Material constants for a finite element model of the intervertebral disk with a fiber composite annulus

Spilker, R. L.<sup>1</sup>; Jakobs, D. M.<sup>2</sup>; Schultz, A. B.<sup>3</sup>

Affiliations

¹Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, N.Y. 12180

²Research Engineer, Danley Machine Company, Chicago, Ill, 60612

³Department of Mechanical Engineering and Engineering Mechanics, University of Michigan, Ann Arbor, Mich. 48109

Abstract

A simple axisymmetric finite element model of a human spine segment containing two adjacent vertebrae and the intervening intervertebral disk was constructed. The model incorporated four substructures: one to represent each of the vertebral bodies, the annulus fibrosus, and the nucleus pulposus. A semi-analytic technique was used to maintain the computational economies of a two-dimensional analysis when nonaxisymmetric loads were imposed on the model. The annulus material was represented as a layered fiber-reinforced composite. This paper describes the selection of material constants to represent the anisotropic layers of the annulus. It shows that a single set of material constants can be chosen so that model predictions of gross disk behavior under compression, torsion, shear, and moment loading are in reasonable agreement with the mean and range of experimentally measured disk behaviors. It also examines the effects of varying annular material propertie

Links

DOI: 10.1115/1.3138575

PubMed: 3959546

WoS: A1986A215400001

History

Received: 1983-06-01

Revised: 1985-08-21

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Cited By (25)

Year	Entry
1993	Fung YC. Bone and cartilage. In: Biomechanics: Mechanical Properties of Living Tissues. 2nd ed. New York, NY: Springer-Verlag; 1993:500-544.
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1999	Kumaresan S, Yoganandan N, Pintar FA. Finite element analysis of the cervical spine: a material property sensitivity study. Clin Biomech (Bristol, Avon). January 1999;12(1):41-53.
1989	Shirazi-Adl A. On the fibre composite material models of disc annulus: comparison of predicted stresses. J Biomech. 1989;22(4):357-365.
1997	Iatridis JC, Setton LA, Weidenbaum M, Mow VC. The viscoelastic behavior of the non-degenerate human lumbar nucleus pulposus in shear. J Biomech. October 1997;30(10):1005-1013.
1999	Arbogast KB, Margulies SS. A fiber-reinforced composite model of the viscoelastic behavior of the brainstem in shear. J Biomech. August 1999;32(8):865-870.
2006	Guerin HAL, Elliott DM. Degeneration affects the fiber reorientation of human annulus fibrosus under tensile load. J Biomech. 2006;39(8):1410-1418.
2000	Kumaresan S, Yoganandan N, Pintar FA, Maiman DJ, Kuppa S. Biomechanical study of pediatric human cervical spine: a finite element approach. J Biomech Eng. February 2000;122(1):60-71.
2000	Elliott DM, Setton LA. A linear material model for fiber-induced anisotropy of the anulus fibrosus. J Biomech Eng. April 2000;122(2):173-179.
2001	Elliott DM, Setton LA. Anisotropic and inhomogeneous tensile behavior of the human anulus fibrosus: experimental measurement and material model predictions. J Biomech Eng. June 2001;123(3):256-263.
1999	Iatridis JC, Kumar S, Foster RJ, Weidenbaum M, Mow VC. Shear mechanical properties of human lumbar annulus fibrosus. J Orthop Res. September 1999;17(5):732-737.
1995	Goel VK, Monroe BT, Gilbertson LG, Brinckmann P. Interlaminar shear stresses and laminae separation in a disc: finite element analysis of the L3-L4 motion segment subjected to axial compressive loads. Spine. March 15, 1995;20(6):689-698.
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1996	Iatridis JC, Weidenbaum M, Setton LA, Mow VC. Is the nucleus pulposus a solid or a fluid? mechanical behaviors of the nucleus pulposus of the human intervertebral disc. Spine. May 15, 1996;21(15):1174-1184.
1996	Iatridis JC. Biomechanics of the Anulus Fibrosus and Nucleus Pulposus of the Human Lumbar Intervertebral Disc and the Effects of Degeneration [PhD thesis]. Columbia University; 1996.
2012	Isaacs JL. Micromechanics of the Annulus Fibrosus: Role of Biomolecules in Mechanical Function [PhD thesis]. Drexel University; May 2012.
1999	Elliott DM. The Fiber-Induced Anisotropic Material Behaviors of the Anulus Fibrosus of the Intervertebral Disc in Tension [PhD thesis]. Duke University; 1999.
2001	Baer AE. The Micromechanical Environment of Intervertebral Disc Cells [PhD thesis]. Duke University; 2001.
1997	Kumaresan S. Clinical Studies of the Human Cervical Spine Using Finite Element Modeling [PhD thesis]. Marquette University; December 1997.
1991	Kasra M. Experimental and Finite Element Dynamic Response Analyses of a Human Lumbar Motion Segment [PhD thesis]. École polytechnique de Montréal; March 1991.
1999	Bass EC. Biaxial Nonlinear Elastic Response of the Human Lumbar Annulus Fibrosus and Its Role in the Determination of a Physiologically Relevant Constitutive Relation [PhD thesis]. Berkeley, CA: Berkeley, University of California; 1999.
2002	Wagner DR. A Mechanistic Strain Energy Function and Experimental Results for the Human Annulus Fibrosus [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2002.
1988	Kim YE. An Analytical Investigation of Ligamentous Lumbar Spine Mechanics University of Iowa; May 1988.
2005	Guerin HAL. A Nonlinear Anisotropic Continuum Model of Human Annulus Fibrosus Mechanical Behavior [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2005.
2006	Panzer MB. Numerical Modelling of the Human Cervical Spine in Frontal Impact [Master's thesis]. University of Waterloo; 2006.