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TECHNICAL PAPERS: Bone/Orthopedic

Hyperelastic Anisotropic Microplane Constitutive Model for Annulus Fibrosus

[+] Author and Article Information
Ferhun C. Caner1

School of Civil Engineering, Technical University of Catalonia (UPC), Jordi Girona 1-3, Barcelona, Spain 08034; Formerly Visiting Scholar, Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208ferhun.caner@upc.edu

Zaoyang Guo

Department of Mechanical and Civil Engineering, University of Glasgow, G12 8LT Glasgow, Scotland; Formerly Research Associate, Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208z.guo@eng.gla.ac.uk

Brian Moran

Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208b-moran@northwestern.edu

Zdeněk P. Bažant

Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208z-bazant@northwestern.edu

Ignacio Carol

School of Civil Engineering, Technical University of Catalonia (UPC), Jordi Girona 1-3, Barcelona, Spain 08034ignacio.carol@upc.edu

1

On leave from School of Civil Engineering, Technical University of Catalonia (UPC), Jordi Girona 1-3, Barcelona, Spain 08034.

J Biomech Eng 129(5), 632-641 (Feb 26, 2007) (10 pages) doi:10.1115/1.2768378 History: Received August 16, 2006; Revised February 26, 2007

In a recent paper, Peng (2006, “An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Interaction for the Human Annulus Fibrosis,” ASME J. Appl. Mech., 73(5), pp. 815–824) developed an anisotropic hyperelastic constitutive model for the human annulus fibrosus in which fiber-matrix interaction plays a crucial role in simulating experimental observations reported in the literature. Later, Guo (2006, “A Composites-Based Hyperelastic Constitutive Model for Soft Tissue With Application to the Human Fibrosis,” J. Mech. Phys. Solids, 54(9), pp. 1952–1971) used fiber reinforced continuum mechanics theory to formulate a model in which the fiber-matrix interaction was simulated using only composite effect. It was shown in these studies that the classical anisotropic hyperelastic constitutive models for soft tissue, which do not account for this shear interaction, cannot accurately simulate the test data on human annulus fibrosus. In this study, we show that the microplane model for soft tissue developed by Caner and Carol (2006, “Microplane Constitutive Model and Computational Framework for Blood Vessel Tissue,” ASME J. Biomech. Eng., 128(3), pp. 419–427) can be adjusted for human annulus fibrosus and the resulting model can accurately simulate the experimental observations without explicit fiber-matrix interaction because, in microplane model, the shear interaction between the individual fibers distributed in the tissue provides the required additional rigidity to explain these experimental facts. The intensity of the shear interaction between the fibers can be adjusted by adjusting the spread in the distribution while keeping the total amount of the fiber constant. A comparison of results obtained from (i) a fiber-matrix parallel coupling model, which does not account for the fiber-matrix interaction, (ii) the same model but enriched with fiber-matrix interaction, and (iii) microplane model for soft tissue adapted to annulus fibrosus with two families of fiber distributions is presented. The conclusions are (i) that varying degrees of fiber-fiber and fiber-matrix shear interaction must be taking place in the human annulus fibrosus, (ii) that this shear interaction is essential to be able to explain the mechanical behavior of human annulus fibrosus, and (iii) that microplane model can be fortified with fiber-matrix interaction in a straightforward manner provided that there are new experimental data on distribution of fibers, which indicate a spread so small that it requires an explicit fiber-matrix interaction to be able to simulate the experimental data.

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Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The top view of intervertebral disk with annulus fibrosus and nucleus pulposus, and oblique view of annulus fibrosus with nucleus pulposus. In the oblique view of annulus fibrosus, its lamellar structure and statistically dominant fiber directions that alternate from one lamella to the other are depicted.

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Figure 2

The distribution of orientation of cell nuclei (and thus of collagen fibers) in aortic media (taken from Ref. 47) shown with circles, and the associated best fit probability density function

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Figure 3

Tensile stress-strain behavior of single layer human anterior outer annulus fibrosus along the fiber direction

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Figure 4

Tensile stress-strain behavior of multi-layer human anterior outer annulus fibrosus; interfiber angle facing the loading direction is 60deg

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Figure 5

Tensile stress-strain behavior of multilayer human anterior outer annulus fibrosus; interfiber angle facing the loading direction is 120deg

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Figure 6

Interfiber angle change against stretch in the loading direction in multilayer human anterior outer annulus fibrosus; interfiber angle facing the loading direction is 60deg

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Figure 7

Stretch in the lateral direction against stretch in the loading direction in multilayer human anterior outer annulus fibrosus; interfiber angle facing the loading direction is 60deg

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Figure 8

Stretch in the through-thickness direction against stretch in the loading direction in multilayer human anterior outer annulus fibrosus; interfiber angle facing the loading direction is 60deg

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