The feeding apparatus of sea urchins, commonly referred to as Aristotle's lantern, is shown in Figure 1 C. This skeleton muscular system holds five teeth firmly in place, in which each jaw contains a single tooth.These jaws work together as a mechanical grasping in such a way that the outward protrusion and inward withdrawal of teeth occur centripetally and simultaneously.A microcomputed tomography (μ-CT) image of a segment of the whole tooth is shown in Figure 1 D. The image reveals that the tooth is formed along an elliptical curve with a T-shaped cross-section. Images of transversal and longitudinal cross-sections of the tooth, displayed in Figures 1 E and 1F, expose other imporant features of the tooth structure. The transversal section shows that the tooth is composed of three structural regions: the primary plates, the stone region, and the secondary plates ( Figure 1 E). The stone region is made of high-aspect-ratio, small-diameter fibers (micrometers in size) surrounded by an organic sheath. The fibers are embedded in a polycrystalline matrix consisting of nanometer-sized particles (10–20 nm in diameter)of magnesium-rich calcite. It was reported that the level of magnesium content varies along the tooth length and is higher at the tip region, which leads to higher hardness and abrasion resistance.The fiber diameter gradually increases from the stone (∼1 μm) to the keel (∼20 μm), where the cleavage fracture of large calcite fibers is dominant (see Figure S1 ). The longitudinal cross-sectional image ( Figure 1 F) of the stone reveals fiber fracture as well as pullout, which is due to the debonding at the interface between the fibers and the organic sheath. Primary plates are typically made of calcite single crystals and are located on the convex surface of the tooth, while the secondary plates populate the concave surface bounding the stone region laterally. The longitudinal section, shown in Figure 1 G, reveals the array of curved primary plates, stacked parallel to each other. The image also shows the fibers and polycrystalline matrix filling the space between plates. The keel ( Figure 1 H) forms the base of the T cross-section and increases the bending stiffness of the tooth. More images of the microstructure of the tooth are provided in Figure S1

In an effort to understand the tooth-wearing mechanism, the current study examines the tribological and wear behavior of the pink sea urchin (Strongylocentrotus fragilis) teeth ( Figures 1 A–1C ). Pink sea urchins are deep-sea marine species (found in a 100-m to 1-km ocean depth) that can grow up to a 10 cm in diameter.Similar to other urchins, they possess hard and mineralized endo- and exoskeletons. They gain their mineral components from seawater; and have been studied for insight into the mechanisms of biomineralization.Among their skeletal elements, teeth are heavily mineralized (∼99% mineralized) with magnesium-enriched calcite.They utilize their teeth to forage food from coral reefs, and scrape and bore holes into rocky substrates to hide from predators or to use as shelters against wave action.This requires their teeth to be tough and wear resistant in abrasive (i.e., sandy) environments.

(G and H) Different regions of the tooth showing the primary plates, stone, and the keel part at the tip (G) and away from the tip region (H). Scale bars, 50 μm.

Stress-strain curves obtained from micropillars fabricated within the stone region, along the longitudinal direction, are shown in Figure S4 . Surprisingly, the measured elastic modulus is almost half the one measured via indentation testing. Such a discrepancy between indentation and micropillar compression tests was also reported for dental enamel.Even though several explanations were advanced in the literature, from artifacts in sample preparation, e.g., ion irradiation, to environmental conditions such as humidity, the investigators could not justify the difference in the reported values. In this work, we found a size effect whereby the doubling of the size of the pillar resulted in a ∼30% increase in Young's modulus. We hypothesize that further increase in the micropillar size would minimize the difference in modulus measured with the two techniques. Unfortunately, the physical size of the stone region in the sea urchin tooth prevented fabrication of larger samples to confirm the hypothesis. Additional research is needed to gain further insight into the effect of testing small samples. In this regard, we refer the reader to the work by Odette and co-workers, who pioneered a number of experiments and analysis approaches to deal with the identification of material constitutive behavior from the testing of small samples.

The mechanical properties of the tooth constituents were also assessed using micropillar quasi-static compression experiments. The micropillar tests provided information on the nature of the compressive uniaxial stress-strain behavior of the stone, as well as the strength of the interface between calcite plates. We note that micropillar compression tests were previously employed in the testing of other biomaterials such as lamellar bone.Focused ion beam (FIB) milling was used to fabricate micrometer-sized pillars from the plate and the stone regions in the sea urchin tooth (see Experimental Procedures ). To assess the cohesive strength of interfaces between primary plates, in the convex side of the tooth, we fabricated micropillars at an oblique orientation relative to the normal interface. A representative set of fabricated micropillars, within the plate region, is shown in Figure 2 D. There are multiple interfaces at oblique angles to the pillar axis, which enables interface characterization under shear loading when the micropillar is axially compressed (see Figure S3 ). A micrograph of a typical micropillar containing an oblique interface is shown in Figure 2 E, where the sliding of the interface is clearly observed. The corresponding shear stress-strain curve is shown in Figure 2 F, from which the interface strength can be inferred. A summary of measured mechanical properties is given in Tables S1–S4 . Such properties are employed in the design of the wear tests and the parametrization of constitutive laws used in the finite-element simulations subsequently discussed.

