The role of the hyoid apparatuses of woodpeckers for energy dissipation.
A woodpecker has a unique structure of a hyoid apparatus compared to the hyoid apparatus of other birds'. The hyoid apparatus starts at the beak tip, surrounds the skull, and ends at the upper beak/front head intersection as shown in Fig. 1, while other birds' hyoid apparatus starts at the beak tip and ends at the neck. The tip of the hyoid apparatus is a tongue having with several barbs to facilitate grabbing insects [1, 2]. According to Zhou et al. , the hyoid apparatus of woodpeckers have a high strength and elasticity, and the reported elastic modulus of the hyoid cartilage is about 1.72-3.70 GPa.
Several researchers have studied the relationship between geometry and wave propagation of various materials. Johnson et al.  reported that the spiral geometry dissipate energy better than that of a cylinder geometry, and the tapered geometry mitigates energy better compared to a straight geometry. The waves of helical waveguides were studied by Treyssede et al. [5, 6]. In this study, we investigated the role of the hyoid apparatus for dissipating energy with regard to its geometry.
We studied the hyoid apparatus on the adult Red-Bellied Woodpecker, Melanerpes carolinus, which is a medium sized bird living in southern United States. The Red-Bellied Woodpecker pecks trees to make a nest or seek insects. Non-living woodpeckers were obtained from the collections of the Department of Wildlife, Fisheries and Aquaculture at Mississippi State University. Hyoid apparatuses were separated from the body of woodpecker. The structure of the woodpecker hyoid apparatus was characterized by using ZEISS Axiovert 200 optical microscope.
Finite element analysis of the hyoid apparatus was performed using the commercial code, ABAQUS-Explicit. The generated model consists of two material parts which are bone/cartilage and muscle. The properties used for the simulation is organized in Table 1. The blast impact was 0.44 MPa with duration of 3.8e-5 seconds.
1. Microstructure and Model Development of the Hyoid Apparatus
The microstructure of the hyoid apparatus is shown in Fig. 2. It is comprised of core cartilage/bone and muscle encasing the hyoid cartilage fully, and the cartilage part changes gradually from being thick (3 mm diameter) and rigid at the beak tip to being thin (1 mm diameter) and flexible at the end . The model of the hyoid apparatus was built based on the observed microstructure.
2. Energy Mitigation
To examine the role of the hyoid apparatus on dissipating shock energy, the model was subjected to a stress wave impact. As shown in Fig. 3, the blast impact was loaded at the tip, and the impulse was analyzed at 4 regions: the tip, the bone split region, the back, and the free end. In Fig. 3, the deformation of the model was exaggerated by 10 times to show the deformation clearly. Most of the deformation was occurred at the free end in the lateral direction. Fig. 4 illustrates the amount of the longitudinal impulse and transverse impulse at the 4 regions. Impulse is defined as the following:
J = [[integral].sup.t2.sub.t1] [nabla]p dt (eq. 1)
where J is impulse, t is time, and p is pressure. As the pressure wave traveled from the tip to the free end, the longitudinal impulse decreased about 97.5% while the transverse impulse increased about 74.7%.
Two factors resulted in a remarkable decrease impulse while the stress wave traveled along the hyoid apparatus. One factor is the thinning structure, and another factor is curvature of the hyoid apparatus. The introduction of shear stresses at the bone split region, back, and free end due to curvature caused conversion of the stress wave from the longitudinal to the transverse wave. The longitudinal and shear bulk velocities are defined as:
[C.sub.l] = [square root of (E (1 - v)/[rho] (1 + v) (1 - 2v))], [C.sub.s] = [square root of (E/2[rho](1 + v))] (eq. 2)
The benefit of the conversion of the stress wave from the longitudinal to the shear wave decreases the wave speed. The decreased wave speed is less harmful. Also, these shear stresses introduce lateral deformation. The tapered structure augments lateral deformation, which aids in dissipating energy and results in reducing the final impulse. The energy dissipating mechanism that the woodpecker's hyoid apparatus uses can be applied to man-made gear for soldiers and athletes.
The unique structure of the hyoid apparatus allows the woodpecker to catch insects from holes of trees. In this study, we also showed that the hyoid apparatus functions to dissipate energy. The tapered structure and curvature of the hyoid apparatus introduce shear stresses and lateral deformation by converting longitudinal stresses to transverse stresses, which help to protect the woodpeckers' head from experiencing abnormally high stresses while pecking.
The authors would like to thank The Department of Agricultural and Biological Engineering for financial support of this study, The Department of Mechanical Engineering and The Center of Advanced Vehicular Systems (CAVS) at Mississippi State University. Also, the authors gratefully acknowledge Dassault Systems Simulia Corporation for the use of Abaqus software.
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Nayeon Lee (a,c) (firstname.lastname@example.org), R. Prabhu (a,c) (email@example.com), Lakiesha N. Williams (a,c) (firstname.lastname@example.org), M.F. Horstemeyer (b,c) (email@example.com)
(a) Department of Agricultural and Biological Engineering, Mississippi State University, Mississippi State, MS 39762-9632, USA
(b) Department of Mechanical Engineering, Mississippi State University, Mississippi State, MS 39762-9552, USA
(c) Center for Advanced Vehicular Systems, Mississippi State University, Mississippi State, MS 39762-5405, USA
Table 1. Material properties used for the simulation. Material properties Values Skeleton [3, 7] Young's modulus 3.72 GPa Poisson ratio 0.3 Density 1850 kg/[m.sup.3] Elastic modulus 0.5 GPa Muscle  Poisson ratio 0.4 Density 1000 kg/[m.sup.3]
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|Author:||Lee, Nayeon; Prabhu, R.; Williams, Lakiesha N.; Horstemeyer, M.F.|
|Publication:||Journal of the Mississippi Academy of Sciences|
|Date:||Apr 1, 2014|
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