Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

Abstract

The V–W exponential hyperelastic model is adopted to describe the instantaneous elastic response of the periodontal ligament (PDL). The general theoretical framework of constitutive modeling is described based on nonlinear continuum mechanics, and the elasticity tensor used to develop UMAT subroutine is formulated. Nanoindentation experiment is performed to characterize mechanical properties of an adult pig PDL specimen. Then the experiment is simulated by using the finite element (FE) analysis. Meanwhile, the optimized material parameters are identified by the inverse FE method. 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. Therefore, the model and its implementation into FE code are validated. By using the model, we simulate the tooth movement under orthodontic loading to predict the mechanical responses of the PDL. The results show that local concentrations of stress and strain in the PDL are found.

Keywords:

• hyperelastic constitutive model
• finite element simulation
• nanoindentation
• parameter identification
• periodontal ligament

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors are grateful to the funding supports by National Natural Science Foundation of China [grant number 51305208] and Postdoctoral Science Foundation Project of Jiangsu province [grant number 1102046C].