Nonlinear finite element analyses: Advances and challenges in dental applications

Abstract 

Objectives

To discuss the development and current status of application of nonlinear finite element method (FEM) in dentistry.

Data and sources

The literature was searched for original research articles with keywords such as nonlinear, finite element analysis, and tooth/dental/implant. References were selected manually or searched from the PUBMED and MEDLINE databases through November 2007.

Study selection

The nonlinear problems analyzed in FEM studies were reviewed and categorized into: (A) nonlinear simulations of the periodontal ligament (PDL), (B) plastic and viscoelastic behaviors of dental materials, (C) contact phenomena in tooth-to-tooth contact, (D) contact phenomena within prosthodontic structures, and (E) interfacial mechanics between the tooth and the restoration.

Conclusions

The FEM in dentistry recently focused on simulation of realistic intra-oral conditions such as the nonlinear stress–strain relationship in the periodontal tissues and the contact phenomena in teeth, which could hardly be solved by the linear static model. The definition of contact area critically affects the reliability of the contact analyses, especially for implant–abutment complexes. To predict the failure risk of a bonded tooth–restoration interface, it is essential to assess the normal and shear stresses relative to the interface. The inclusion of viscoelasticity and plastic deformation to the program to account for the time-dependent, thermal sensitive, and largely deformable nature of dental materials would enhance its application. Further improvement of the nonlinear FEM solutions should be encouraged to widen the range of applications in dental and oral health science.

Keywords: Finite element analysis, Nonlinear, Contact stress, Interfacial stress, Viscoelasticity