Considerations for determining relaxation constants from creep modeling of nonlinear suture tissue

• Four creep–relaxation models are evaluated to predict suture behavior.
• Creep data from the midsagittal suture in rabbits is used for the model evaluation.
• Two of the models were able to accurately replicate creep data.
• All interrelated relaxation predictions are physically relevant.
• Variability in stress exponent proved to be most important in modeling.

The interrelation between creep and relaxation response of a nonlinear material is a widely studied topic with major implications in the study of viscoelasticity. When considering maxillary expansion, a common orthodontic treatment, a variety of appliances and protocols may be utilized placing the midpalatal suture in a creep or relaxation scenario; hence, it is imperative to fully understand the suture׳s viscoelastic behavior in prediction of patient response to maxillary expansion. The presented study considers four approaches to a full creep–relaxation model, including both separable and inseparable functions. Each model is fit to rabbit midsagittal suture creep data from the literature and then transformed into its subsequent relaxation form for evaluation. Due to a lack of experimental relaxation data in the literature for this tissue, an additional study considering medial collateral ligament data was used to further evaluate ideal model candidates based on the initial analysis. Results from the study presented here show that the suture׳s creep behavior is best described through functions with variable stress exponents. In addition, the four models tested were found to give a physically reasonable range of relaxation predictions. Such findings further highlight the necessity to explore the creep–relaxation behavior of a material using a variety of approaches when building a comprehensive viscoelastic model.