To gain insight into the tooth wear mechanism, knowledge of the mechanical properties of the tooth constituents is crucial. Hence, nanoindentation and in situ scanning electron microscopy (SEM) micropillar compression tests were performed for this purpose. Samples sectioned along the longitudinal and transversal orientations were prepared for nanomechanical testing as described in Experimental Procedures . Low-depth indentation maps were obtained through single loading-unloading cycles with a spacing of 10 μm between each indentation. Data analysis revealed an average Young's modulus (E) and hardness (H), at the tip of the tooth in the longitudinal and transversal directions, to be E= 77.3 ± 4.8 GPa, H= 4.3 ± 0.5 GPa and E= 70.2 ± 7.2 GPa, H= 3.8 ± 0.6 GPa, respectively ( Figure S2 ). These results are consistent with previous studies of indentation on sea urchin teeth.In addition, indentations with cyclic incremental loading were performed in the longitudinal direction to establish a visco-plastic-damage model for the stone region. A representative indentation load-displacement curve is displayed in Figure 2 A. The modulus for each cycle was calculated based on the Oliver-Pharr methodusing the unloading data. Indentation cycles revealed a monotonic decrease in modulus with increasing indentation depth ( Figure 2 B). This stiffness degradation is attributed to damage accumulation through irreversible deformation, and is modeled via finite-element simulations using a visco-plastic-damage model previously employed in the modeling of bone. Note S3 summarizes the employed constitutive law together with the procedure used for its parametrization. Experimental evidence of damage is shown in Figure 2 C, where cracks are observed emanating from the corners of the indentation mark. Crack growth occurs around the fibers rather than through the fibers. This manner of crack deflection was previously observed in the fracture surface of sea urchin teeth as a result of the weak organic sheath/matrix interfaces.

(A–C) Representative cyclic indentation load-displacement curve, in the stone region along the longitudinal direction (A): experimental measurement (red dashed line) and finite-element modeling simulation (blue solid line). (B) Young's modulus as a function of indentation depth: experimental measurement (red solid line) and simulated results (blue solid line). Experimental error bars correspond to one standard deviation. (C) Image of residual indentation mark at the end of the cyclic indentation. Scale bar, 5 μm.

In Situ SEM Wear Tests

33 Schoberl T.

Jager I.L. Wet or dry—hardness, stiffness and wear resistance of biological materials on the micron scale. , 34 Pontin M.G.

Moses D.N.

Waite J.H.

Zok F.W. A nonmineralized approach to abrasion-resistant biomaterials. 20 Carnevali M.C.

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Melone G. The Aristotle's lantern of the sea-urchin Stylocidaris affinis (Echinoida, Cidaridae): functional morphology of the musculo-skeletal system. 14 Killian C.E.

Metzler R.A.

Gong Y.T.

Churchill T.H.

Olson I.C.

Trubetskoy V.

Christensen M.B.

Fournelle J.H.

De Carlo F.

Cohen S.

et al. Self-sharpening mechanism of the sea urchin tooth. Figure 3 Components of the In Situ SEM Wear Experiment with the Tooth Tip in Contact with the Diamond Substrate Show full caption (A) Left panel: schematic of the tooth-UNCD substrate. F N indicates the applied normal load on the tooth and V is the scratch velocity. Right panel: SEM image of the tooth in contact with the substrate. E Tooth , ν Tooth and E UNCD , ν UNCD are the elastic modulus and Poisson's ratio for the tooth and UNCD, respectively. R Tooth is the tooth radius of curvature. Scale bar, 100 μm. (B) Snapshots of recorded video during the wear experiment inside the SEM chamber. Scale bars, 30 μm. (i) The arrow indicates detached debris from the stone region. (ii) Onset of plate fracture. (iii) Chipping of plates from the convex side of the tooth. The deformation behavior of the sea urchin tooth (i.e., self-sharpening) was examined using a novel in situ SEM wear experiment. In the experiments, a tooth glued into a special holder was compressed against an ultra-nanocrystalline diamond (UNCD) substrate ( Figure 3 A). Such experimental design is in direct contrast to conventional scratch experiments, where the tip is typically made from diamond and the wearing surface is the substrate.Hence, our methodology focuses on revealing the role of tooth microstructure and constituent properties, on deformation and wearing, under well-controlled and measurable contact conditions. The diamond substrate is selected because of its hardness and wear resistance to activate and accelerate the tooth-chipping process. Details regarding the experimental setup and instrumentation employed in the wear experiments are provided in Experimental Procedures . In the experiments, a trapezoidal load-time profile is applied to the tooth to achieve a target compressive load, which is held constant during sliding. To mimic the motion of teeth inside the sea urchin mouthparts, scratching is performed along the radial direction (i.e., y direction in Figure 3 A), where the opening and closing of teeth occur simultaneously.Motion in this direction along with lateral motion of Aristotle's lantern, including rotation, shifting, and tilting, provide the required tooth functionalities of scraping, grinding, and biting.

