Parametric and non-parametric identification of macro-mechanical models

1.1 INTRODUCTION Since the very beginning of Engineering Sciences, engineers have been interested in numerical simulations of whatever physical system they were considering, in order to obtain accurate predictions of the behavior of the system they were building under various circumstances: such predictions allow one in turn to optimize the target realization (mechanical structure, chemical plant, : : :). The main causes of errors in simulated models are recognized to be the too large simpliication of the underlying physical phenomenon (e.g. using linear elastic models in Structural Mechanics), or the numerical errors during the numerical computations (e.g. due to the non-linearities when using some plastic model). However, a third cause of error should not be neglected: even under given physical hypotheses, some internal laws must be given before actually computing a simulated behavior. Those can reduce to a few coeecients (e.g. Young and Poisson modules in the elastic model), or take more complex form (e.g. the whole plasticity convex for elasto-plastic models of structures). This paper is concerned with the identiication of the constitutive law of materials in the framework of one-dimensional elasto-visco-plastic rheological models. The behavior of such a material can be approached by considering it is well approximated by the reaction of an assembly of elementary modules representing the basic possible