Principes variationnels et exploitation de measure de champs en élasticite

Sometimes parameters pertaining to constitutive materials or to the overall definition of a mechanical structure need to be identified in an indirect manner from experimental measurements. Field measurements provide rich data and, as such, are particularly well suited to material or structural parameter identification problems. In this article, identification techniques specifically devised for the exploitation of field measurements are presented. The identification of distributed elastic moduli is used as a model problem, but other identification problems can be treated along similar lines. This article emphasizes the fact that one is by no means limited to using output least-squares cost functions for solving such identification problems. Indeed, the availability of field measurements allow to define other criteria, well-suited to this type of data and directly linked to fundamental variational principles. Most of this article is devoted to two criteria of this family, namely the error in constitutive equation and the reciprocity gap functional. Various illustrative examples, generally of a synthetic (i.e., purely numerical) nature are provided.