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Research Papers

Finite Element Analysis of Ramming in Ovis canadensis

[+] Author and Article Information
Parimal Maity1

Department of Mechanical Engineering, Composite Vehicle Research Center, Michigan State University, 2727 Alliance Drive, Lansing, MI-48910parimal.iitk@gmail.com

Srinivasan Arjun Tekalur

Department of Mechanical Engineering, Composite Vehicle Research Center, Michigan State University, 2727 Alliance Drive, Lansing, MI-48910

1

Corresponding author.

J Biomech Eng 133(2), 021009 (Jan 31, 2011) (9 pages) doi:10.1115/1.4003321 History: Received July 20, 2010; Revised November 22, 2010; Posted December 22, 2010; Published January 31, 2011; Online January 31, 2011

The energy produced during the ramming of bighorn sheep (Ovis canadensis) would be expected to result in undesirable stresses in their frontal skull, which in turn would cause brain injury; yet, this animal seems to suffer no ill effects. In general, horn is made of an α-keratin sheath covering a bone. Despite volumes of data on the ramming behavior of Ovis canadensis, the extent to which structural components of horn and horn-associated structure or tissue absorb the impact energy generated by the ramming event is still unknown. This study investigates the hypothesis that there is a mechanical relationship present among the ramming event, the structural constituents of the horn, and the horn-associated structure. The three-dimensional complex structure of the bighorn sheep horn was successfully constructed and modeled using a computed tomography (CT) scan and finite element (FE) method, respectively. Three different three-dimensional quasi-static models, including a horn model with trabecular bone, a horn model with compact bone that instead of trabecular bone, and a horn model with trabecular bone as well as frontal sinuses, were studied. FE simulations were used to compare distributions of principal stress in the horn and the frontal sinuses and the strain energy under quasi-static loading conditions. It was noticed that strain energy due to elastic deformation of the complex structure of horn modeled with trabecular bone and with trabecular bone and frontal sinus was different. In addition, trabecular bone in the horn distributes the stresses over a larger volume, suggesting a mechanical link between the structural constituents and the ramming event. This phenomenon was elucidated through the principal stress distribution in the structure. This study will help designers in choosing appropriate material combinations for the successful design of protective structures against a similar impact.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Axial view of the CT scan of Ovis canadensis showing keratin layer and trabecular or spongy bone of the horn structure

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Figure 2

Schematic representation of the cross-sectional view of horn models with (a) trabecular bone and keratin layer and (b) compact bone and keratin layer

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Figure 3

Three-dimensional solid model and FE mesh of the horn considering ((a), (d)) trabecular bone and keratin layer, ((b), (e)) compact bone and keratin layer, and ((c), (f)) trabecular bone, frontal sinus, and keratin layer

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Figure 4

Finite element model of the horn consists of (a) trabecular bone and keratin layer and (b) trabecular bone keratin layer and frontal sinus illustrating impact load and constraints

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Figure 5

(a) Bone porosity in the horn and (b) normalized cross-sectional area of the horn bone as a function of length

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Figure 6

Compressive principal stresses in horn sheath ((a)–(f)) and trabecular bone ((g)–(l)) for bone modulus of elasticity (Ebone) of 20 GPa, 16 GPa, 12 GPa, 6 GPa, 2 GPa, and 0.8 GPa, respectively. Views of the keratin layer and trabecular bone include x-z plane of the left side and z-y plane of the right side.

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Figure 7

The maximum values of compressive and tensile principal stresses of keratin layer and bone for different modulus of elasticity of the bone

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Figure 8

The maximum values of compressive and tensile principal strains of keratin layer and bone for different modulus of elasticity of the bone

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Figure 9

Strain energy of the horn considering trabecular bone and compact bone

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Figure 10

The volume of the trabecular bone stressed plotted against the minimum principal stress for different modulus of elasticity of the bone (Ebone); some of the data has been truncated in order to show the differences

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Figure 11

The volume of the keratin layer stressed plotted against the minimum principal stress in horn with trabecular bone for different modulus of elasticity of the bone (Ebone); some of the data has been truncated in order to show the differences

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Figure 12

The volume of the bone stressed plotted against the minimum principal stress of horn model with trabecular bone and compact bone for different modulus of elasticity of the bone

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Figure 13

Strain energy for horn model with trabecular bone and horn model with trabecular bone and frontal sinus for different bone modulus of elasticity

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Figure 14

The compressive principal stress distribution in a slice through the frontal sinus for bone modulus of elasticity (Ebone) of (a) 20 GPa, (b) 16 GPa, (c) 12 GPa, (d) 6 GPa, (e) 2 GPa, and (f) 0.8 GPa

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