Non-linear approximation method by an approach in stages

This work presents a new methodology of approximation of functions. The identification is done graphically, stage-by-stage, taking into account the form of the generating functions. The above method is developed in this article within the scope of an efficient tool for modeling physical systems and as a reliable curve-fitting method that can use any basic function. Thus, it represents a non-linear identification procedure. On the one hand, simulated cases that do not represent any physical model are studied, and on the other hand, real cases that model physical systems as rubber behavior law are illustrated. The Ogden hyperelastic and the extended Gent–Thomas models for rubber materials are shown to give an accurate prediction of Treloar’s classical data with the help of mechanical parameters evaluated by the stage approach. Critical and comparative analyses of the stage approach are presented with the usual non-linear iterative procedures such as the non-linear least squares.