On a mathematical model of a human root dentin

Objective: On the basis of recent experimental data, a new mathematical model that predicts creep in human root dentin has been developed. Method: 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. Significance: 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.