Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Daniel, W. J. T. (2001) Three-dimensional orthotropic viscoelastic finite element model of a human ligament. Computer Methods in Biomechanics and Biomedical Engineering, 4 3: 265-279. doi:10.1080/10255840108908008

Author Daniel, W. J. T.
Title Three-dimensional orthotropic viscoelastic finite element model of a human ligament
Journal name Computer Methods in Biomechanics and Biomedical Engineering   Check publisher's open access policy
ISSN 1025-5842
Publication date 2001-01-01
Sub-type Article (original research)
DOI 10.1080/10255840108908008
Open Access Status Not Open Access
Volume 4
Issue 3
Start page 265
End page 279
Total pages 15
Editor John Middleton
Nigel Shrive
Place of publication Switzerland
Publisher OPA
Language eng
Subject C1
280404 Numerical Analysis
730220 Injury control
Abstract Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.
Keyword Anterior cruciate ligament
Finite element model
Constitutive equations
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mechanical & Mining Engineering Publications
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Created: Wed, 15 Aug 2007, 01:24:47 EST