Constitutive Characterization of the Nonlinear Viscoelastic Response of Vocal Fold Tissues

Abstract

Previous empirical studies have shown that vocal fold tissues exhibit nonlinear viscoelastic behaviors under different loading conditions. Hysteresis and strain rate-dependence of stress-strain curves have been observed for different layers of vocal fold tissues when subjected to cyclic tensile loading [1,2]. Nonlinear viscoelastic response has also been described for vocal fold tissues subjected to constant strain and constant stress tests under both tensile loading and large-strain shear deformation conditions [3,4]. These findings cannot be adequately described by many of the traditional constitutive formulations of linear and quasilinear viscoelasticity. For instance, models based on Y. C. Fung’s quasilinear viscoelastic theory typically apply two separate functions to describe the time dependence and the strain dependence of stress (e.g., the reduced relaxation function G(t) and the elastic response σe(ε), respectively), and combine the two functions by the Boltzmann superposition principle [5]. Such formulations assume that time dependence and strain dependence can be separated. However, recently obtained stress relaxation data of vocal fold tissues under various magnitudes of applied shear strain indicated that they are not separable, as relaxation became slower with increasing strain [4]. This paper attempts to characterize some nonlinear viscoelastic behaviors of vocal fold tissues under tensile and shear deformation conditions based on an implementation of the Bergstrom-Boyce model [6,7].