A generalized self consistent model for effective elastic moduli of human dentine

Closed-form expressions are presented for effective material properties of human dentine in this paper. The derivation is based a Generalized Self Consistent Method and the strain energy principle. The Generalized Self Consistent Model for cell model of fiber-reinforced composites is extended to the case of hollow cylinder model and the corresponding cell model is chosen to consist of a circular hollow cylinder filled with liquid or gas phase, which surrounded by a circular cylindrical shell of matrix phase. Each layer of cylindrical shell is here considered as a kind of composite consisting of collagen fibrils, with mineralized hydroxyapatite, loosely connected to their neighbours, and water (or gas in the case of dry dentine composite). Using the cell model, the effect of Poisson’s ratio and volume fraction of intertubular dentine on effective mechanical constants is analyzed. Results obtained from the proposed model are compared with those from other models such as nano-indentation method.