Elsevier

Journal of Dentistry

Volume 36, Issue 7, July 2008, Pages 463-471
Journal of Dentistry

Review
Nonlinear finite element analyses: Advances and challenges in dental applications

https://doi.org/10.1016/j.jdent.2008.03.010Get rights and content

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.

Introduction

The finite element method (FEM) involves a series of computational procedures to calculate the stress and strain in each element, which performs a model solution. Such a structural analysis allows the determination of stress and strain resulting from external force, pressure, thermal change, and other factors. This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. The results obtained can then be studied using visualization software within the FEM environment to view a variety of parameters, and to fully identify implications of the analysis.

Linear static models have been employed extensively in FEM studies. A constant elastic modulus that represents the linear stress–strain relationship of a material is input into a program. Linear analyses are valid if the structure exhibits a linear stress–strain relationship up to a stress level known as the proportional limit, and all the volumes are bonded as one unit. However, the validity of a linear static analysis may be questionable when the study objectives are to explore more realistic situations that are usually encountered in the intra-oral environment. The realistic situations will give rise to nonlinearities, which can be grouped into the following principal categories: (1) Material nonlinearities; (2) Changing interrelation of objects; and (3) Geometric nonlinearities. Material nonlinearities cause the stiffness of a structure to change with different load levels, and are expressed in a program as nonlinear stress–strain relationships. Many factors that influence stress–strain properties include the time- and path-dependent load history in elastoplastic response, environmental conditions such as temperature, and the amount of time that a load is applied in creep response. The dynamic behavior of the periodontal ligament (PDL) and oral soft tissues may well be simulated with this theory. Changing interrelation of objects is also a structural behavior that is commonly seen intra-orally in tooth-to-tooth and material-to-tissue contacts. Geometric nonlinearities are characterized by large deformations and/or rotations, and occasionally seen in dental materials such as the dental wires. Changing geometric configuration can cause the structure to respond nonlinearly. Often, the stiffness of a structure increases as the deflection increases.

Nonlinear analysis has become an increasingly powerful approach to predict stress and strain within structures in a realistic situation that cannot be solved by a linear static model. The key elements required for the design and appropriate utilization of this methodology should be fully clarified. This paper reviews the recent developments in the application of the nonlinear FEM in dentistry under the following headings: (1) nonlinear simulation of periodontal ligament property, (2) plastic and viscoelastic behaviors in materials, (3) tooth-to-tooth contact analysis, (4) contact analyses in implant structures and (5) interfacial stress in restorations.

Section snippets

Nonlinear simulation of periodontal ligament property

The force–displacement relationship of a tooth under applied force is represented not by a linearity but by a nonlinear curve.1 To assume the linear elasticity as a constant material property of the periodontal ligament may lead to an erroneous solution. If an intermediate constant is used as the elastic modulus of PDL, the tooth displacement would be too small under a relatively low bite force, and too high under a high load. The use of the linear static model is suitable only for expression

Plastic and viscoelastic behaviors in materials

Plasticity is characterized by an unrecoverable and path-dependent phenomenon, and begins when stress exceeds the material's yield point. Large deformation and large strain geometric nonlinearities are often associated with a plastic material response. Creep is the time-dependent material nonlinearity in which the material continues to deform under a constant load. If a displacement is imposed, the reaction force and stress will disappear over time, which in turn causes stress relaxation.

Tooth-to-tooth contact analysis

Sliding and friction phenomena critically affect the stress and strain created on the contact surfaces between teeth. The problems can be partially solved by performing contact analysis, which is highly nonlinear and difficult to solve due to the following major issues. First, the contact regions are unknown until a sequence of the problem has been solved. Depending upon the load, material, and environmental factors, the surfaces can move in and out of contact with each other in a highly

Contact analysis in implant structures

Contact and friction play important roles in the mechanical behavior of implant prostheses. The contact elements may be defined in two or more of the following components: implant bodies, threads, abutments, abutment screws, cylinders, and bone. The contact zones in the FEM models transfer only pressure and tangential frictional forces, while tension is not transferred. Since the screw joint integrity at the implant–abutment joint is essential for long-term success of implant restoration,

Interfacial stress in restorations

Stress analysis at the tooth–restoration complex has been performed to predict the failure risk at the interface as well as within the bonded tooth structures. In a linear static analysis, an interfacial surface between individual structures with different elastic properties shares the same node, representing the perfect bond. This conventional approach occasionally leads to erroneous interpretation in the FEM results.

