Mathematical formulation of a constitutive Lambert-type differential equation for predicting the dynamic response of materials

Abstract

This paper presents a mathematical formulation of a constitutive Lambert-type differential equation on the basis of the stress decomposition theory in order to predict the dynamic behavior of a variety of materials. The expansion of the nonlinear elastic spring force law required in terms of a generalized form of the Newton’s binomial function of deformation provided, under relaxation of stress conditions, the time versus deformation variation as a Chapman-Richards-type growth model. Numerical applications carried out demonstrated successfully the ability of the model to reproduce the S-shaped response of viscoelastic materials. It has been shown that an increase of viscoelastic characteristics, increases significantly the sensitivity of the model, which becomes flexible enough for experimental data fitting.