Modeling viscoelastic behavior of periodontal ligament with nonlinear finite element analysis

Abstract Background/purpose The function and role of periodontal ligament (PDL) are of interest in a number of fields. Due to the complexity of the geometry and the impossibility of obtaining specimens, the mechanical properties of PDL remain uncertain. The object of this study was to investigate the viscoelastic behavior of PDL by means of nonlinear finite element analysis. Materials and methods In order to consider nonlinear force-displacement behavior, we proposed a finite strain viscoelasticity material model to represent PDL tissue. The strain energy consists of two kinds. The first is nonlinear in time, called viscoelasticity, and the other is geometrically nonlinear, called hyperelasticity. We obtained the material properties by retrograde calculation based on Ross's experiments. Results The results demonstrate that viscoelastic properties mainly result from volumetric changes. The sources of volumetric change are fluids and the vascular system. Second, by combining the nonlinear geometric properties, we can simulate nonlinear load–displacement relationships. We found that the finite strain viscoelastic model can model both nonlinear load–displacement relationships and nonlinear time–displacement relationships. Conclusion The nonlinear finite strain viscoelastic model can simulate both the creeping behavior and nonlinear load displacement behavior of teeth, and may be the best-fitting model for understanding the mechanical properties of PDL.