In Vitro Experimental Research On Periodontal Ligament Based On Hyper-viscoelastic Constitutive Model

Periodontal ligament(PDL)is the connective tissue connecting teeth and alveolar bone,which has the function of buffering and transmitting mastication.In orthodontic treatment,force is the only external physical inducement of tooth movement.Biomechanical response of PDL under orthodontic force directly affects the reconstruction of alveolar bone and tooth movement.In this paper,the central incisor of mandible was used as the experimental object.Two sets of fixtures were designed,customized and fitted on the high-precision M-100 loading machine.Then the loading machine was employed to conduct two kinds of mechanical experiments on PDL..One was the tensile and compressive experiment perpendicular to the long axis of the tooth,the other was the shear experiment parallel to the long axis of the tooth.The layered study of PDL along the long axis of tooth was carried out,and the linear viscoelastic solid constitutive model of PDL was constructed.The results shows that different layers have significant influence on the viscoelastic mechanical response of PDL.Higher instantaneous elastic modulus leads to lower creep compliance and higher relaxation modulus.The generalized Kelvin model and the generalized Maxwell model show the creep and relaxation characteristics of PDL.The more the model parameters,the higher the fitting accuracy.The relaxation time of PDL is one order of magnitude less than that of creep,which indicates that the relaxation effect of PDL is shorter than creep effect.To have a deep understanding of the dynamic mechanical response of periodontal ligament in the process of mastication and orthodontic movement,we studied its dynamic viscoelastic properties by shear experiments parallel to the long axis of teeth.It was found that the periodontal ligament exhibits viscoelastic fluid characteristics independent of frequency and amplitude.According to the experimental data,we defined PDL as viscoelastic fluid biomaterial,and used viscoelastic fluid constitutive model to characterize its mechanical properties for the first time.The dynamic shear viscosity coefficient is larger than the static shear viscosity coefficient,and increases with the increase of frequency and amplitude.Compared with the static force,the dynamic force such as chewing improved the viscosity coefficient of PDL and enhanced the function of fixing teeth.This conclusion can be directly applied to clinical practice.Based on this experimental finding,we propose a "PDL flow conjecture".In addition,we compared three methods of in vitro stretching,compression and shear,and determined the distortion characteristics of in vitro compression.We have confirmed that PDL is a kind of nonlinear viscoelastic fluid biomaterial,but the theoretical system of nonlinear viscoelasticity is not perfect.Based on the existing linear viscoelastic theory,we made a theoretical innovation.For the first time,instantaneous hyperelasticity and time-dependent nonlinear viscoelasticity are integrated into a system model.The generalized Voigt-Kelvin hyper-viscoelastic creep model and the generalized Jinlai-Maxwell hyper-viscoelastic relaxation model were constructed.The three characteristics of PDL,namely,instantaneous elasticity,creep and relaxation,were characterized from both mathematical and physical aspects.The results show that the creep compliance of PDL decreases with the increase of stress,while the relaxation modulus increases with the increase of strain.Our innovative hyper-viscoelastic constitutive model can be applied to other nonlinear viscoelastic materials.