Threat-Protection Mechanics of an Armored Fish

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Research paper Threat-protection mechanics of an armored fish

Juha Songa, Christine Ortiza,∗, Mary C. Boyceb,∗ a Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, RM 13-4022, Cambridge, MA 02139, USA b Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

ARTICLEINFO ABSTRACT

Article history: It has been hypothesized that predatory threats are a critical factor in the protective functional design of biological exoskeletons or “natural armor”, having arisen through evolutionary processes. Here, the mechanical interaction between the ganoid armor of the predatory fish Polypterus senegalus and one of its current most aggressive threats, a Keywords: toothed biting attack by a member of its own species (conspecific), is simulated and studied. Exoskeleton Finite element analysis models of the quad-layered mineralized scale and representative Polypterus senegalus teeth are constructed and virtual penetrating biting events simulated. Parametric studies Natural armor reveal the effects of tooth geometry, microstructure and mechanical properties on its ability Armored fish to effectively penetrate into the scale or to be defeated by the scale, in particular the Mechanical properties deformation of the tooth versus that of the scale during a biting attack. Simultaneously, the role of the microstructure of the scale in defeating threats as well as providing avenues of energy dissipation to withstand biting attacks is identified. Microstructural length scale and material property length scale matching between the threat and armor is observed. Based on these results, a summary of advantageous and disadvantageous design strategies for the offensive threat and defensive protection is formulated. Studies of predator-prey threat-protection interactions may lead to insights into adaptive phenotypic plasticity of the tooth and scale microstructure and geometry, “adaptive stalemates” and the so-called evolutionary “arms race”. ⃝c 2010 Elsevier Ltd. All rights reserved.

1. Introduction (Reimchen, 1988; Mapes et al., 1989; Mcclanahan and Muthiga, 1989; Kodera, 1994; Zuschin et al., 2003). One common mode It has been hypothesized that environmental and predatory of predator attack is a localized penetration or indentation threats are critical factors in the protective functional into an exoskeleton with a relatively sharper object (e.g., design of biological exoskeletons or “natural armor”, which tooth, claw, beak, shell protrusions, etc.) (Vermeij, 1987; arise through processes such as co-evolution and escalation Zuschin et al., 2003) that induces complex local multiaxial between predators and prey (Vermeij, 1987; Dietl and Kelley, stress and strain concentrations, which dissipate the energy 2002). Evidence for predator-related exoskeletal damage of the attack and can potentially lead to failure or and repair has been reported extensively in the literature fracture of the armor and/or threat (Bruet et al., 2008;

∗ Corresponding author. Tel.: +1 617 253 2342; fax: +1 617 258 6936. E-mail addresses: [email protected] (C. Ortiz), [email protected] (M.C. Boyce). 1751-6161/$ - see front matter ⃝c 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jmbbm.2010.11.011 2 JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) –

