Qualitative methods for inverse scattering in solid mechanics.

Abstract

Inverse problems are widely studied today, and appear in a large range of applications: tomography and imaging, material constitutive property identification, non destructive control... The present subject comes within the scope of this last prospect. It concerns the research of new methods, fast numerically, allowing qualitative object identification (inclusions, cavities, cracks...) embedded in linear elastic solid medium, knowing (at least partially) the surface response to dynamical loadings. Most of the classical methods implemented to solve this kind of problems are dealing with an iterative minimization process, requiring high number of direct simulations. In the present context (three-dimensional elastic waves propagation), these are very expensive. The recent emergence of non-iterative probing methods allows to consider the study of this type of problems in a new light. Earlier works have shown in particular, within the framework of the hypothesis adopted in this subject, the interest of methods such as the Topological Sensitivity or the Linear Sampling for an approximate but fast detection. The present study comes within the scope of the development of the two methods mentioned with application within the framework of the mechanics of deformable solids, i.e. inverse scattering problems in acoustic and elastic media. This work has been done within the framework of a joint Ph.D. program between the Department of Civil Engineering at the University of Minnesota and the Laboratoire de Mécanique des Solides at the Ecole Polytechnique (France).