Fig. 2 shows a simplified 2D FEM model of an endodontically treated

Conclusions

The nonlinear FE analysis has become an increasingly powerful approach to predict stress and strain within structures in a realistic situation that cannot be solved by conventional linear static models. The nonlinear simulation of the PDL properties enhances a precise estimation of the stress and strain with wide range of tooth movement. The determination of the elastic, plastic, and viscoelastic material properties of a target material often requires mechanical testing prior to FEM analyses.

Acknowledgement

This study was supported by KAKENHI 20592307 (to N.W.) and High-Tech Research Project 2005–2009 (to Iwate Medical University), both from JSPS/MEXT.

References (63)

  • DeHoff et al.

    Shear stress relaxation of dental ceramics determined from creep behavior

    Dental Materials

    (2004)
  • P.H. DeHoff et al.

    Creep functions of dental ceramics measured in a beam-bending viscometer

    Dental Materials

    (2004)
  • N. De Jager et al.

    Finite element analysis model to simulate the behavior of luting cements during setting

    Dental Materials

    (2005)
  • D. Garriga-Majo et al.

    Optimisation of the superplastic forming of a dental implant for bone augmentation using finite element simulations

    Dental Materials

    (2004)
  • X. Xu et al.

    Comparative study of torsional and bending properties for six models of nickel-titanium root canal instruments with different cross-sections

    Journal of Endodontics

    (2006)
  • A.A. Mahmoud et al.

    Prediction of permanent deformation in cast clasps for denture prostheses using a validated nonlinear finite element model

    Dental Materials

    (2007)
  • B. Dejak et al.

    Finite element analysis of stresses in molars during clenching and mastication

    Journal of Prosthetic Dentistry

    (2003)
  • B. Dejak et al.

    Finite element analysis of mechanism of cervical lesion formation in simulated molars during mastication and parafunction

    Journal of Prosthetic Dentistry

    (2005)
  • H. Muraki et al.

    Finite element contact stress analysis of the RPD abutment tooth and periodontal ligament

    Journal of Dentistry

    (2004)
  • D. Bozkaya et al.

    Mechanics of the tapered interference fit in dental implants

    Journal of Biomechanics

    (2003)
  • L.A. Lang et al.

    Finite element analysis to determine implant preload

    Journal of Prosthetic Dentistry

    (2003)
  • I. Alkan et al.

    Influence of occlusal forces on stress distribution in preloaded dental implant screws

    Journal of Prosthetic Dentistry

    (2004)
  • C.L. Lin et al.

    Numerical simulation on the biomechanical interactions of tooth/implant-supported system under various occlusal forces with rigid/non-rigid connections

    Journal of Biomechanics

    (2006)
  • C.L. Lin et al.

    Mechanical interactions of an implant/tooth-supported system under different periodontal supports and number of splinted teeth with rigid and non-rigid connections

    Journal of Dentistry

    (2006)
  • W.C. Martin et al.

    Implant abutment screw rotations and preloads for four different screw materials and surfaces

    Journal of Prosthetic Dentistry

    (2001)
  • P.F. Hubsch et al.

    A finite element analysis of the stress at the restoration-tooth interface, comparing inlays and bulk fillings

    Biomaterials

    (2000)
  • C.L. Lin et al.

    Integration of CT, CAD system and finite element method to investigate interfacial stresses of resin-bonded prosthesis

    Computer Methods and Programs in Biomedicine

    (2003)
  • C.L. Lin et al.

    Evaluation of a reinforced slot design for CEREC system to restore extensively compromised premolars

    Journal of Dentistry

    (2006)
  • T. Ikeda et al.

    Effects of polymerization shrinkage on the interfacial stress at resin–metal joint in denture-base: a non-linear FE stress analysis

    Dental Materials

    (2006)
  • G. Couegnat et al.

    Structural optimization of dental restorations using the principle of adaptive growth

    Dental Materials

    (2006)
  • I. Ichim et al.

    Restoration of non-carious cervical lesions. Part I. Modelling of restorative fracture

    Dental Materials

    (2007)
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