Inverse Problems and Imaging (IPI)

Detecting the localization of elastic inclusions and Lamé coefficients

Pages: 779 - 794, Volume 8, Issue 3, August 2014      doi:10.3934/ipi.2014.8.779

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Nuno F. M. Martins - CEMAT-IST and Departamento de Matemática, Faculdade de Ciências e Tecnologia (NULisbon), Universidade Nova de Lisboa, Quinta da Torre, Caparica, Portugal (email)

Abstract: In this paper we develop and analyse a direct method, based on the so called reciprocity gap functional, for retrieving the location of an elastic inclusion. The method requires a pair of displacement (imposed) and traction (measured) data, on an accessible part of the boundary. We provide a criterion for the choice of displacement that, in one hand, provides more accurate results and on the other, does not require the Lamé parameters of background medium. We use this property to develop a two boundary measurements direct method for retrieving both Lamé parameters. Several numerical examples are presented in order to illustrate the accuracy and stability of the proposed methods.

Keywords:  Inverse obstacle problems, linear elasticity, center of mass, Lamé parameters, reciprocity gap functional.
Mathematics Subject Classification:  65N21, 65N35, 35J25.

Received: July 2013;      Revised: July 2014;      Available Online: August 2014.