Wang et al., 2009). Biological armor systems utilize many Here, the interaction between the ganoid armor of protective structural design principles to resist penetrating P. senegalus and one of its current most aggressive threats, a attacks (Ortiz and Boyce, 2008) including, for example, local biting attack by its own species, was simulated and studied. energy-dissipating inorganic–organic composite nano- and The teeth of P. senegalus are monocuspid and conical, and microstructures (Currey and Taylor, 1974; Wang et al., 2001), consist of two layers—a cone of dentin capped by an outer multilayering and grading (Bruet et al., 2008), crystallographic layer of enameloid (Fig. 2(a) and (b)) (Clemen et al., 1998; and shape-based anisotropy (Wang et al., 2009), fibrous Wacker et al., 2001), both of which are comparable in material reinforcement at joints (Gemballa and Bartsch, 2002), and properties and length scale to the dentin and ganoine layers active offensive components (Reimchen, 1983; Song et al., of the armor. In our previous works (Bruet et al., 2008; 2010). Mechanical strategies for resisting penetration include; Wang et al., 2009), a predatory toothed bite on a P. senegalus (1) armor which defeats the threat via deforming and/or ganoid scale was approximated computationally using finite fracturing the threat, (2) armor which dissipates the energy element analysis (FEA) where the tooth was idealized by an of the threat via plastic deformation and/or a multitude of infinitely rigid indenter and penetrated into an individual cracking events within the armor, and (3) a combination quad-layered scale. In the current study, the indenter is of both of these mechanisms. In all cases, the armor modeled as deformable, thereby more closely representing design also needs to minimize the back-displacements and the true biological threat, i.e. the tooth. The geometry of stress levels transmitted to the underlying soft tissues the indenter was approximated from optical and scanning and vital organs of the animal. In this study, the role of electron microscopy images of typical P. senegalus teeth. geometry, microstructure, and deformability of the threat The role of the threat (tooth) geometry (e.g. end-radius, relative to that of the armor on threat-protection mechanical cone angle), multi-layered structure, and deformability on interactions (e.g. penetration resistance, energy dissipation, penetration resistance, local stress and strain distributions, local stress/strain distributions, etc.) are investigated. Such and energy dissipation of both the threat and armor during a virtual predatory biting attack was parametrically studied. a mechanistic approach to predator–prey offensive and Based on these results, a summary of advantageous and defensive interactions is relevant to elucidating universal disadvantageous design strategies for the offensive threat principles that direct ecological interactions and resulting and defensive protection was formulated. Studies of such a evolutionary outcomes (Herre, 1999; Dietl and Kelley, 2002) system where the offensive threat and defensive protection and also can provide insights in the design of synthetic are comparable may lead to insights into adaptive phenotypic protective systems. plasticity of tooth and scale microstructure, predator–prey The model system chosen for this research is the “living “adaptive stalemates” and the so-called evolutionary “arms fossil” fish Polypterus senegalus, which possesses a particu- race” (Agrawal, 2001; Dietl and Kelley, 2002). larly robust and efficient ganoid armor (Sire, 1990; Bruet et al., 2008; Wang et al., 2009) and belongs to the ancient family Polypteridae, which appeared 96 Myr ago in the Cretaceous 2. Methods period (Daget et al., 2001) and still lives today at the bottom of freshwater, muddy shallows and estuaries in Africa 2.1. Geometry of P. senegalus teeth (Kodera, 1994). A “living fossil” generally refers to a living species that is anatomically similar to a fossil species which The skull of a P. senegalus specimen was extracted from first appeared early in the history of the lineage (when the its dead body (total length: ∼15 cm). Teeth from the upper ancestral form first appeared before evolutionary processes), jaw were imaged using an optical microscope (Eclipse L150, thereby having experienced a long period of evolutionary Nikon, Japan) and scanning electron microscope (SEM, JEOL stasis (Eldredge and Stanley, 1984). The existence of living JSM 6060, Peabody, MA). SEM samples were imaged at a fossils has been attributed to stabilizing selection caused 10 kV acceleration voltage after fixation on a steel support by particular ecological circumstances, e.g. reduced compe- using conductive tape and sputter-coating with ∼5 nm of tition, isolated habitats, etc. (Darwin, 1859). The scales of gold–palladium in a Denton Vacuum Desk II (Moorestown, P. senegalus retain many characteristics of the dermal armor NJ). The geometry of 25 teeth from the premaxillary and of ancient palaeoniscoids and possess four mineralized lay- maxillary regions was quantified using optical and SEM ers (from outer to inner); ganoine, dentin, isopedine, and images including; half cone angles, height, end radii, and bone (Sire, 1994; Sire et al., 2009). The ganoid armor of an- shape. The teeth were found to be monocuspid and conical cient palaeoniscoids would have been exposed to the many (Fig. 2(a), (b)). The tooth-end radii (measured by SEM) varied large extinct invertebrate predators that existed at that time between 5 and 30 µm (mean ± standard deviation = 11.7 ± (Romer, 1933; Ørvig, 1968; Brett and Walker, 2002). Today, the 5.6 µm (Fig. 2(c))), a half cone angle (θ/2) of ∼22◦, and a total primary predators of P. senegalus are known to be members height of ∼500 µm (Fig. 2(d)). P. senegalus teeth consist of of its own species and its carnivorous vertebrate relatives two material layers—a cone of dentin capped by an outer (Romer, 1933). Powerful bites occur during territorial fighting layer of enameloid, equal to approximately a quarter of the and feeding, posing significant risk of injury (Kodera, 1994) total tooth height, thickness ∼100 µm (Clemen et al., 1998; (Fig. 1(a), (b)). P. senegalus feeds opportunistically, and easily Sasagawa et al., 2009; Wacker et al., 2001). Enameloid is preys on many animals it can fit in its mouth via biting, in- a hypermineralized tissue containing non-prismatic, apatite cluding fishes (including its own species), frogs, insects, and crystals and a collagenous organic matrix (Sasagawa et al., crustaceans (Kodera, 1994; Raji et al., 2003)(Fig. 1(c)–(e)). 2009). Ganoine is also hypermineralized (<5 wt% organic) JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) – 3

(a) Territorial fighting between two (b) Territorial fighting between two comparable sized comparable sized Polypterus ornatipinnis. Polypterus ornatipinnis.

(c) Predatory attack of Polypterus endlicheri (d) Predatory attack of Polypterus delhezi on prey endlicheri on prey fish. fish.

(e) Predatory attack of P. senegalus on prey fish.

Fig. 1 – (a) Ornate Polypterus Aggression Video, YouTube, Web, created on Sept. 20, 2007. Last accessed on Dec 20, 2010. http://www.youtube.com/watch?v=51oLrMBqN3s&feature=related. (b) Polypterus fights Video, YouTube, Web, created on July 17, 2007. Last accessed on Dec 20, 2010. http://www.youtube.com/watch?v=q1Xc2WP7KQk&feature=related. (c) Polypterus endlicheri endlicheri vs. Polypterus ornatipinnis Video, YouTube, Web, created on Jan. 14, 2007. Last accessed on Dec 20, 2010. http://www.youtube.com/watch?v=um3Pl-GUYy0&NR=1. (d) 55 for sengal bichir and others, African theme, Aquatic Predators: Primitive Fishes Forums – Bichirs and Rope Fish, Web, created on Nov. 18, 2005. Last accessed on Dec 20, 2010. http://www.freewebs.com/fruitbat/Pdelhezi22b.jpg. (e) Miscellaneous Oddballs VII – Bichirs do eat fish, Aqualand, Last accessed on Dec 20, 2010. http://aqualandpetsplus.com/Oddbal1410.jpg.

