JOURNALOFTHEMECHANICALBEHAVIOROFBIOMEDICALMATERIALS ( ) ± available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/jmbbm 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 13­4022, 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 quad­layered 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 predator­prey threat­protection interactions may lead to insights into adaptive phenotypic plasticity of the tooth and scale microstructure and geometry, “adaptive stalemates” and the so­called 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 co­evolution 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 predator­related 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. E­mail addresses: [email protected] (C. Ortiz), [email protected] (M.C. Boyce). 1751­6161/$ ­ 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. energy­dissipating 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 shape­based 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 quad­layered 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 back­displacements 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. end­radius, relative to that of the armor on threat­protection mechanical cone angle), multi­layered 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 so­called 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 bot­ tom 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 sputter­coating 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 tooth­end radii (measured by SEM) varied large extinct invertebrate predators that existed at that time between 5 and 30 µm (mean ± standard deviation D 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,