A nonlinear elastic model of the periodontal ligament and its numerical calibration for the study of tooth mobility.

A large strain nonlinear elastic isotropic "split" law is proposed for modeling the behaviour of the periodontal ligament. This law allows for a better description of the stiffening response of this tissue and, concomitantly, for a more accurate calibration of its elastic properties. Indeed, fine finite element simulations of an upper human incisor attached to its surrounding alveolar bone by an intermediate layer of ligament were run using that "split" law for the ligament. A good correlation was established with available experimental data on such a tooth under axial loading. Values of 0.010-0.031 MPa for the initial Young's modulus and of 0.45-0.495 for Poisson's ratio were determined. A sensitivity analysis of the results with respect to material and numerical parameters of the model was also carried out. Finally, a comparison of the simulation results using this "split" law with standard ones obtained with the linear elastic law, shows a significant improvement.