A nonlinear interface constitutive law is formulated for modeling the mechanical behavior of the periodontal ligament. This gives an accurate interpolation of the few available experimental results and provides a reasonably simple model for mechanical applications. The model is analyzed from the viewpoints of both mathematical consistency and effectiveness in numerical calculations. In order to demonstrate the latter, suitable two- and three-dimensional nonlinear interface finite elements have been implemented.
Issue Section:
Technical Papers
1.
McGuinness
, N. J. P.
, Wilson
, A. N.
, Jones
, M. L.
, and Middleton
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, 1991
, “A Stress Analysis of the Periodontal Ligament Under Various Orthodontic Loadings
,” European Journal of Orthodontics
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, pp. 231
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.2.
Middleton
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, M. L.
, and Wilson
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, 1996
, “The Role of the Periodontal Ligament in Bone Modeling: The Initial Development of a Time-Dependent Finite Element Model
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, and Jacobsen
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, “Elastic Modulus of the Periodontal Ligament
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5.
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, Braak
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, C.
, and de Groot
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, “Stress-Absorbing Elements in Dental Implants
,” J. Prosthet. Dent.
, 64
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), pp. 198
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.6.
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, J. B.
, 1992
, “Biomechanical Factors Affecting the Bone-Dental Implant Interface
,” Clinical Materials
, 10
, pp. 153
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.7.
Ralph
, W. J.
, 1982
, “Tensile Behavior of the Periodontal Ligament
,” Journal of Periodontal Research
, 17
, p. 423
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.8.
Pini, M., 1999, “Mechanical Characterization and Modeling of the Periodontal Ligament,” PhD thesis, University of Trento, Trento, Italy.
9.
Pini, M., Vena, P., and Contro, R., 2000, “Parameter Identification of a Non-Linear Constitutive Law for the Periodontal Ligament Allowing for Tensile and Shear Laboratory Tests,” Proc. XIII Convegno Italiano di Meccanica Computazionale, Brescia, Italy, 13–15 November 2000.
10.
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11.
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12.
Pietrzak, G., Botsis, J., Curnier, A., Zysset, P., Scherrer, S., Wiskott, A., and Belser, U., 1998, “Numerical Identification of Material Properties of the Periodontal Ligament,” Societe de Biomecanique, Actes du 23e`me Congres, INSA, Lyon, France, p. 203.
13.
Natali, A., Pavan, P., Pini, M., and Ronchi, R., 2000, “Numerical Analysis of Short Time Response of Periodontal Ligament,” Proc. 12th Conference of the European Society of Biomechanics, Dublin, Ireland.
14.
Goland
, M.
, and Reissner
, E.
, 1944
, “The Stresses in Cemented Joints
,” J. Appl. Mech.
, 11
, pp. A17–A27
A17–A27
.15.
Jones
, J. P.
, and Whittier
, J. S.
, 1967
, “Waves at a Flexibly Bonded Interface
,” ASME Trans. J. Appl. Mech.
, 34
, pp. 905
–909
.16.
Klarbring
, A.
, 1991
, “Derivation of a Model of Adhesively Bonded Joints by the Asymptotic Expansion Method
,” Int. J. Eng. Sci.
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, pp. 493
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18.
Needleman
, A.
, 1990
, “An Analysis of Tensile Decohesion Along an Interface
,” J. Mech. Phys. Solids
, 38
, pp. 289
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.19.
Hibbitt, Karlsson & Sorensen, 2001, “ABAQUS User’s Manuals,” Release 6.2, Pawtucket, RI, USA.
20.
Corradi, L., and Genna, F., 2002, “Finite Element Analysis of the Jaw-Teeth/Dental Implant System: A Note About Geometrical and Material Modeling,” Computer Modeling in Engineering and Sciences, to appear.
21.
Goodman, R. E., Taylor, R. L., and Brekke, T. L. 1968, “A Model for the Mechanics of Jointed Rock,” Journal of Soil Mechanics and Foundation Division, Proceedings of the ASCE, 94, pp. 637–659.
22.
Meijer
, H. J. A.
, Starmans
, F. J. M.
, Steen
, W. H. A.
, and Bosman
, F.
, 1993
, “A Three-Dimensional, Finite-Element Analysis of Bone Around Dental Implants in an Edentulous Human Mandible
,” Arch. Oral Biol.
, 38
, pp. 491
–496
.23.
Ja¨ger, K., and Dietrich, H., 1991, “Measuring Masticatory Forces with Strain Gages,” RAM, 7, pp. 39–42.
24.
Perelmuter, M. N., 2001, “Development of a Micromechanically Based Interface Law for the Periodontal Ligament,” Internal Report, Landau Network–Centro Volta Fellowship, Department of Civil Engineering, University of Brescia, Italy.
25.
Salvadori, A., 2000, “Symmetric Galerkin BEM for Domains Connected by Cohesive Interfaces: Formulation and Implementation,” Proc. XIII Convegno Italiano di Meccanica Computazionale, Brescia, Italy, 13–15 November 2000.
Copyright © 2002
by ASME
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