Advanced search
Publication Cover
Computer Methods in Biomechanics and Biomedical Engineering Volume 5, 2002 - Issue 2
Submit an article Journal homepage
314
Views
80
CrossRef citations to date
0
Altmetric
Original Articles

A Nonlinear Elastic Model of the Periodontal Ligament and its Numerical Calibration for the Study of Tooth Mobility

G. Pietrzak Laboratoire de Mécanique Appliquée et d' Analyse de Fiabilité, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
,
A. Curnier Laboratoire de Mécanique Appliquée et d' Analyse de Fiabilité, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
,
J. Botsis Laboratoire de Mécanique Appliquée et d' Analyse de Fiabilité, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
,
S. Scherrer Section de Médecine Dentaire, Faculté de Médecine, Université de Genève, 19 rue Barthélemy-Menn, Genève, CH-1205, Switzerland
,
A. Wiskott Section de Médecine Dentaire, Faculté de Médecine, Université de Genève, 19 rue Barthélemy-Menn, Genève, CH-1205, Switzerland
&
U. Belser Section de Médecine Dentaire, Faculté de Médecine, Université de Genève, 19 rue Barthélemy-Menn, Genève, CH-1205, Switzerland
Pages 91-100 | Published online: 14 Sep 2010

  • Atkinson , T.S. and Ralph , W.J. 1977 . In vitro strength of the human periodontal ligament . J. Dent. Res. , 56 (1} ) : 48 – 52 .
  • Ball , J.M. 1977 . Convexity conditions and existence theorems in nonlinear elasticity . Arch. Rational. Mech. Anal. , 63 : 337 – 403 .
  • Chiba , M. , Yamane , A. , Ohshima , S. and Komatsu , K. 1990 . vitro measurement of regional differences in the mechanical properties of the periodontal ligament in the rat mandibular incisor . Arch. Oral Biol. , 35 (2} ) : 153 – 161 .
  • Chiba , M. and Komatsu , K. 1993 . Mechanical responses of the periodontal ligament in the transverse section of the rat mandibular incisor at various velocities of loading in vitro . J. Biomechanics , 26 (4/5} ) : 561 – 570 .
  • Curnier , A. 1994 . Computational Methods in Solid Mechanics , Dordrecht : Kluwer Academic Publishers .
  • Durkee , M.C. 1996 . The non-linear stress-strain behavior of the periodontal ligament and its effect on finite element models of dental structures , University of Maryland . Ph.D. Thesis
  • Durkee , M.C. , Rekow , E.D. and Thompson , V.P. 1996 . Periodontal ligament stress patterns in a non-linear finite element model . J. Dent. Res. , 76 : 148 (special issue}, (abstract #2430}
  • Durkee , M.C. 1997 . The tensile and compressive behavior of fixed human periodontal ligament . J. Dent. Res. , 75 : 321 (special issue}, (abstract #1473}
  • Durkee , M. C. , Rekow , F.D. and Thompson , V.P. 1998 . PDL stress patterns in a 3D non-linear finite element model . J. Dent. Res. , 77 : 277 (special issue}, (abstract #1370}
  • Giargia , M. and Lindhe , J. 1997 . Tooth mobility and periodontal disease . J. Clin. Periodontol. , 24 : 785 – 795 .
  • Komatsu , K. and Chiba , M. 1993 . The effect of velocity of loading on the biomechanical response of the periodontal ligament in transverse sections of the rat molar in vitro . Arch. Oral Biol. , 38 (5} ) : 369 – 375 .
  • Mandel , U. , Dalgaard , P. and Viidik , A. 1986 . A biomechanical study of the human periodontal ligament . J. Biomechanics. , 19 (8} ) : 637 – 645 .
  • Moxham , B.J. and Berkovitz , B.K.B. 1982 . “ The effects of external forces on the periodontal ligament--the response to axial loads ” . In The periodontal ligament in health and disease , Edited by: Berkovitz , B.K.B. , Moxham , B.J. and Newman , H.N. Pergamon Press . 1982
  • Mühlemanu , H.R. 1954 . Tooth mobility (iii}: The mechanism of tooth mobility . J. Periodontol , 25 : 128 – 137 .
  • Mühleman , H.R. 1967 . Tooth mobility: A review of clinical aspects and research findings . J. Periodontol , 38 : 686 – 713 .
  • Parfitt , G.J. 1960 . Measurement of physiological mobility of individual teeth in an axial direction . J. Dent. Res. , 39 : 608 – 618 .
  • Picton , D.C. 1963 . Vertical movement of cheek teeth during biting . Arch. Oral Biol. , 8 : 108 – 118 .
  • Picton , D.C. 1984 . Changes in axial mobility of undisturbed teeth and following sustained intrusive forces in adult monkeys (macaca fascicularis} . Arch. Oral Biol. , 29 (12} ) : 959 – 964 .
  • Picton , D.C. 1990 . Tooth mobility-an update . Eur. J. Orthod. , 12 (1} ) : 109 – 115 .
  • Pietrzak , G. 1997 . Continuum mechanics modeling and augmented Lagrangian formulation of large deformation frictional contact problems , Lausanne : LMAF-DGM-EPFL . Ph.D. Thesis
  • Pioletti , D.P. 1997 . Viscoelastic properties of soft tissues: Application to knee ligaments and tendons , Lausanne : LGM-DP-EPFL . Ph.D. Thesis
  • Rajaonah , R.R.D. 1990 . Étude d'une loi de comportement visco-Élastique , Lausanne : LMA-DGM-EPFL . Ph.D. Thesis
  • Ralph , W.J. 1980 . The in vitro rupture of human periodontal ligament . J. Biomechanics , 13 (4} ) : 269 – 273 .
  • Ralph , W.J. 1982 . Tensile behaviour of the periodontal ligament . J. Periodontal. Res. , 17 (4} ) : 423 – 426 .
  • Rateitschak , H. , Rateitschak , E.M. and Wolf , M.F. 1989 . Porodontologie , Stuttgart : Georg Thieme .
  • Rees , J.S. and Jacobsein , P.H. 1997 . Elastic modulus of the periodontal ligament . Biomaterials , 18 : 995 – 999 .
  • Schroeder , H.E. 1987 . Orale strukturbiologie , Stuttgart, New York : Georg Thieme Verlag .
  • Veronda , D.R. and Westmann , R.A. 1970 . Mechanical characterization of skin-finite deformation . J. Biomechanics , 3 : 111 – 124 .
  • Williams , K.R. and Edmundson , J.T. 1984 . Orthodontic tooth movement analysed by the finite element method . Biomaterials , 5 : 347 – 351 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.