and enamel-like, but in contrast to enameloid, is non- 2009). Dentin consists of collagen and apatite with a reduced collagenous and composed of rod-like and pseudoprismatic mineral content (∼70–80 wt%) relative to enamel and ganoine apatite crystallites aligning perpendicular to the surface (Driessens and Verbeeck, 1990; Daget et al., 2001; Sire et al., (Ørvig, 1967; Meunier, 1987; Sasagawa et al., 2009; Sire et al., 2009). 4 JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) –

to local penetration events (Fig. 3(a), (b)). The interfaces between material layers were assumed to be perfectly bonded with a discrete change in mechanical properties from one layer to another. The modulus (E) and yield stress (σY) values used for each of the four scale material layers were quantified via nanoindentation and FEA methods as described in detail in our prior works (Bruet et al., 2008; Wang et al., 2009) (Table 1). In this study, we focused on penetrations which were localized to the top two layers of the armor for the load levels examined here and do not extended deeply into the 3rd or 4th layers (isopedine and bone) of the armor. Tooth model. A representative model tooth was constructed (Fig. 2(d), Fig. 3(b)) based on the geometric information provided by optical microscopy and SEM (i.e. half cone angle of 22◦ and a height of 500 µm). Indentation was applied by displacing the distal end of the tooth (distal to the contact with the scale) towards the scale whereupon the proximal tip of the tooth penetrated into the scale and, depending on the tooth structure and properties, also began to deform. Parametric studies were carried out on the role of the tooth deformability, multi-layered structure, size scale and Fig. 2 – (a) Optical microscope image of typical teeth of P. geometry on penetration resistance, local stress and strain senegalus (b) scanning electron microscope (SEM) image of a distributions, and energy dissipation of both the tooth and typical individual P. senegalus tooth, showing an end radius armor during indentation (Table 1). of ∼14 µm, (c) tooth end-radius distribution of P. senegalus First, virtual indentations were performed by a perfectly = measured using SEM images (n = number of teeth, rigid tooth for three different tooth end-radii (Rtooth 5, 15 m = mean, σ = standard deviation) and (d) a representative and 30 µm), chosen based on the experimentally measured tooth of P. senegalus with definitions of relevant geometric distribution (Fig. 1(c)). The tooth end radii were normalized parameters a half cone angle (θ/2) of ∼22◦, an end radius by the ganoine thickness (tG = 12 µm) utilized in the scale model (Rn = R /t ). Axisymmetric rigid elements (RAX2 (Rtooth) of ∼12 µm, enamel thickness, tE, of ∼100 µm tooth tooth G (Wacker et al., 2001) and a height, h, of ∼500 µm. in ABAQUS element library) were used for the perfectly rigid tooth model. The second set of simulations were carried out using a 2.2. Finite element analysis (FEA) model deformable monolithic enameloid tooth that was entirely composed of enamel and the mechanical properties of the A hypothetical predatory biting attack of an individual P. sene- tooth enameloid (subscript “E”) were varied while the ganoine galus tooth penetrating into an individual P. senegalus ganoid (subscript “G”) mechanical properties were kept constant. The scale was simulated using nonlinear finite element analysis ratio of the mechanical properties of the tooth enameloid (FEA) (ABAQUS/standard). Biting events were modeled as a relative to the ganoine layer of the scale model is henceforth penetration of an indenter (an enamel/dentin tooth) into an defined as the mechanical ratio, ME/G, and is applied to individual quad-layered scale; the symmetry of the geometry both the modulus and the yield stress (i.e., ME/G = modulus and materials allowed for axisymmetric simulations (Fig. 3). ratio = EE/EG = yield stress ratio = σY,E/σY,G). ME/G was Indentations were carried out for loading and unloading up to varied between 0.5 and 3, where the ratio of modulus to yield maximum loads of 0.25, 0.50, and 0.75 N. This virtual microin- strength for the enameloid was maintained at a constant dentation induces complex local multiaxial stress and strain of E/σY = 22.5 which was assumed to be equivalent to the concentrations in both armor and threat systems as shown experimentally determined E/σY of ganoine (Bruet et al., in Fig. 3(a). We note that microcracking was not a dominant 2008). Three different tooth end radii (Rtooth = 5, 15 and 30 µm) mechanism of plasticity in the ganoine and dentin for max- were employed for these simulations as well. imum loads below 1 N and cracking is observed to initiate The third set of simulations involved a bi-layered tooth ∼ above 1 N in Vickers microindentation experiments (Bruet model composed of an outer enameloid layer and inner et al., 2008). Hence, these loads were chosen for comparison dentin layer. The mechanical properties of the enameloid of the effect of a deformable tooth compared to a rigid were, first, assumed to be the same as the scale ganoine indentor. (E = 55 GPa, σY = 2 GPa) and, second, 2× stiffer and harder Scale model. The quad-layered ganoine/dentin/isopedine/bone than the scale ganoine. The tooth dentin was assumed to scale was constructed following protocols and boundary have the same mechanical properties as the scale dentin conditions reported in our earlier works (Bruet et al., 2008; (E = 25 GPa, σY = 400 MPa). The thickness of the enameloid Wang et al., 2009)(Fig. 3(b)). The bottom surface of the layer was varied from 3 to 200 µm and was normalized by scale model was fixed with no movement allowed and the the ganoine thickness (tG = 12 µm), tE/G. For the deformable individual scale was assumed to be large enough as compared tooth models, four-node bilinear axisymmetric quadrilateral JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) – 5

Table 1 – Mechanical properties and layer thickness values utilized in finite element simulations of predatory toothed biting attack on individual quad-layered ganoid scale of P. senegalus including the modulus (E), yield stress (σY) and layer thickness values used for each of the four scale and two tooth material layers. For the parametric studies, E, σY, and the thickness of tooth enameloid was varied (Habelitz et al., 2001; Marshall et al., 2001; Lippert et al., 2004; Mahoney et al., 2004; Bruet et al., 2008; Sasagawa et al., 2009; Sire et al., 2009).

