A Theoretical Characterization of Time Dependent Materials by Using a Hyperlogistic-Type Model

Abstract

In this work, the classical mechanical Voigt model is modified and extended to finite deformations by using a rational elastic spring force function to describe accurately the nonlinear time-dependent deformation response of some viscoelastic materials. As theoretical results, a hyperlogistic-type function has been found as the deformation versus time relationship. This growth model appeared powerful to reproduce mathematically as shown by numerical works, any S-shaped experimental data. Compared with some previous models, the present one-dimensional formulation gives the advantage to assure or to control via an explicit material parameter, to speak, via the coefficient of inertia, the nonlinearity of the model. The proposed model demonstrated then the importance to consider in the material modeling the inertial coefficient.