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Qualitative Methods for Inverse Scattering in Solid Mechanics

Abstract : Context. 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...) em- bedded 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. Project overview. 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. The main lines for this research work are: • The discussion of the methods' capabilities and performances especially when employed in the context of classical numerical tools such as finite element models. • The application of these developments to the combined qualitative identification, geometry and material parameters, of unknown defects embedded. • The extension of these methods as well as the demonstration of their usefulness in time-domain inverse scattering or using multi-frequency measurements of the scattered fields. • The study of theoretical issues raised by the developments of these methods. • The comprehension of the theoretical links which can exist between topological sensitivity and linear sampling.
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Submitted on : Wednesday, January 19, 2011 - 11:23:46 AM
Last modification on : Wednesday, November 17, 2021 - 12:28:16 PM
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  • HAL Id : pastel-00557545, version 1


Cédric Bellis. Qualitative Methods for Inverse Scattering in Solid Mechanics. Solid mechanics [physics.class-ph]. Ecole Polytechnique X, 2010. English. ⟨pastel-00557545⟩



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