Linear, bilinear, exponential, and hyperelastic models of the periodontal ligament (PDL) of human incisors were analyzed. Results showed that the elastic properties of PDL depend on its location and were best described by exponential functions. Parameters of the elastic differential modulus E (ε) of the periodontal ligament (minimum, average, and maximum values) in its various sections (cervical, middle, and apical) from the mesial and distal sides were determined. The differential elastic modulus of PDL was incremental, and its deformation behavior was quite accurately approximated by the regression equation. Linear and bilinear elastic models of PDL were considered and the model constants were determined. To study the hyperelastic properties of PDL, neo-Hookean, Mooney–Rivlin, Ogden, and polynomial phenomenological models were used. Calculations were carried out using the Mathcad 13.0 and ANSYS 2022 R2 software. The parameters of the models and the closeness of correlation between experimental and calculated data were determined. The polynomial model ( r = 0.999) showed the highest correlation with the experimental values, but the neo-Hookean model ( r = 0.948) — the lowest one. The values of Young’s modulus and of other elastic and hyperelastic characteristics of the periodontal ligament were compared in order to study the factors affecting the mechanical behavior of PDL.

分析了人类门牙牙周膜 (PDL) 的线性、双线性、指数和超弹性模型。结果表明，PDL 的弹性特性取决于其位置，最好用指数函数来描述。弹性微分模量参数E ( ε确定牙周膜各个部分（颈部、中部和根尖）的近中和远中侧的牙周韧带（最小值、平均值和最大值）。PDL的微分弹性模量是增量的，其变形行为可以通过回归方程相当准确地近似。考虑了 PDL 的线性和双线性弹性模型并确定了模型常数。为了研究 PDL 的超弹性特性，使用了 Neo-Hookean、Mooney-Rivlin、Ogden 和多项式唯象模型。使用Mathcad 13.0和ANSYS 2022 R2软件进行计算。确定了模型的参数以及实验数据和计算数据之间的相关紧密度。多项式模型 ( r= 0.999）显示与实验值的相关性最高，但 Neo-Hookean 模型（r = 0.948）的相关性最低。比较牙周膜的杨氏模量以及其他弹性和超弹性特性的值，以研究影响 PDL 机械行为的因素。