Numerical reconstruction of a cluster of small elastic inclusions

Abstract

We consider a problem of reconstructing a cluster of small elastic inclusions which are located close to each other. We show that the location of the cluster and the elastic moment tensor associated with it can be reconstructed by the measurements of the displacement vectors on the boundary corresponding to the traction applied on the boundary. The detected elastic moment tensor represents the overall (or effective) property of the cluster of inclusions. We implement this idea of reconstruction for the two-dimensional linear isotropic elasticity to demonstrate its viability. We also perform a numerical study on the relation between the elastic moment tensor and the total size of the inclusions of general shape. © 2007 IOP Publishing Ltd.