The multi-scale meso-mechanics model of viscoelastic dentin

Human dentin is a hierarchical material with multi-level micro-/nano-structures, consisting of tubule, perti-tubular dentin (PTD) and intertubular dentin (ITD) as the major constituents at microscale; and the PTD and ITD are further composed of collagen and hydroxyapatite (HAp) crystals with different volume fractions at nanoscale. In most cases, the HAp is considered as elastic while the collagen as viscoelastic material. It is of great significance to study the hierarchical structure and viscoelasticity of human dentin to understand the mechanical properties of dentin for further development of restorative materials. Based on this, this paper focuses on mul-tiscale modeling of the elastic properties and dynamic viscoelastic response of dentin and establishes a bottom-up micromechanics model from nano-to macro-scale. In order to study the nanostructural effect on the viscoelastic behavior of hierarchical structures, the homogenization theories of random platelets composites (HTRPC) and the locally-exact homogenization theory (LEHT) are introduced for the homogenization of heterogeneous ma-terials of microstructures at different levels. The HTRPC, based on Eshelby Inclusion theory, is used to predict the effective modulus of PTD and ITD. The LEHT is a method for homogenizing multiphase dentin characterized by repeated unit cells (RUCs). The resulting predictions are in very good agreement with several experimental data from the literature. In addition, the results of nanostructrual effect on dentin show that the viscoelasticity of dentin is majorly contributed by collagen and the HAp greatly provide the strength and hardness of dentin. Furthermore, the ageing effect on dentin's viscoelasticity is considered from the proposed multiscale micro -mechanics model. It is demonstrated that the ageing effect is much more influential in affecting the loss moduli of dentin than the storage.