivores may result in an auto-occlusion
system capable of self-correcting the bite
(Evans and Sanson, 2006).
Stabilizing musculature and its associated neural feedback system has received
little attention in the feeding mechanics literature, but may also be vital to
processing tough materials.
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Acknowledgments |
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