Functional consequences of tooth design: effects of blade shape on energetics of cutting

Gnathostome dental structures come in a wide range of shapes and sizes,from the triangular-shaped bladed teeth in the great white and other sharks,to the tall intricate molars of horses and other mammalian herbivores. The main function of dental structures is the capture, retention and/or reduction of food for ingestion. In order to perform these functions, the dental forms must overcome the resistance of the food item to fragmentation (arising from its toughness, hardness, etc.). This study examined one aspect of tooth design– blade morphology – by measuring the cutting efficiency of different blade configurations with identical blade edges on a set of prey items.

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.

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.

We designed a double-bladed guillotine system(Fig. 1), which is a good approximation to the dentition in carnivores and allows blades to be replaced and varied. A force transducer (LC703-100; Omegadyne, Inc., Sunbury, OH, USA)and an LVDT (Model 7307-W3-A0; Pickering, Inc., Farmingdale, NY, USA) for measuring displacement, were mounted on a 10 cm×10 cm aluminum base plate. The force transducer supported a fixed blade oriented vertically, edge pointed up. A linear dovetail slider (Unislide A2512-P10; Velmex, Inc.,Bloomfield, NY, USA) was attached perpendicular to the base plate. A small platform supporting the second (moving) blade, oriented edge-downward, was attached to the slide carriage of the linear slider. The blades were positioned such that they passed each other without touching (the clearance was not measured precisely, but was less than 100 μm) when the slide carriage was lowered. The core rod of the LVDT was attached to the slide carriage to track the displacement of the moving blade.

We used pre-sharpened utility blades (Stanley, Heavy Duty 0.024 in/0.61 mm blade width, Stanley Tools Product Group, New Britain, CT, USA) as the cutting implements for the double guillotine. The blades were secured to the testing machine using machine screws, oriented as described above, and tested to ensure that the blades did not contact (which would add frictional forces to the results). To create notched blade morphologies, the utility blades were cut at appropriate angles and glued together with epoxy resin (Ace Hardware Corp., Oak Brook, IL, USA) with the sharpened edges on the interior(Fig. 2). All blades,regardless of their configuration, bore identical cutting edges. We tested four different blade morphologies: (1) unaltered straight blades, and (2)blades cut and glued to create 120 deg. notches, (3) 90 deg. notches, and (4)60 deg. notches. We mounted notched blades on the upper (moving) platform in conjunction with a straight blade mounted on the fixed platform. Analogous triangular `fang' blades complementary to the three notched blades were also made and mounted on the moving platform, with the matching notched blades on the fixed platform.

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.

Knox™ 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.

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).

Salmon muscle and shrimp abdominal muscle showed similar deformation and fragmentation patterns. Using paired straight blades, the muscle was pinched and compressed until the two blades started to pass each other; the muscle then deformed both along and between the blades before the fracture finally initiated. When using a notched–straight blade pair on salmon and shrimp muscle, there was minimal pinching or deformation along the blade edge and the cut (almost exclusively due to the notched blade) was noticeably cleaner; only the connective tissue (myosepta) between the muscle bundles failed to cut completely.

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).

Shrimp tails with the cuticle intact exhibited a different failure pattern. When two straight blades were used, the cuticle bent beneath the blades and fractured at a location away from the blades' point of contact with the specimen. The fracturing cuticle produced considerable twisting and pinching in the underlying flesh, yielding a ragged and messy tear rather than a cut(Fig. 4B). When a notched blade was paired with a straight blade, the cuticle fractured at the point of contact of the notched blade and the flesh was more cleanly cut. With a 60 deg. notched blade or a fang–notch pair, the cuticle offered markedly less resistance, which resulted in minimal deformation of the cuticle or underlying muscle; the cuticle and flesh sliced simultaneously(Fig. 4C).

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.

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.

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: F_3,33=0.278; P=0.841)nor the maximum force measured (ANOVA: F_3,33=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: F_3,32=13.715; P<0.001), shrimp with cuticle (ANOVA: F_3,31=24.919; P<0.001) and whole smelt (ANOVA: F_3,34=8.494; P<0.001). The same patterns were seen in values of maximum force: shrimp muscle (ANOVA: F_3,32=26.658; P<0.001), shrimp with cuticle(ANOVA: F_3,31=16.116; P<0.001) and whole smelt(ANOVA: F_3,34=12.475; P<0.001).

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).

The presence of a notch in the cutting blades affected the fracture patterns observed during our cutting experiments. When paired straight blades were used, tough biological tissues such as the salmon, smelt and shrimp muscle largely deformed rather than fractured, often resulting in the muscle being pinched between the blades. The deformation included both sliding and shearing along the blade edge, and bending or `kinking' between blades. (See section below on difficulties in cutting tough materials.) When a shrimp with intact cuticle was cut using paired straight blades, the cuticle constrained the muscle within, preventing any pinching and sliding along the blades. The cuticle itself was bent by the paired straight blades; when the cuticle finally fractured, it was as a result of this bending. The underlying muscle was then cut after the cuticle fractured.

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.

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.

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).

Regardless of possible difficulties with deformation and lateral forces pushing the dentition apart, many carnivorous animals succeed in fragmenting tough prey with bladed dentitions. Although the jaws and dental surfaces themselves probably do not bend (the gnathostome jaw is stiffer than the thin blades used in this study), given the typically large mobility of the jaw joint, animals trying to cut tough prey materials must find some way to prevent tough materials (like salmon muscle) from pushing the dental surfaces out of alignment. The results of this study show that simply having irregular shaped bladed dentition can allow for fracture to occur at lower strain levels, and eliminate a good deal of the deformation that causes these problems. The relief angle of a tooth, defined as the angle between the movement of the tool and its trailing edge (called clearance in the engineering literature), can work to prevent teeth from being separated by food (Evans and Sanson, 2003). 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.

The authors would like to thank M. Coates, M. Westneat, D. Jablonski and S. Kidwell for comments and discussion of early drafts of this manuscript. We would also like to thank A. Evans and one anonymous reviewer for numerous insightful comments which have greatly improved this manuscript. Technical assistance was given by D. Plitt and the University of Chicago Central Shop in the construction of the notched blades.