title: On a mathematical model of a human root dentin.
abstract: OBJECTIVE
  On the basis of recent experimental data, a new mathematical model that predicts creep in human root dentin has been developed.
  
  
  METHODS
  The chosen constitutive model comprises fractional derivatives of stress and strain and the restrictions on the coefficients that follow from the Clausius-Duhem inequality.
  
  
  RESULTS
  The four constants describing mechanical properties of the human dentin at constant temperature are calculated from a highly non-linear system involving Mittag-Leffler-type functions. Special attention is paid to thermodynamical restrictions that should be observed in determining parameters of the model from experimental results.
  
  
  CONCLUSIONS
  The proposed model allows us to predict behavior of a human dentin in different load situations. Also it could be used for describing mechanical properties of dentin that are important in the development of 'dentin-like' restorative materials.
authors.affiliation: Clinic of Dentistry, Faculty of Medicine, University of Novi Sad, 21000 Novi Sad, Serbia and Montenegro.
authors.forename: Ljubomir M
authors.initials: LM
authors.lastname: Petrovic
authors.forename: Dragan T
authors.initials: DT
authors.lastname: Spasic
authors.forename: Teodor M
authors.initials: TM
authors.lastname: Atanackovic
mesh_terms: D000465:Algorithms; D003804:Dentin / Q000502:physiology*; D004548:Elasticity; D006801:Humans; D008954:Models, Biological; D017711:Nonlinear Dynamics; D013314:Stress, Mechanical; D013696:Temperature; D013816:Thermodynamics; D014092:Tooth Root / Q000502:physiology*; D014783:Viscosity; D016474:Weight-Bearing / Q000502:physiology