The paper is designed to provide a theoretical mechanical model taking into account elastic, viscous and inertial nonlinearities simultaneously, for predicting the time dependent response of some materials under a constant loading. Numerical illustrations are carried out to investigate the effects of rheological coefficients action on the model.

In this paper, a one-dimensional nonlinear modified and extended Voigt model with constant material parameters is formulated to represent mathematically the time deformation behavior of a variety of viscoelastic materials. A binomial law is used as a nonlinear elastic force function. Numerical illustrations performed show that the hyperlogistic-type solution obtained is very useful to reproduce any S-shaped experimental curve.