Material layers of FEA models Modulus, E (GPa) Yield stress, σY (GPa) Layer thickness (µm) Ganoine (outer) 55 2 12 Dentin 25 0.4 45 Scale Isopedine 14.5 0.22 43 Bone (inner) 13.5 0.18 300

Monolithic rigid tooth Enameloid Rigid Rigid 400

Monolithic deformable tooth Enameloid 25–165 0.4–6 400

Enameloid 55, 110 2, 4 0–400 Bi-layered, deformable tooth Dentin 25 0.4 0–400 elements (CAX4R or CAX4H in ABAQUS element library) were 3. Results used with optimized meshes for convergence. 3.1. Indentation of the scale by a rigid tooth: the effect of Simulated indentation curves were reported as force tooth end-radius versus normalized penetration depth where the penetration depth was normalized by the ganoine thickness (h/tG). Total The sharpness of the tooth relative to the ganoine layer energy dissipation by all layers (for the loads and depths used was found to have a large effect on penetration resistance in these simulations, only ganoine and dentin contribute) into the quad-layered scale as evidenced by the force versus was calculated, which corresponds to the area between the depth curves (Fig. 4(a)), the corresponding energy dissipation loading and unloading curves. Energy dissipation contributed (Fig. 4(b)), and the details of the stress and strain distributions by each layer was also calculated. Local stress and strain (Figs. 5 and 6). As the tooth becomes sharper for the given half cone angle of 22 degrees, in particular as the tooth end-radius contours in the vicinity of the contact point were reported as is reduced below the thickness of the ganoine layer (R = von Mises stress (S), circumferential stress (S11), radial stress tooth 5 µm, Rn = 0.42), the penetration depth increases dramat- tooth (S22), interfacial normal stress (S33), shear stress (S23) (GPa), ically allowing the tooth penetration to essentially reach the as well as the equivalent plastic strain (PEEQ). underlying dentin layer as the load approaches 1 N (Fig. 4(a)).

Fig. 3 – (a) Schematic diagram of an individual tooth-armored scale system in P. senegalus during a hypothetical predatory attack illustrating the development of a multiaxial stress field in both the tooth and scale due to the localized penetration and (b) schematic of the corresponding finite element model approximating the hypothetical predatory attack shown in part (a). 6 JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) –

Fig. 4 – The effect of tooth end-radius (for a perfectly rigid tooth) on the predicted finite element simulations of the load-bearing capability and energy dissipation within an individual armored scale of P. senegalus during a virtual microindentation, simulating a hypothetical generic biting predatory attack. Tooth end-radii and penetration depths were normalized by the thickness of the outer ganoine Fig. 5 – The effect of tooth end-radius (for a perfectly rigid layer. (a) Load–depth curves for three different tooth tooth) on the predicted finite element simulations of the end-radii as a function of maximum load and (b) total contours of stress and plastic strain within an individual energy dissipation and energy dissipation in the secondary armored scale of P. senegalus during a virtual underlying dentin layer as a function of maximum load for microindentation, simulating a hypothetical generic three different tooth end-radii. predatory biting attack; von Mises stress (S), S33, S23 (fully loaded to 0.75 N) and fully unloaded from 0.75 N (PEEQ), for At the loads and depths utilized in these simulations, only tooth end radii of 0.42, 1.25, and 2.5 normalized by the the two outer layers of the scale (ganoine and dentin) con- thickness of the outer ganoine layer. tribute to the deformation (as will be shown later in the contours of Fig. 5). The total energy dissipation (Fig. 4(b), sym- bution of dentin to the energy dissipation increases with bols) increases nonlinearly with maximum load with the rate increasing indenter radius — again, due to a more domi- of increase enhanced by tooth sharpness. The contributions of the energy dissipation for the ganoine and dentin layers nant pressure as opposed to shear condition in the ganoine depend on the tooth’s end-radius (Fig. 4(b), bar graphs), with when the indenter radius is blunt, e.g. for the blunt tooth (Rn = 2.5) at a 0.75 N maximum load, the dentin dissi- the dentin contributing relatively more for blunter teeth. The tooth deformation by the blunt indenter results in a more pressure- pates approximately 30% of the total energy as compared to 8% for the sharper tooth (Rn = 0.42). However, in all cases dominated uniaxial strain-like condition beneath the inden- tooth ter as compared to the condition of ganoine shearing away the ganoine dissipates more energy via plastic deformation and up along the side of the cone angle for the case of the than the dentin. sharp indenter. This difference leads to greater plastic defor- The calculated contours for stress and plastic equivalent mation of the ganoine with the sharp indenter which in turn strain are shown in Fig. 5 when fully loaded to 0.75 N (S, S33, leads to greater energy dissipation needed to accommodate S23) and after fully unloaded from 0.75 N (PEEQ). The sharpest tooth (R = 5 µm, Rn = 0.42) induces larger areas and a sharp indentation at any given load compared to blunt in- tooth tooth dentation (where the same load by a blunt indenter is accom- greater magnitudes of stress and plastic deformation in modated more by a nearly uniaxial strain-like compression both the ganoine and dentin layers compared to the blunter condition beneath the indenter which is a pressure domi- teeth (Fig. 5), clearly showing the ganoine shearing up nated condition with less dissipation). The relative contri- the side of the cone angle leading to a pileup on the JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) – 7