Tooth , while the UNCD is considered as a rigid bulk half-space (see 35 K.L. Johnson, Contact mechanics, Cambridge University Press, 1987. ( F N ) Y = ( R Tooth E ∗ ) 2 ⋅ ( π σ Y ) 3 6 , (Equation 1)

where E* is the reduced elastic modulus and σ Y is the tooth yielding stress. The derivation of 36 Ellers O.

Telford M. Forces generated by the jaws of clypeasteroids (Echinodermata: Echinoidea). To estimate the applied mean contact stress and the required load to reach such pressure on the tooth, we employed a Hertzian contact mechanics analysis. The analysis can be conceptualized as the plane-strain problem of a curved elastic body pressed against a rigid half-space. In this regard, the shape of the tooth is treated as a curve with an equivalent radius of curvature, R, while the UNCD is considered as a rigid bulk half-space (see Figure 3 A). Under these conditions, the force required to initiate tooth yielding is given bywhere E* is the reduced elastic modulus and σis the tooth yielding stress. The derivation of Equation 1 is given in Note S1 . To ensure applicability of Equation 1 , we performed several indentation experiments, on the UNCD substrate, at various maximum prescribed displacements. The load-displacement curves as well as the characterization of the tooth tip before and after the tests are provided in Figure S5 . When the contact stress exceeds the stone yield stress, several “pop-in” events were observed in the load-displacement curves. SEM images of the tooth revealed deformation and cracking of the stone region. Thus, it was concluded that Equation 1 is a good estimator of the normal load needed to initiate yielding in the stone. We note that the biting forces from Aristotle's lanterns, from other species in Echinoidea, can range from ∼1 to 50 Newton,depending on the food source. The applied normal force in our experiment, for one tooth, ranges from hundreds of microNewtons up to 1 Newton, which results in 1- to ∼5-Newton force for the whole lantern, due to the presence of five teeth.

37 Ruina A. Slip instability and state variable friction laws. The wear tests were carried out inside a scanning electron microscope using a commercial nanomechanical testing system (Alemnis). The details of sample preparation and implementation are given in Experimental Procedures . Wear tests were performed by translating the substrate in the y direction, as schematically illustrated in Figure 3 A. The scratch parameters such as the tooth-tip velocity, V, as well as the sliding length, L, were chosen to perform the test in the stable friction regime.The applied normal stress was selected to achieve a mean pressure equivalent to the yield stress of the tooth. This ensured that no cracks would appear during the initial loading step, as revealed by the quasi-static tooth indentation tests, while sliding could potentially cause tooth chipping upon accumulation of plasticity and damage. As shown in Figure 3 B(i), some debris left by wear of the stone region is observed. As the stone region is worn and flattened, interface cracking between plates could initiate and propagate due to compression-shear loading and stress buildup in the calcite plates region. That this is indeed the case is observed in Figure 3 B(ii) and (iii), where the SEM images reveal the shedding of primary plates on the convex side of the tooth. To the best of our knowledge, these are the first experimental images capturing plate chipping, in three dimensions, and the associated tooth self-sharpening mechanism.

38 Williams J.A. Wear and wear particles—some fundamentals. w = f ( μ , F N , V , t , H Tooth , a ) . Here, F N is the applied normal load, μ is the friction coefficient, V and t are the imposed sliding speed and duration, respectively, H Tooth is the hardness of the tooth, and a is the contact radius. Using Buckingham's dimensional analysis, 39 Buckingham E. On physically similar systems, illustrations of the use of dimensional equations. w i a i = f ( μ , L a , F N a 2 H Tooth ) . (Equation 2)

