Wencheng Tang

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

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.

Development and parameter identification of a visco-hyperelastic model for the periodontal ligament

The present study developed and implemented a new visco-hyperelastic model that is capable of predicting the time-dependent biomechanical behavior of the periodontal ligament. The constitutive model has been implemented into the finite element package ABAQUS by means of a user-defined material subroutine (UMAT). The stress response is decomposed into two constitutive parts in parallel which are a hyperelastic and a time-dependent viscoelastic stress response. In order to identify the model parameters, the indentation equation based on V-W hyperelastic model and the indentation creep model are developed. Then the parameters are determined by fitting them to the corresponding nanoindentation experimental data of the PDL. The nanoindentation experiment was simulated by finite element analysis to validate the visco-hyperelastic model. The simulated results are in good agreement with the experimental data, which demonstrates that the visco-hyperelastic model developed is able to accurately predict the time-dependent mechanical behavior of the PDL.

DETERMINATION OF VISCOELASTIC PROPERTIES OF THE PERIODONTAL LIGAMENT USING NANOINDENTATION TESTING AND NUMERICAL MODELING

Viscoelasticity of the periodontal ligament (PDL) plays an important role in load transmission between tooth and alveolar bone, as well as tooth movement. This paper provides a novel nanoindentation experiment in combination with a rheological model to characterize the viscoelastic mechanical properties of the PDL. Two creep models of the indentation experiments with a Berkovich and a spherical indenter based on Zener model were developed. The hardness and reduced modulus were determined by using the Berkovich indenter. The parameters were identified through curve fittings. The fitting results show that the creep models are both in good agreement with the experimental data. Meanwhile, the models were both validated by comparing the numerical curves for load–depth relationship in loading segment with the corresponding experimental data. It is found that the spherical indenter is more suitable for testing the viscoelastic mechanical properties of the PDL than Berkovich indenter. Hence, the nanoindentation experiment with spherical indenter was simulated to further evaluate the Zener model by finite element analysis. The good agreement between the simulated results and experimental data demonstrates that the Zener model is capable of describing the viscoelastic mechanical behavior of the PDL.

Study on Stress Distribution in Periodontal Ligament of Impacted Tooth Based on Hyperelastic Model

Previous studies have not produced a comprehensive description of the nonlinear hyperelastic stress-strain behavior of the periodontal ligament (PDL) of impacted tooth. In the present study, a simulation was applied to get the stress distribution in the PDL of impacted tooth. Firstly, a novel finite element modeling method for the PDL of impacted tooth based on CT image and reverse engineering was adopted herein. Furthermore, a group of uniaxial tensile experiment data from human PDL was used for fitting of several hyperelastic energy functions. At last, a traction was simulated, in which the angel between the traction force and the central axis of the impacted tooth is 45e , and the stress distribution of the PDL was calculated by ABAQUS. The results showed that the third-order Ogden model and third-order reduced polynomial model are also able to better reflect the material properties of the PDL. The stress in the top areas of the PDL is largest and most concentrated when the traction force load in the crown of the impacted tooth.

Study on the Center of Resistance of Tooth Based on Spatial Kinematics

This paper presents a three-dimensional method to locate the center of resistance (CRE) with a spatial kinematic method and finite element analysis. Firstly, finite element analyses with hypoelastic and also isotropic constitutive model of periodontal ligament were conducted to get the tooth displacements under various boundaries. Then a spatial kinematic method was used to solve the location of CRE with the derived displacements. Finally, the influences of the type of constitutive model, the magnitude and direction of torque on the location of CRE were analyzed. The results make a good agreement with experimental data in literatures; and it shows that there is not a fixed location of CRE, the location of resistance center is in a range rather than on a fixed point. Keywords-orthodontics; center of resistence; spatial kinematisc; finite element analysis; hypoelastic.

A Novel Finite Element Modeling Method for Periodontal Ligament of Impacted Maxillary Tooth

How to build a precise finite element model for periodontal ligament (PDL) of impacted tooth is a key step in numerical simulation of orthodontics. However, it is difficult to obtain accurate three-dimensional model of impacted tooth which embed in alveolar bone. In this paper, combined with reverse engineering and CT image, a new finite element method is introduced. Firstly, create the surface model of impacted tooth after separating it from CT image by using threshold. Secondly, filter the superfluous points in point cloud by programming. Then grid the point cloud, and smooth the curved surface to create the closed 3D entity model. Finally, the finite element model of impacted tooth and periodontal ligament (PDL) were built by finite element pre-processing. Compared with the traditional modeling method, the new approach is faster, more precise, which served as a more effective and practical means for orthodontics simulation.