Fig. 6 – The effect of tooth end-radius (for a perfectly rigid tooth) on the predicted finite element simulations of the contours of circumferential (S11) and radial stresses (S22) within an individual armored scale of P. senegalus during a virtual microindentation, simulating a hypothetical generic predatory biting attack; S11, S22 viewed along the indentation loading 3-axis for normalized tooth end radii of 0.42 (a), 1.25 (b) and 2.5 (c) at a maximum load of 0.75 N.

surface (S23 contours). The blunt indenters instead give the tooth (i.e., as the mechanical ratio ME/G decreases) results a more compression (S33 contours) and pressure focused in a marked shift of force vs. depth (i.e. penetration into deformation beneath the indenter with a single vertical the scale) curves to the left along the depth axis relative to shear band emanating into the ganoine from the edge of the perfectly rigid tooth (Fig. 7(a), black solid line) where, for the contact. The unloaded plastic strain contours reveal the any given indentation load, there is a dramatic reduction in extensive permanent impression from the sharp indenter penetration of the tooth into the scale as ME/G is reduced. (again indicative of the plasticity-dominated nature of this However, this decrease is accompanied by an increase in the indentation), as compared to the near full recovery from total deformation (displacement of the top surface of the the blunt indentation (where the stress field was more tooth which includes the effects of penetration into the scale pressure dominated and elastic as compared to one of as well as tooth deformation) where Fig. 7(a), solid lines, extensive plastic shear). The plastic strain contours also show a shift of force vs. depth curves to the right along reveal the plasticity in both the ganoine and the dentin, the depth-axis, relative to the perfectly rigid tooth (Fig. 7(a), again showing the dentin to contribute to the dissipation black solid line). This trend holds for the sharp as well as and its relative contribution to be greater during the blunt the blunt indenters. The penetration into the scale under an indentation. Lastly, for the sharpest tooth, the surface tensile indentation load of 0.75 N is shown as a function of ME/G in circumferential stress (S11) and compressive radial stress Fig. 7(b), revealing that once ME/G is greater than 1.5, the tooth (S22) are conducive to initiating disadvantageous radial is essentially rigid compared to the scale. cracking around the pile-up of the surface (Fig. 6). In contrast, When the tooth enameloid is taken to be more compliant the blunter teeth (R = 15 µm, Rn = 1.25 and = tooth tooth and softer than the ganoine (ME/G 0.5), the tooth exhibits R = 30 µm, Rn = 2.5) exhibit a sign inversion tooth tooth the greatest deformation and exhibits the lowest penetration with compressive circumferential (S11) and tensile radial efficiency into the scale (Figs. 7(a), and 8). The scale in turn (S22) stress fields on the ganoine surface, promoting more responds in an elastic manner since the stress levels needed advantageous circumferential cracking (Fig. 6). to plastically deform the tooth are never at a high enough level to yield the ganoine (Fig. 8). Therefore, this is a situation 3.2. Indentation of the scale by a deformable monolithic where the armor “defeats” the threat and the energy of the enameloid tooth: the effect of the mechanical properties of the biting attack is dissipated by the deformation of the tooth as tooth enameloid opposed to the deformation of the armor. When the material properties of the tooth enameloid are comparable to the scale The microstructure and mechanical properties of the teeth ganoine (ME/G = 1), the indentation is accommodated by are in reality comparable to those of the scale and are, thus, deformation of both the tooth and the scale (Figs. 7 and 8). expected to have an important role on the mechanics of In this case, the shape of the tooth leads to a stress field that penetration events. The effect of allowing the tooth to be first yields the tooth (particularly the sharp tooth) whereby, deformable has significant consequences on the force vs. once the tooth has yielded it essentially becomes more indentation “depth” results (Fig. 7(a)), the depth of the tooth compliant than the still elastic ganoine and deformation and penetration into the scale (Fig. 7(b)), the energy dissipation dissipation primarily occurs in the tooth. For these reasons, (Fig. 7(c)) and the nature of the stress and strain distributions we see a stronger dependence of the dissipation (Fig. 7(c)) (Fig. 8). Fig. 7(a) shows that an increase in deformability of and deformation (Fig. 8) on indenter radius for the case 8 JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) –

of the mechanically matching threat and armor than for the other cases. When ME/G is increased beyond 1.5, the tooth essentially behaves as a rigid entity (Figs. 7(a)–(c) and 8). Examining the case of ME/G = 2, the depth is nearly completely attributable to penetration of the tooth into the scale. Dissipation is all seen to be attributed by plasticity within the scale (with contribution from both the ganoine and the dentin of the scale) and the stress and strain contours are nearly identical to those when the indenter is rigid (this observation holds for the sharp as well as the blunt indenters).

