Nonlinear viscoelastic properties of human dentin under uniaxial tension

Dentin is a viscoelastic tissue that contributes to the load distribution in human teeth and leads to their fracture resistance. Despite previous researches on the time-dependent behavior of dentin, it is not very clear whether the viscoelastic behavior of this tissue is linear or nonlinear, and what viscoelastic constitutive equations mechanically characterize it. Therefore, the aim of this study was to describe the viscoelastic behavior of human dentin and determine the best-fitting viscoelastic model for this tissue.

After preparation of human dentin specimens from 50 subjects, tensile stress relaxation tests were performed at 1%, 3%, 5% and 7% strain amplitudes. We first evaluated the viscoelastic linearity of this tissue and then fitted the experimental data using different constitutive models, namely, 2-, 3- and 4-term Prony series for linear viscoelasticity, Fung's quasilinear viscoelastic model, and also Schapery and modified superposition models for nonlinear viscoelasticity.

Despite an almost linear trend at small strains up to 5%, the relaxation rate generally depended on strain amplitude, indicating some degree of nonlinearity in dentine viscoelasticity. According to the results of data fitting using different models, the modified superposition formulation could best capture the viscoelastic behavior of human dentin.

In this study, we have quantitatively examined the viscoelastic behavior of human dentin, using a large number of samples. We have obtained the coefficients of various viscoelastic formulations, which can be utilized in subsequent researches on human dentin assuming linear, quasilinear or nonlinear viscoelasticity for this tissue.