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TECHNICAL PAPERS

An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Shear Interaction for the Human Annulus Fibrosus

[+] Author and Article Information
X. Q. Peng, Z. Y. Guo

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208

B. Moran

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208b-moran@northwestern.edu

J. Appl. Mech 73(5), 815-824 (May 16, 2005) (10 pages) doi:10.1115/1.2069987 History: Received December 13, 2004; Revised May 16, 2005

Based on fiber reinforced continuum mechanics theory, an anisotropic hyperelastic constitutive model for the human annulus fibrosus is developed. A strain energy function representing the anisotropic elastic material behavior of the annulus fibrosus is additively decomposed into three parts nominally representing the energy contributions from the matrix, fiber and fiber-matrix shear interaction, respectively. Taking advantage of the laminated structure of the annulus fibrosus with one family of aligned fibers in each lamella, interlamellar fiber-fiber interaction is eliminated, which greatly simplifies the constitutive model. A simple geometric description for the shearing between the fiber and the matrix is developed and this quantity is used in the representation of the fiber-matrix shear interaction energy. Intralamellar fiber-fiber interaction is also encompassed by this interaction term. Experimental data from the literature are used to obtain the material parameters in the constitutive model and to provide model validation. Determination of the material parameters is greatly facilitated by the partition of the strain energy function into matrix, fiber and fiber-matrix shear interaction terms. A straightforward procedure for computation of the material parameters from simple experimental tests is proposed.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 12

Stretches in x2 direction versus stretches in x1 direction for multilayer AO annulus fibrosus with 2α=60 deg

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Figure 1

Schematic of intervertebral disk showing the laminated structure of the annulus fibrosus

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Figure 2

Exact geometric description of the fiber-matrix interaction

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Figure 3

Simple shear deformation of fiber reinforced composites

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Figure 4

Uniaxial tensile deformation of fiber reinforced composites

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Figure 17

Stress versus Lagrangian strain in biaxial deformation

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Figure 5

Annulus fibrosus with two families of fibers

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Figure 6

Initial tensile stress-strain behavior of multilayer AO annulus fibrosus with 2α=120 deg (used to obtain fiber material parameters C10 and D1)

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Figure 13

Stretches in x3 direction versus stretches in x1 direction for multilayer AO annulus fibrosus with 2α=60 deg

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Figure 14

Angle changes between the two fibers for multilayer AO annulus fibrosus with 2α=120 deg

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Figure 15

Stretches in x2 direction versus stretches in x1 direction for multilayer AO annulus fibrosus with 2α=120 deg

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Figure 16

Stretch in x3 direction versus stretch in x1 direction for multilayer AO annulus fibrosus with 2α=120 deg

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Figure 7

Tensile stress-strain behavior along fiber direction of single-layer AO annulus fibrosus (used to obtain fiber material parameters C2 and C3)

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Figure 8

Tensile stress-strain behavior of multilayer AO annulus fibrosus with 2α=60 deg (used to obtain fiber-matrix shear interaction factor f(I4))

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Figure 9

Tensile stress-strain behavior of multilayer AO annulus fibrosus with 2α=120 deg (used to obtain fiber-matrix shear interaction factor f(I4))

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Figure 10

Fiber-matrix interaction factor f(I4) expressed by a sigmoid function as Eq. 43

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Figure 11

Angle changes between the two fibers for multilayer AO annulus fibrosus with 2α=60 deg

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