3.3. Indentation of a scale by a deformable bi-layered a enameloid-dentin tooth: the effect of the tooth enameloid thickness

Here, the role of the underlying dentin layer is explored by varying the thickness of the enameloid cap while fixing the external geometry of the tooth. The load–depth indentation behavior for the bi-layered tooth model was observed to depend on the tooth enameloid thickness (Rn = 1.25, M = tooth E/G 1 and 2, Fig. 9(a)). As the tooth enameloid thickness relative to the ganoine layer is increased (tE/G = 0.5 → 10), penetration into the scale increases (Fig. 9(a), dashed lines, shift of force vs. depth curves to the right of the depth-axis) b and total deformation (scale penetration plus tooth apex displacement) is reduced (Fig. 9(a), solid lines, shift of force vs. depth curves to the left of the x-axis) relative to and ap- proaching the all enameloid tooth (Fig. 9(a), black solid line). Above tE/G ∼ 2, the tooth penetration into the scale exhibits identical behavior (Rn = 1.25, M = 1 and 2, tooth E/G Fig. 9(a)) equivalent to that of a monolithic all-enameloid tooth. A quantitative assessment of penetration into the scale (h/tG) as a function of enameloid thickness (tE/G) is provided in Fig. 9(b) and shows that for tE/G ≤ 2, the scale penetration depths decrease as the enameloid becomes thinner and for tE/G > 2, the penetration events are independent of enameloid thickness and the tooth behaves as a mono- c lithic enameloid tip. This overall trend for scale penetration as a function of enameloid thickness was similar for both M = 1 and 2. Fig. 7 – The effect of the mechanical properties E/G Stress and strain contours of the tooth-scale system were (indentation stiffness and yield strength) of the tooth found to depend on the tooth’s enameloid thickness relative enamel relative to the scale ganoine, i.e., the mechanical to the scale ganoine (tE/G = 1 and 10, ME/G = 1, Fig. 10). ratio, ME/G, on the normalized penetration depth and The thinner the enameloid layer, the more compliant the energy dissipation, predicted by finite element simulations system and the more stress and strain incurred by the dentin during a virtual microindentation using a deformable tooth layer. Highly localized normal and shear stress fields around that simulates a hypothetical generic predatory attack of P. the junction between the enameloid and dentin layers in senegalus. Predictions for three different tooth end-radii are the tooth model are observed. The thick enameloid layer shown (0.42, 1.25 and 2.5). Penetration depths were (t = 10) does not transfer the load into the dentin layer and normalized with the thickness of the ganoine layer and the E/G concentrated stress fields were observed near the apex of the energy dissipation of each component (tooth, scale) were tooth, indicating the increased probability of the fracture at normalized by the total energy dissipation (tooth + scale). this location. This suggests that any cracks that may initiate (a) Load–depth curves of the whole tooth-scale system and in sharp and thick enamel caps might be arrested by or near scale system for M / = 0.5, 1 and 2 at the normalized E G the dentin junction. While the enamel thickness (for the cases tooth end radius of 0.42, as compared to rigid tooth case. of t = 1 and 10) show an influence of the bilayer on the (b) Normalized penetration depth for tooth end radii of 0.42, E/G stress and strain fields within the tooth, the stress and strain 1.25 and 2.5 as a function of M / . (c) Energy dissipation in E G fields in the scale for these two cases are nearly identical. the tooth and the scale for normalized tooth end-radii of This is expected for this case where ME/G = 1 and would 0.42, 1.25 and 2.5 for ME/G = 0.5, 1.0, 2.0. also be anticipated for cases where ME/G > 1. For cases JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) – 9

Fig. 8 – The effect of the mechanical properties (indentation stiffness and yield strength) of the tooth enamel relative to the scale ganoine, i.e. the mechanical ratio, ME/G, on the simulations of contours of stress and plastic equivalent strain, predicted by a virtual FEA microindentation using a deformable tooth which simulates a hypothetical generic predatory attack of P. senegalus: (a) Von Mises stress (S) at a maximum depth when fully loaded, and (b) equivalent plastic strain (PEEQ) when unloaded for three deformable tips with normalized tip end radii of 0.42, 1.25, and 2.5 with respect to the thickness of the ganoine layer at the mechanical ratios of enamel (tip) to ganoine (scale), 0.5, 1.0 and 2.

where ME/G < 1, the deformation of the enameloid cap would example, interactions between snails (gastropod mollusks) be more severe and, therefore, a greater interaction with and crabs that prey upon them, can lead to the evolution deformation of the tooth dentin would be expected which, in of thicker, larger shells, external shell ornamentation, and turn, would influence the extent of penetration into the scale. variable macroscopic shell geometries in prey and strong, geometrically-specialized claws of the crab (Vermeij, 1987; Seed and Hughes, 1995; Dietl and Kelley, 2002). Prey han- 4. Discussion dling by crabs has been observed (Elner, 1978; Williams, 1978; Hughes, 1989; Seed and Hughes, 1995), shell failure Predator–prey interactions are widely thought to lead to so- modes documented (Zuschin et al., 2003), shell failure loads called “evolutionary arms races” in which predators evolve measured (Elner, 1978; Hughes, 1989), crab claw forces an- enhanced weapons and prey evolved improved defensive alyzed, (Taylor, 2000) and the effectiveness of crab claw capabilities (Vermeij, 1987; Agrawal, 2001; Dietl and Kel- morphologies considered (Seed and Hughes, 1995). In an- ley, 2002). The process leads to progressive elaboration of other case, the magnitude and contribution of the impact weapons and defenses, and in some may result in “adap- and cavitation forces generated by the thoracic raptorial ap- tive stalemates” due to costs, tradeoffs, and constraints pendage hammer of the mantis shrimp (stomatopods) was (Vermeij, 1987; Agrawal, 2001; Dietl and Kelley, 2002). For experimentally quantified using high speed imaging, force 10 JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) –