To characterize the tooth-wearing phenomena and its relationship with independent variables, we conducted a dimensional analysis.For this purpose the tooth wear, w, is expressed as a function of several dimensionless variables. We note that w may refer to the flattening of the stone and potential chipping of the plates. The former is calculated based on the change in contact area, while the latter is calculated from removed area, in the plate region, times the thickness of the plate. In both cases, w is characterized by comparing before and after SEM imaging in each wear test. In the case investigated here (i.e., when only the tooth wears),. Here, Fis the applied normal load, μ is the friction coefficient, V and t are the imposed sliding speed and duration, respectively, His the hardness of the tooth, and a is the contact radius. Using Buckingham's dimensional analysis,the above equation can be reduced to a simpler nondimensional form given by (for details see Note S2

In the above equation, the power, “i” can be 2 for the flattening area ( w 2 ≡ A fl ) or 3 for the volume of chipping ( w 3 ≡ V cp ). In addition, F N /a2 can be defined as the nominal contact stress, and L is the sliding length equal to Vt. In the following, conditions under which self-sharpening may occur are revealed.

CL ). In a second type, the nominal contact stress was kept constant and equal to the stone yield stress (case W CS ). For the latter case, the flattened area was imaged and measured at specific sliding intervals of ∼1,000 μm, and employed to update the contact area. Subsequently, an updated load was employed in order to keep F N /a2 constant. The force leading to a prescribed contact stress and the initial contact radius, a 0 , were obtained from a contact mechanics analysis (see CL and W CS ), different wearing mechanisms were observed. Recorded SEM videos along with images of the tooth tips reveal, in both cases, flattening in the stone region. Videos of the wear experiments (S2, CL case, and over the range of L/a 0 investigated, only an increase in flattened area, without plate chipping, was observed ( CS case, continuous chipping and shedding of plates were observed ( 0 (see CL case even when the dimensionless sliding distance is much larger than for the W CS case. Careful examination of the stone flattening and chipped plates, shaded in red in 0 , a sharp reduction in the width of the flattened region is observed ( Figure 4 Characterization of Tooth Tips before and after Wear Tests Show full caption (A and B) SEM images of the tooth tip in pristine condition (i), and after wear tests (ii–v) as a function of scratch length: (A) under constant normal load, W CL , and (B) under constant nominal contact stress, W CS . The blue and red regions correspond to the flattened stone and chipped plates. Scale bars, 20 μm. (C) Quantification of the stone flattened area (A fl ) and the chipped volume of the plates (V cp ) as a function of normalized scratch length, L/a 0 . (D) Width of the flattened region as a function of L/a 0 . Error bars correspond to one standard deviation. Two types of wear experiments were carried out. In one type, the load corresponding to the onset of yielding was kept constant during the entire sliding process (case W). In a second type, the nominal contact stress was kept constant and equal to the stone yield stress (case W). For the latter case, the flattened area was imaged and measured at specific sliding intervals of ∼1,000 μm, and employed to update the contact area. Subsequently, an updated load was employed in order to keep F/aconstant. The force leading to a prescribed contact stress and the initial contact radius, a, were obtained from a contact mechanics analysis (see Note S1 ). Despite using the same initial contact stress in both cases (Wand W), different wearing mechanisms were observed. Recorded SEM videos along with images of the tooth tips reveal, in both cases, flattening in the stone region. Videos of the wear experiments ( Videos S1 S3 , and S4 ) are provided. When holding the load constant, Wcase, and over the range of L/ainvestigated, only an increase in flattened area, without plate chipping, was observed ( Figure 4 A). By contrast, when the normal force was increased to maintain the nominal contact stress constant, Wcase, continuous chipping and shedding of plates were observed ( Figure 4 B). This is also evident in a plot of measured flattened area and volume of chipped plates as a function of dimensionless sliding length, L/a(see Figure 4 C). This plot clearly shows that no plate chipping occurs for the Wcase even when the dimensionless sliding distance is much larger than for the Wcase. Careful examination of the stone flattening and chipped plates, shaded in red in Figure 4 B, clearly reveals the self-sharpening mechanism. The stone flattened area increases up to a point because when a plate(s) is chipped, a part of the flattened area is simultaneously removed ( Figure 4 B(iii–v)). Microstructural features such as the connection between stone and plates seem to facilitate this process. Indeed, high-magnification SEM images ( Figure S1 ) reveal that fibers in the stone region bend and penetrate the plate layering in the convex part of the tooth. Quantitatively, Figure 4 C shows a jump in the chipping volume when a new plate(s) detach from the tooth tip. Interestingly, at the same L/a, a sharp reduction in the width of the flattened region is observed ( Figure 4 D), indicative of the self-sharpening process. These experimental results reveal that by keeping the normal load constant during the wear test, tip blunting occurs, whereas the tooth remains sharp when the nominal contact stress is kept constant and equal to the yield stress of the stone. These results were consistently observed in several experiments. Additional wear experimental results are given in Figure S6

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