This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67–76;Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306–312;Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908–214;Weiss et al., 2002, J. Biomech., 35, pp. 943–950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.
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June 2006
Technical Papers
A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments
P. Vena,
P. Vena
Department of Structural Engineering,
e-mail: vena@stru.polimi.it
Laboratory of Biological Structure Mechanics (LaBS)
, Politecnico di Milano, Milan, Italy
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D. Gastaldi,
D. Gastaldi
Department of Structural Engineering,
Laboratory of Biological Structure Mechanics (LaBS)
, Politecnico di Milano, Milan, Italy
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R. Contro
R. Contro
Department of Structural Engineering,
Laboratory of Biological Structure Mechanics (LaBS)
, Politecnico di Milano, Milan, Italy
Search for other works by this author on:
P. Vena
Department of Structural Engineering,
Laboratory of Biological Structure Mechanics (LaBS)
, Politecnico di Milano, Milan, Italye-mail: vena@stru.polimi.it
D. Gastaldi
Department of Structural Engineering,
Laboratory of Biological Structure Mechanics (LaBS)
, Politecnico di Milano, Milan, Italy
R. Contro
Department of Structural Engineering,
Laboratory of Biological Structure Mechanics (LaBS)
, Politecnico di Milano, Milan, ItalyJ Biomech Eng. Jun 2006, 128(3): 449-457 (9 pages)
Published Online: December 12, 2005
Article history
Received:
July 26, 2005
Revised:
December 12, 2005
Citation
Vena, P., Gastaldi, D., and Contro, R. (December 12, 2005). "A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments." ASME. J Biomech Eng. June 2006; 128(3): 449–457. https://doi.org/10.1115/1.2187046
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