Abstract
The periodontal ligament (PDL) is a soft bio-logical tissue which shows a strongly nonlinear and time dependent mechanical behavior. Re-cent experiments on rabbit PDL revealed that the rate of stress relaxation is strain dependent. This nonlinear behavior of PDL cannot be de-scribed well by the separable quasi linear vis-coelasticity theory which is usually used in tis-sue biomechanics. Therefore, PDL requires a more general description which considers this nonlinearity and time dependency. The purpose of this study was to model strain dependent stress relaxation behavior of PDL using modi-fied superposition method. It is shown herein that modified superposition method describes viscoelastic nonlinearties well and shows a good compatibility with available experimental PDL data. Hence, the modified superposition model is suggested to describe periodontal ligament data, because it can suitably demon-strate both elastic nonlinearity and strain-dependent stress relaxation behavior of PDL.
Highlights
In order to obtain a set of constitutive parameters for periodontal ligament (PDL), invitro experimental data were analyzed, and the fit of the rate function was done with R2 value of 0.999 for tension relaxation using nonlinear least square method
QLV model had been applied for PDL, with QLV theory, the time dependent portion of model G(t) is independent of strain, as experimental data shows the relaxation behavior differs at different strain levels and depends on tissue dilatation too
In this study the time dependent portion of model depends on strain to consider strain history dependence of tissue, too
Summary
The human PDL stabilizes the tooth in bone and provides nutritive, proprioceptive and reparative functions [1]. It is composed of collagenous fibers and a gelatinous ground substance including cells and neurovascular tissue [2]. The PDL strongly binds the tooth root to the supporting alveolar bone and absorbs occlusal loads and distributes the resulting stress over the alveolar bone [3]. This causes PDL to play a major role in tooth mobility which is very important in prosthodontic and orthodontic treatment and selection of an optimal force system for orthodontic treatment [4]. The PDL has a determinant influence on tooth instantaneous mobility because of lower stiffness in comparison with surrounding tissues [5], and long term movement because of bone remodeling [6]
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