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On a mathematical model of a human root dentin
Ljubomir M Petrovic1, Dragan T Spasic, Teodor M Atanackovic
1Clinic of Dentistry, Faculty of Medicine, University of Novi Sad, 21000 Novi Sad, Serbia and Montenegro.
Summary
A new mathematical model predicts creep in human root dentin using fractional calculus. This model aids in understanding dentin mechanics for dental materials and treatments.
Area of Science:
- Biomaterials Science
- Mechanical Engineering
- Dental Research
Background:
- Human root dentin exhibits complex viscoelastic behavior under sustained loads (creep).
- Accurate modeling of dentin's mechanical properties is crucial for restorative dentistry and understanding tooth structure.
- Existing models may not fully capture the time-dependent deformation of dentin.
Purpose of the Study:
- To develop a novel mathematical model for predicting creep in human root dentin.
- To incorporate fractional calculus into a constitutive model for dentin.
- To ensure the model adheres to thermodynamic principles.
Main Methods:
- Developed a constitutive model using fractional derivatives of stress and strain.
- Applied restrictions derived from the Clausius-Duhem inequality to model coefficients.
- Calculated four material constants from a non-linear system involving Mittag-Leffler functions.
Main Results:
- Successfully modeled the mechanical properties of human dentin at constant temperature.
- Identified key constants governing dentin's creep behavior.
- Highlighted the importance of thermodynamical restrictions in parameter determination.
Conclusions:
- The proposed model accurately predicts human dentin behavior under various loading conditions.
- This model can inform the design of 'dentin-like' restorative materials.
- Provides a framework for analyzing dentin's viscoelasticity in dental applications.