Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

Abstract

The V-W exponential hyperelastic model is adopted to describe the instantaneous elastic response of the periodontal ligament (PDL). The general theoretical framework of constitutive modeling is described based on nonlinear continuum mechanics, and the elasticity tensor used to develop UMAT subroutine is formulated. Nanoindentation experiment is performed to characterize mechanical properties of an adult pig PDL specimen. Then the experiment is simulated by using the finite element (FE) analysis. Meanwhile, the optimized material parameters are identified by the inverse FE method. The good agreement between the simulated results and experimental data demonstrates that the V-W model is capable of describing the mechanical behavior of the PDL. Therefore, the model and its implementation into FE code are validated. By using the model, we simulate the tooth movement under orthodontic loading to predict the mechanical responses of the PDL. The results show that local concentrations of stress and strain in the PDL are found.

A biomechanical case study on the optimal orthodontic force on the maxillary canine tooth based on finite element analysis

“…The upper strain of 2.4% was baseless, and whether the strain of 2.4% may be related to root resorption would require further studies, although it was related to the tooth movement rate. In addition, the PDL was assumed to be an inaccurate linear elastic material in their simulation, which also affected the accuracy of their results (Huang et al, 2016; Anneke et al, 2017). On the other hand, Liao et al (2016) just considered the PDL stress but ignored the strain, and as a result, the optimal forces of the canine distal translation and tipping were 35-100 and 14-50 g, respectively, as defined by local hydrostatic pressure, and 76-266 and 37-135 g as defined by volumeaveraged hydrostatic stress.…”

In vivo effects of different orthodontic loading on root resorption and correlation with mechanobiological stimulus in periodontal ligament

“…where l i are the deviatoric principal stretches obtained from the principal stretches, J 1I is the elastic volume strain, and m i , a i and D i are the parameters used in such a hyperelastic model [35]. The hyperelastic constitutive model was also proposed to fit PDL's viscoelastic behaviour [34], and has been adopted widely in dental biomechanics [11,36]. Its accuracy had also been validated [34] by correlating with the previous in vitro studies on PDLs of human cadavers [37] as well as other mathematical models [37,38].…”

3-D finite element analysis of the effects of post location and loading location on stress distribution in root canals of the mandibular 1st molar

“…However, for simplicity, and utility on finite element analysis, many authors have capitulated to the assumption and focused on finding the most suitable elastic modulus values of periodontal ligament as a homogenous, isotropic, and linear elastic material 3 , 6 , 16 , 24 , 25 . However, recent authors have regarded the periodontal ligament as a non-linear, hyperelastic material, and have found variable elastic modulus values for periodontal ligament 13 . The influence of periodontal ligament as a non-linear hyperelastic material should be considered in further studies.…”