Visco-hypoelastic model of photo-polymerization process for small changes of temperature

• Autorzy: Gambin W.
• Języki publikacji: EN

Abstrakty

EN

The aim of the paper is to propose a model for estimation of the shrinkage stress in photo-cured dental restorations. Up to now, the elastic and viscoelastic models of photo-curing process use an incremental approach with a large number of time steps, with a fixed Young’s modulus and viscosity within each of the time increments. The elastic approach with a stepped increasing Young’s modulus gives the stress values too high. On the other hand, the incremental viscoelastic approach requires long-lasting computations. In the present paper, a consistent model of the photo-curing process for the case of small temperature changes is proposed. The proposition bases on the Maxwell model, in which the Young’s modulus and the viscosity are continuous functions of time. The assumptions of the model follow from the dental practice, as well as from a physical nature of the process and from the rules of continuum mechanics. A performed incremental analysis of the process enables to formulate an integral model of the process, with an explicit rule for the shrinkage stress for 1D and 3D cases. The model has been tested for the material data of dental composite Clearfil F2. Results of the calculations coincide with the values of stresses measured in thin layers of Clearfil F2.

Słowa kluczowe

EN

photopolymerization; shrinkage stress; dental composites; viscoelasticity; hypoelasticity; Maxwell model; time-dependent parameters

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2010
• Tom: Vol. 62, nr 5
• Strony: 379--403
• Opis fizyczny: Bibliogr. 30 poz.

Twórcy

autor

Gambin W.

• Faculty of Mechatronics Institute of Micromechanics and Photonics, Applied Mechanics Division, Warsaw University of Technology Św. Andrzeja Boboli 8 02-525 Warszawa, Poland,

Bibliografia

• 1. B.S. Dauvillier, A.J. Feilzer, A.J. de Gee, C.L. Davidson, Visco-elastic parameters of dental restorative materials during setting, J. Dental Research, 79, 818–823, 2000.
• 2. A.J. Feilzer, B.S. Dauvillier, Effect of TEGMA/BisGMA ratio on stress development and viscoelastic properties of experimental two-paste composites, J. Dental Research, 82, 824–828, 2003.
• 3. R. Ajlouni, S.E. Bishara, M.M. Soliman, C. Oonsombat, J.F. Laffoon, J. Warren, The use of Ormocer as an alternative material for bonding orthodontic brackets, Angle Orthod., 75, 106–108, 2005.
• 4. A. Versluis, W.H. Douglas, M. Cross, Does an incremental filling technique reduce polymerization shrinkage stress? J. Dental Research, 75, 871–878, 1996.
• 5. A. Versluis, D. Tantbirojn, W.H. Douglas, Does dental composites always shrink toward the light? J. Dental Research, 77, 1435–1445, 1998.
• 6. P. Kowalczyk, W. Gambin, Techniques of shrinkage stress reduction in dental restoration, International Journal of Material Forming, 1, 755–758, 2008.
• 7. P. Kowalczyk, Influence of the shape of the layers in photo-cured dental restorations on the shrinkage stress peaks – FEM study, Dental Materials, 25, e83–e91, 2009.
• 8. B.S. Dauvillier, P.F. Hübsh, M.P. Aarnts, A.J. Feilzer, Modeling of viscoelastic behavior of dental chemically activated composites during curing, Journal of Biomedical Materials Research Part B: Applied Biomaterials, 58, 16–26, 2001.
• 9. M.M. Winkler, T.R. Katona, N.H. Paydar, Finite element stress analysis of three filling techniques for class V light-cured composites restorations, J. Dental Research, 75, 1477–1483, 1996.
• 10. Abaqus Analysis User’s Manual, Vol. 6.7, Section 17.4.1, Hypoelastic behavior, Hibbitt, Karlsson and Sorensen Inc., 2008.
• 11. C. Truesdell, Hypoelasticity, J. Ration. Mech. Anal. 4, 83–133, 1955.
• 12. A.C. Eringen, Nonlinear Theory of Continuous Media, McGraw-Hill, 1962.
• 13. P.F. Hübsh, J. Middleton, J. Knox, A finite element analysis of the stress at the restoration-tooth interface, comparing inlays and bulk fillings, Biomaterials, 21, 1015–1019, 2000.
• 14. M. Barink, P.C.P van der Mark, W.M.M. Fennis, R.H. Kuijs, C.M. Kreulen, N. Verdonschot, A three-dimensional finite element model of the polymerization process in dental composites, Biomaterials, 24, 1427–1435, 2003.
• 15. D.L. Hussey, P.A. Biagioni, P.J. Lamey, Thermographic measurement of temperature change during resin composite polymerization in vivo, Journal of Dentistry, 23, 267–271, 1995.
• 16. F.P. Jacobs, Rapid prototyping & manufacturing, fundamentals of stereolithography, Society of manufacturing engineers, Deaborn, MI, USA 1992.
• 17. F. Rueggerberg, K. Tamareselvy, Resin cure determination by polymerization shrinkage, Dental Materials, 11, 265–268, 1995.
• 18. D. Alster, A.J. Feilzer, A.J. de Gee, C.L Davidson, Polymerization contr action stress in thin resin composite layers as a function of layer thickness, Dental Materials, 13, 146–150, 1997.
• 19. Y.M. Huang, C.P. Jiang, Curl distortion analysis during photo polymerization of stereolithography using dynamic finite element method, Int. J. Adv. Manuf. Technol., 21, 586–595, 2003.
• 20. Y.M. Huang, C.P. Jiang, Numerical analysis of a mask type stereolithography process using a dynamic finite-element method, Int. J. Adv. Manuf. Technol., 21, 649–655, 2003.
• 21. Y.M. Huang, J.Y. Jeng, C.P. Jiang, Increased accuracy by using dynamic finite element method in the constrain-surface stereolithography system, J. Mat. Proc. Tech., 140, 191–196, 2003.
• 22. E. Andrzejewska, Photopolymerization kinetics of multifunctional monomers, Prog. Polym. Sci., 26, 605–665, 2001.
• 23. A.C. Pipkin, T.G. Rogers, A nonlinear integral representation for viscoelastic behavior, J. Mech. Phys. Solids, 16, 59–72, 1968.
• 24. Abaqus Theory Manual, Vol. 6.7, Section 4.1.8, Viscoelasticity, Hibbitt, Karlsson and Sorensen Inc., 2008.
• 25. G. Eliades, D.C.Watts, T. Eliades [Eds.], Dental Hard Tissues and Bonding, Springer, Berlin, Heidelberg 2005.
• 26. A. Vearsulis, D. Tantbirojn, M.R. Pintado, R. de Long, W.H. Douglas, Residual shrinkage stress distributions in molars after composite restoration, Dental Materials, 20, 554–564, 2004.
• 27. R.R. Braga, J.L. Ferracane, Contraction stress related to degree of conversion and reaction kinetics, J. Dental Research, 81, 114–118, 2002.
• 28. A.J. Feilzer, A.J. de Gee, C.L. Davidson, Setting stress in composite resin in relation to configuration of the restoration, J. Dental Research, 66, 1636–1639, 1987.
• 29. L.W. Morland, E.H. Lee, Stress analysis for linear viscoelastic materials with temperature variation, Transaction of the Society of Rheology, 4, 233–263, 1960.
• 30. M.L. Wiliams, R.F. Landel, J.D. Ferry, Structural analysis of viscoelastic materials, AIAA Journal, 5, 785–808, 1964.