ical configurations of the skull, thoracic shield, mandible and jaw depressor muscle (Anderson and Westneat, 2006). Evidence for predation-related exoskeletal penetration and repair in armored fish has been reported in the literature (Reimchen, 1988; Mapes et al., 1989; Mcclanahan and Muthiga, 1989; Kodera, 1994). A substantial literature also exists on the origins of natural armor strength and toughness (Currey and Taylor, 1974; Bruet et al., 2005; Barthelat and Espinosa, 2007). It is instructive to consider the specialized case of fighting between the same species where the threat and protection are comparable, such as the case of P. senegalus studied here. Stomatopods, for example, fight territorially amongst each other, resulting in threat damage in the form of missing raptorial appendages or a diactyl with a broken heel (Caldwell and Dingle, 1975). However, they are known to use less lethal modified strikes with a closed diactyl against competitors of a the same species which are directed at the heavily armored ridged telson or tail shell, which is conversely used as a protective shield during fighting and as an enclosure to seal and block off the entrance to their dwellings (Caldwell and Dingle, 1975). Telson armoring among various species of stomatopods has been observed to correlate with strike crushing power (Caldwell and Dingle, 1975). Only where there is intense competition for dwelling space do a few species of stomatopods use lethal strikes at the head and thorax of its opponent (Caldwell and Dingle, 1975). While there is much interest in this area, the detailed mechanical mechanisms of the interaction between the b protective structures of prey and the offensive structures of predators, and the roles of material, microstructure, and geometric design on these interactions has yet to be explored Fig. 9 – The effect of the tooth enamel thickness relative to rigorously. Here, we have focused on a single common type of the scale ganoine thickness (tE/G) on the predicted threat, in particular for armored fish, a localized penetration load–depth behavior and normalized penetration depth approximating a toothed biting attack. We present a general (relative to ganoine thickness) for two different mechanical methodology that can be expanded to other types of ratios of enamel to ganoine (ME/G, indentation stiffness predatory attacks which exhibit different types of mechanical and yield strength) of 1 and 2, predicted by finite element loading situations, such as peeling, drilling, hammering, analysis of a virtual microindentation using a deformable and fatigue loading (Vermeij, 1987), as well as threats and tooth which simulates a hypothetical generic predatory natural armor systems with varied geometric characteristics attack of P. senegalus. A normalized tip end radius of 1.25 (internal porosity, corrugations, buttresses, (Vermeij, 1993) relative to the scale ganoine thickness was employed. (a) tooth and claw morphologies (Seed and Hughes, 1995)) and Normalized load–depth curves of the whole tooth-scale active offensive components (Reimchen, 1983; Song et al., = system and scale system for ME/G 1 at the tooth end 2010). While the predator and prey under investigation in radius of 1.25 depending on the thickness of enamel, as this study (both P. senegalus) are comparable, parametric compared to the monolithic enamel tooth case. (b) simulations enabled assessment of asymmetric situations = Normalized penetration depth for ME/G 1 and 2 as a (inequality, where the armor or threat are significantly function of tE/G. weaker or stronger relative to each other) and specifically, the determination of under what conditions and how the offensive threat or defensive protection would dominate in measurements and acoustic analysis (Patek and Caldwell, the interaction. Failure of the armor could result in internal 2005). These raptorial appendages are known to be able to soft tissue and organ damage leading to death, infection, fracture the shells of snails, crabs, and clams, and the num- as well as subsequent predatory and territorial fighting ber of strikes needed to catastrophically break shells of var- vulnerability (Reimchen, 1988; Mapes et al., 1989; Mcclanahan ious sizes has been recorded, as well as differences in at- and Muthiga, 1989; Kodera, 1994; Zuschin et al., 2003). Failure tacking methods to improve efficiency (e.g. impact of shell of a tooth can lead to reduced feeding rates and territorial apex, lip, shearing of side whorls, use of diactyl tip for more fighting vulnerability (Magalhaes, 1948; Kent, 1983; Geller, compliant tissues) (Caldwell and Dingle, 1975). For predatory 1990). A fundamental understanding of threat-protection fish, the biomechanics of biting and the generation of bite design principles and mechanisms underlying predator–prey forces has been considered (Westneat, 2004), for example for interactions has great potential to yield insights into the placoderm Dunkleosteus terrelli by analyzing the anatom- evolutionary pathways (Vermeij, 1987; Dietl and Kelley, 2002). JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) – 11

Fig. 10 – The effect of the tooth enamel thickness relative to the scale ganoine thickness (tE/G) on the simulations of contours of stress and plastic equivalent strain, predicted by finite element analysis of a virtual microindentation usinga deformable tooth that simulates a hypothetical generic predatory attack of P. senegalus. FEA predictions of von Mises stress (S), S22, S11 and S33 at a maximum depth when fully loaded, and S33, S23 and equivalent plastic strain (PEEQ) when fully unloaded for two thickness ratios of enamel to ganoine, 1 and 10, using a deformable tooth with a normalized tip end radius of 1.25 with respect to the thickness of the ganoine layer at the mechanical ratio of enamel to ganoine, ME/G = 1.

Table 2 – Comparison of P. senegalus tooth and scale systems in terms of shape, composite materials, multi-layered structure as well as the layer thickness.

