In a recent paper, Peng et al. (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 et al. (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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e-mail: ferhun.caner@upc.edu
e-mail: z.guo@eng.gla.ac.uk
e-mail: b-moran@northwestern.edu
e-mail: z-bazant@northwestern.edu
e-mail: ignacio.carol@upc.edu
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October 2007
Technical Papers
Hyperelastic Anisotropic Microplane Constitutive Model for Annulus Fibrosus
Ferhun C. Caner,
Ferhun C. Caner
Ramón y Cajal Researcher and Lecturer
School of Civil Engineering,
e-mail: ferhun.caner@upc.edu
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 60208
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Zaoyang Guo,
Zaoyang Guo
Lecturer
Department of Mechanical and Civil Engineering,
e-mail: z.guo@eng.gla.ac.uk
University of Glasgow
, G12 8LT Glasgow, Scotland; Formerly Research Associate, Department of Mechanical Engineering, Northwestern University
, 2145 Sheridan Road, Evanston, Illinois 60208
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Brian Moran,
Brian Moran
Professor
Department of Civil and Environmental Engineering,
e-mail: b-moran@northwestern.edu
Northwestern University
, 2145 Sheridan Road, Evanston, Illinois 60208
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Zdeněk P. Bažant,
Zdeněk P. Bažant
Walter P. Murphy Professor of Civil Engineering and Materials Science
Department of Civil and Environmental Engineering,
e-mail: z-bazant@northwestern.edu
Northwestern University
, 2145 Sheridan Road, Evanston, Illinois 60208
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Ignacio Carol
Ignacio Carol
Professor
School of Civil Engineering,
e-mail: ignacio.carol@upc.edu
Technical University of Catalonia (UPC)
, Jordi Girona 1-3, Barcelona, Spain 08034
Search for other works by this author on:
Ferhun C. Caner
Ramón y Cajal Researcher and Lecturer
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 60208e-mail: ferhun.caner@upc.edu
Zaoyang Guo
Lecturer
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 60208e-mail: z.guo@eng.gla.ac.uk
Brian Moran
Professor
Department of Civil and Environmental Engineering,
Northwestern University
, 2145 Sheridan Road, Evanston, Illinois 60208e-mail: b-moran@northwestern.edu
Zdeněk P. Bažant
Walter P. Murphy Professor of Civil Engineering and Materials Science
Department of Civil and Environmental Engineering,
Northwestern University
, 2145 Sheridan Road, Evanston, Illinois 60208e-mail: z-bazant@northwestern.edu
Ignacio Carol
Professor
School of Civil Engineering,
Technical University of Catalonia (UPC)
, Jordi Girona 1-3, Barcelona, Spain 08034e-mail: ignacio.carol@upc.edu
J Biomech Eng. Oct 2007, 129(5): 632-641 (10 pages)
Published Online: February 26, 2007
Article history
Received:
August 16, 2006
Revised:
February 26, 2007
Citation
Caner, F. C., Guo, Z., Moran, B., Bažant, Z. P., and Carol, I. (February 26, 2007). "Hyperelastic Anisotropic Microplane Constitutive Model for Annulus Fibrosus." ASME. J Biomech Eng. October 2007; 129(5): 632–641. https://doi.org/10.1115/1.2768378
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