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Research Papers

Nonlinear Model for Viscoelastic Behavior of Achilles Tendon

[+] Author and Article Information
Cyril J.F. Kahn1

LEMTA, Cell and Tissue Engineering Group, Nancy-Université, 2 Avenue de la Forêt de Haye, BP 160, 54504 Vandoeuvre-lès-Nancy Cedex, Francecyril.kahn@ensem.inpl-nancy.fr

Xiong Wang

LEMTA, UMR 7563, Cell and Tissue Engineering Group, Nancy-Université, CNRS, 2 Avenue de la Forêt de Haye, BP 160, 54504 Vandoeuvre-lès-Nancy Cedex, France; Physiopatholgie, Pharmacologie et Ingénierie Articulaires, UMR 7561, Nancy-Université, CNRS, 9 Avenue de la Forêt de Haye, 54500 Vandoeuvre-Lès-Nancy, Francexiong.wang@ensem.inpl-nancy.fr

Rachid Rahouadj

LEMTA, UMR 7563, Cell and Tissue Engineering Group, Nancy-Université, CNRS, 2 Avenue de la Forêt de Haye, BP 160, 54504 Vandoeuvre-lès-Nancy Cedex, Francerachid.rahouadj@ensem.inpl-nancy.fr

1

Corresponding author.

J Biomech Eng 132(11), 111002 (Oct 15, 2010) (8 pages) doi:10.1115/1.4002552 History: Received March 21, 2010; Revised September 09, 2010; Posted September 15, 2010; Published October 15, 2010; Online October 15, 2010

Although the mechanical properties of ligament and tendon are well documented in research literature, very few unified mechanical formulations can describe a wide range of different loadings. The aim of this study was to propose a new model, which can describe tendon responses to various solicitations such as cycles of loading, unloading, and reloading or successive relaxations at different strain levels. In this work, experiments with cycles of loading and reloading at increasing strain level and sequences of relaxation were performed on white New Zealand rabbit Achilles tendons. We presented a local formulation of thermodynamic evolution outside equilibrium at a representative element volume scale to describe the tendon’s macroscopic behavior based on the notion of relaxed stress. It was shown that the model corresponds quite well to the experimental data. This work concludes with the complexity of tendons’ mechanical properties due to various microphysical mechanisms of deformation involved in loading such as the recruitment of collagen fibers, the rearrangement of the microstructure (i.e., collagens type I and III, proteoglycans, and water), and the evolution of relaxed stress linked to these mechanisms.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Mean stress-strain curve of rabbit Achilles tendons (n=10). Stress response as a function of strain (ε̇=2×10−2 s−1). (a) Muscle insertion and (b) bone insertion.

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Figure 2

Mean section of Achilles tendon. Section of Achilles tendon obtained by MRI (solid line), ellipse (dashed line). Areas + and − are nearly equivalent.

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Figure 3

Typical response curves of rabbit Achilles tendon to sequences of relaxation at different prestrain values (n=3). Successive relaxations at different strain level (k, 2×10−2, l, 4×10−2, m, 6×10−2, n, 8×10−2, p, 6×10−2) presented in (a) the sequences of strain applied as a function of time, (b) the stress-strain curve, and (c) the stress-time curve. The  ∗ represents the mean value of the relaxed stress during relaxation tests, which shows an hysteresis effect of the relaxed stress toward history of loading.

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Figure 4

Typical response curves of rabbit Achilles tendon corresponding to several sequences of loading, unloading, and reloading cycles at different prestrain values (n=3): (a) sequences of strain applied as a function of time and (b) response of an Achilles tendon to successive cycles of solicitation at different prestrain levels 2, 5, 9×10−2, and 0.1

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Figure 5

Schematic link between elastic stress, instantaneous stress, and relaxed stress

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Figure 6

Schema of the algorithm used to compute instantaneous stress

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Figure 7

Typical curves of fitting experimental data: (a) and (b) fit of successive relaxations in function of strain and time, respectively, and (c) fit of cyclic loading. (●) is the experimental data, red solid line is the theoretical instantaneous stress, and green dashed line is the relaxed stress.

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