Mapping of Elastic and Hyperelastic Properties of the Periodontal Ligament

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.