The relevant geometric and material features of the the scale armor maintains additional safety mechanisms via offensive threat (tooth) and defensive protection (armored its additional two innermost underlying layers (isopedine, scale) for P. senegalus are summarized in Table 2. Here, we see bone) that are absent in the tooth microstructure. The that a length-scale matching takes place between the threat thickness of the outermost layer is an order of magnitude (represented by the tooth end-radius) and the protective outer larger for the tooth enameloid compared to the scale ganoine, layer of the armor (ganoine thickness), in order that the likely in order to compensate for increased stress/strain underlying energy dissipating layers of the scale (dentin) may concentrations due to the reduced radius of curvature of be accessed and more efficiently contribute to protection the tooth compared to the scale (discussed further below). and penetration resistance during an interaction. There is also a matching between constituent materials and the Phenotypic plasticity resulting in changes in structure, length outer bi-layered microstructural arrangement employed in scale, and geometry, of both the scales and teeth can result the threat and protective structures (enameloid-dentin for in changes of their function and effectiveness. Even though the tooth vs. ganoine-dentin for the scale). For the case of we focus on the tooth in this study, it should be noted that extremely aggressive threats and higher loading situations, phenotypic plasticity can be beneficial for the scale as well 12 JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) –

Table 3 – Advantages and disadvantages of penetrating threat and corresponding protective natural armor systems.

System Advantages Disadvantages

Predatory threat 1. Increased sharpness (penetration, permanent 1. Sharper, thicker capping layers leads to damage to armor, advantages radial cracking intense and larger stress/strain fields in promoted) threat, reduction in use of more efficient 2. Increased mechanical properties (stiffness, underlying layers for energy dissipation hardness, strength) 2. Thicker hypermineralized capping layers; 3. Thick capping layer (penetration, permanent energetic cost biomineralization, weight damage to armor) 3. Blunter tips promote disadvantageous 4. Bi-layered structure (toughness, crack arrest) circumferential cracking

Prey armor 1. Increased flatness (reduce stress/strain 1. Larger volume compared to threat that concentrations) leads to higher energetic cost for 2. Comparable or greater mechanical properties to biomineralization, weight threat 2. Thicker hypermineralized capping layers; 3. Optimal thickness of the hardest and stiffest energetic cost biomineralization, weight outmost layer, resulting in the minimizing energy cost and armor weight/maximizing penetration resistance, sacrificial fracture 4. Multi-layered structure to provide effective penetration resistance, toughness, and non-catastrophic pathways for energy dissipation

(for example, variable number, thickness, and porosity of requires a relatively large radius of curvature as compared material layers). to the threat’s geometry, as well as mechanical matching The design advantages and disadvantages for a local- where ideally the armor should have comparable or greater ized penetrating threat and its corresponding protective mechanical properties than the threat. The first line of de- natural armor are shown in Table 3. For the threat, sharp- fense is the outer ganoine layer which has high stiffness ening, increasing mechanical properties (e.g. stiffness, hard- and strength which can act to defeat nominal threats. En- ness, strength), and increasing the thickness of the outer ergy dissipation mechanisms of armor systems are also then hypermineralized capping layer, will enable increased effi- controlled by their microstructures and composite structures ciency of penetration and wear resistance, e.g. chiton or sea and composition. Indeed, the organic matrix of mineralized urchin teeth that are sharpened and strengthened by incor- tissues plays a key role in energy dissipation (Wang et al., porating iron or magnesium ions in them (van der Wal et al., 2001). Graded mechanical properties in connection with min- 2000; Wang et al., 1997). Sharper threats also maintain the eral contents such as the P. senegalus scale system provide advantage of inducing local stress distributions in the armor multilayering effects that alter the surface failure modes, re- that promote radial cracking, as opposed to blunter tips which distribute stress and strain distributions and effective energy are expected to induce circumferential cracking modes. Con- dissipation by utilizing the underlying compliant layers. Of- versely, sharper teeth will result in large disadvantageous ten the two strategies of defeating the threat and dissipat- stress concentrations in the threat making it vulnerable to ing the threat attack are combined in one armor system to crack initiation, propagation, and ultimately failure. Catas- maximize penetration resistance, as we have found in the trophic fracture of the entire tooth is mitigated by the bi- P. senegalus system. However, the highly mineralized layer layered structure composed of a thick, stiff, hard enameloid of the armor system also requires larger energy and related outer layer encapsulating a more compliant, soft and ductile mineral sources from the environment during biomineral- dentin inner core which provides toughness, energy dissipa- ization. Therefore, reduction of the total mineralization pro- tion, and can arrest cracks emanating from the enameloid cesses may be advantageous by optimizing the thickness of (Imbeni et al., 2005; Wang et al., 1997). However, for sharper each layer in the system. teeth the high stress concentrations resulting in plasticity and potentially fracture of the enameloid layer are expected to result in disadvantageous blunting during subsequent attacks, thereby reducing penetration effectiveness. Lastly, Acknowledgements energetic costs associated with biomineralization, in particular of the hypermineralized tooth enameloid, layer exist. We gratefully acknowledge support of the US Army There are two main strategies for effective defense mech- through the MIT Institute for Soldier Nanotechnologies anisms of armor systems: defeating threats by means of (Contract DAAD-19-02-D0002), the National Security Science deforming or fracturing the threat and, hence, eliminat- and Engineering Faculty Fellowship Program (N00244-09- ing its ability to penetrate, or, alternatively, providing non- 1-0064), the National Science Foundation MIT Center for catastrophic, sacrificial avenues for deformation and fracture Materials Science and Engineering (DMR-0819762), the MIT events within the armor’s microstructure to dissipate the International Science and Technology Initiatives—France and energy of the attack without allowing full penetration. The Israel Seed Funds. We are grateful to Dr. R. Jensen from multilayered microstructural design of the armored scale pro- the US Army Research Laboratory for useful discussions on vides for both of these strategies. Defeating the threat system this topic, as well as Dr. M. Wund (College of New Jersey) JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) – 13

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