Research On Numerical Modeling And Experiment Of The Orthdontic Periodontal Ligament

Tooth movement is a very complex process that not only includes instantaneous displacement caused by deformation of the periodontal ligament (PDL),but also a time-dependent long displacement due to bone remodeling in orthodontic, and the PDL plays an important role. It is believed that the mechanical responses within the PDL under orthodontic loading are responsible for the remodeling of the alveolar bone. So it is important to understand thoroughly the mechanical properties of the PDL for exploring the mechanics of orthodontic tooth movement, developing new orthodontic appliances and proposing better treatment plans. A combined approach of experiment, theoretical modeling and finite element (FE) simulation is used to deeply investigate biomechanical properties of the PDL in this dissertation. Nanoindentation technology is adopted to test the PDL, and hyperelastic model, viscoelastic model and visco-hyperelastic model are developed. The nanoindentation experiments of the PDL are numerically simulated based on those models through FE method.For the complexity of experimental testing for the PDL, the nanoindentation technology is proposed to test experimentally the biomechanical properties of the PDL. The principal theory of nanoindentation testing technology is introduced. Pig PDL specimens are tested at different loading rates by using Berkovich indenter and spherical indenter, respectively. Based on the indentation data with Berkovich indenter, the elastic modulus and hardness of the PDL are obtained, and the results show that the value of them decreases with the increase of the indentation depth. In order to enrich the experimental data of the PDL and solve the problem for current in vivo experiment of human PDL, research on developing and designing the experimental appliances for testing the comprehensive properties of the PDL and for in vivo testing is performed.For the defect of conventional hyperelastic model, the V-W hyperelastic model is proposed to investigate the instantaneous mechanical behavior of the PDL. The constitutive equation for the hyperelastic model are deduced based on continuum mechanics and the elasticity tensor used to develop UMAT subroutine which implements the model into FE software is formulated. Inverse FE method is used to identify the optimized model parameters by means of simulating the loading phase of nanoindentation experiment for the PDL. 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. By using the model, the tooth movement under orthodontic loading is simulated to predict the mechanical responses of the PDL. The simulated results show that the stresses within the PDL are concentrated at the alveolar crest on the buccal and lingual aspects, as well as at the mesical and distal sides closest to the incisor root apex, and some are found to be localized to the PDL. Finally, the V-W model is used to simulate the four existing shear experiments of the PDL and comparisons of numerical results and experimental data prove the validity of the model and its UMAT subroutine.Considering the contribution of the fiber in the PDL, the fiber-reinforced model is introduced to develop a fiber-reinforced hyperelastic model of the PDL based on the V-W model. The constitutive equation and elastic tensor for the model are deduced and the parameters of the model are obtained by means of the nonlinear curve fittings between the model and four existing tension experimental data with different strain rates. The parameters obtained from experiment with a low strain rate are adopted to simulate tooth movement under the orthodontic loading. The simulated results show that distribution of stress in the PDL is similar to that obtained by using V-W model.For the PDL represents the time-dependent mechanical property, Zener model is used to describe the viscoelastic mechanical behaviors of the PDL. According to the creep compliance for Zener model and theory of nanoindentation technology, indentation creep models with Berkovich indenter and spherical indenter are developed and the corresponding equations for load-indentation depth relationship are deduced. The parameters are obtained by curve fittings between the creep models and creep data of nanoindentation experiments for the PDL, then the creep models are validated by comparing load-indentation depth curves and experimental data. The comparison results demonstrate that spherical indenter is more suitable than Berkovich indenter to test the viscoelastic PDL. The FE implementation methods of Zener model with differential and integral type are investigated and their stiffness matrices are deduced. UMAT subroutine for integral type is adopted to simulate nanoindentation experiment with spherical indenter. The good agreement between simulated result and experimental data validates the UMAT subroutine developed.A visco-hyperelastic model that can accurately describe the biomechanical properties of the PDL is proposed and developed based on aforesaid hyperelastic model and viscoelastic model. According to the model, the constitutive equation in iteration format and Jacobian matrix are deduced. The visco-hyperelastic model is composed of V-W hyperelastic model and relaxation model, so that the parameters can be identified by them. The load-indentation depth equation for spherical indenter is formulated based on V-W model and nanoindentation theory, so the parameters for V-W model are obtained by curve fitting between theoretical load-depth curve and experimental data with low loading rate. Similarly, creep parameters can be obtained by curve fitting between indentation creep model and creep experimental data with high loading rate, then relaxation parameters can be computed according to the relationship between creep compliance and relaxation modulus. Finally, the visco-hyperelastic model is adopted to simulated the loading phase of nanoindentation experiment with a high loading rate by FE method, and the model is validated through comparison between simulated result and experimental data.