Identification of elastic inclusions and elastic moment tensors by boundary measurements

We consider the problem of identifying unknown inclusions inside an elastic body by means of traction–displacement relations measured on the boundary. Based on the asymptotic formula of Ammari et al (2003 J. Elast. at press), we propose an algorithm to reconstruct unknown inclusions. The algorithm of this paper detects the location and the elastic moment tensors (elastic Polya–Szego tensors) of the inclusion. Since the elastic moment tensors carry information on the size of the inclusion, we can represent the inclusion in two dimensions by a disc of the detected size with the detected centre. We also propose an algorithm to find an ellipse which represents the elastic moment tensors. For this purpose, we explicitly compute elastic moment tensors associated with ellipses. Several results of numerical experiments are presented. We emphasize that only shear stresses are used for the reconstruction of the inclusion: linear traction to detect elastic moment tensors and quadratic polynomials to detect the location.