On a mathematical model of a human root dentin

Dental Materials

Volumn 21, Issue 2, 2005, Pages 125-128

  Petrovic, Ljubomir M ^a   Spasic, Dragan T ^b   Atanackovic, Teodor M ^b  

^a UNIVERSITY OF NOVI SAD   (Serbia)

^b UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

Dentin; Fractional derivative; Viscoelasticity; Zener model

Indexed keywords

CREEP; DENTISTRY; FUNCTIONS; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; STRAIN; STRESS RELAXATION; STRESSES; VISCOELASTICITY;

CREEP TESTS; HUMAN ROOT DENTIN; RESTORATIVE MATERIALS; STRESS RELAXATION TESTS;

DENTAL MATERIALS;

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; DENTIN; ELASTICITY; HUMAN; MECHANICAL STRESS; NONLINEAR SYSTEM; PHYSIOLOGY; TEMPERATURE; THERMODYNAMICS; TOOTH ROOT; VISCOSITY; WEIGHT BEARING;

ALGORITHMS; DENTIN; ELASTICITY; HUMANS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; STRESS, MECHANICAL; TEMPERATURE; THERMODYNAMICS; TOOTH ROOT; VISCOSITY; WEIGHT-BEARING;

EID: 12344294500     PISSN: 01095641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dental.2004.01.004     Document Type: Article

References (14)

1. Pashley D.H., Ciucchi B., Sano H., Carvalho R.M., Russel C.M. Bond strength versus dentine structure: a modeling approach. Arch Oral Biol. 40:1995;1109-1118
2. Jantarat J., Palamara J.E.A., Lindner C., Messer H.H. Time dependent properties of human root dentin. Dent Mater. 18:2002;468-493
3. Atanackovic T.M., Guran A. Theory of elasticity for scientists and engineers. 2000;Birkhauser, Boston
4. Oldham K.B., Spanier J. The fractional calculus. 1974;Academic Press, New York
5. Samko S.G., Kilbas A.A., Marichev O.I. Fractional integrals and derivatives, theory and applications. 1993;Gordon & Breach, Amsterdam
6. Bagely R.L., Torvik P.J. On the fractional calculus model of viscoelastic behavior. J Rheol. 30:1986;133-155
7. Atanackovic T.M. A modified Zener model of a viscoelastic body. Continuum Mech Thermodyn. 14:2002;137-148
8. Bagely R.L., Torvik P.J. A generalized derivative model for an elastomer damper. Shock Vib Bull. 49:1979;135-143
9. Bagely R.L., Torvik P.J. A theoretical basis for the application of fractional calculus to viscoelasticity. J Rheol. 27:1983;201-210
10. Gorenflo R., Mainardi F. Carpinteri A., Mainardi F. Fractional calculus: integral and differential equations of fractional order. 1997;273-276 Springer, Wien
11. Gorenflo R., Mainardi F. On Mittag-Leffler-type functions in fractional evolution processes. J Comput Appl Math. 118:2000;283-299
12. Podlubny I. Fractional differential equations. 1999;Academic Press, San Diego
13. Atanackovic T.M., Spasic D.T. On viscoelstic compliant contact impact models. Trans ASME J Appl Mech. 2004;. in press
14. Spasic D.T., Charalambakis N.C. Forced vibrations with fractional type of dissipation. Proceedings of the International Conference on Nonsmooth/Nonconvex Mechanics with application in engineering. 2002;. p. 323-30