Detecting the localization of elastic inclusions and Lamé coefficients

Nuno F. M. Martins

doi:10.3934/ipi.2014.8.779

Article Contents

2014, Volume 8, Issue 3: 779-794. Doi: 10.3934/ipi.2014.8.779

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Detecting the localization of elastic inclusions and Lamé coefficients

Nuno F. M. Martins^1,

1.
CEMAT-IST and Departamento de Matemática, Faculdade de Ciências e Tecnologia (NULisbon), Universidade Nova de Lisboa, Quinta da Torre, Caparica

Received: June 30, 2013

Revised: June 30, 2014

Published: July 2014

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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.

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Mathematics Subject Classification: 65N21, 65N35, 35J25.

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