Identification of small well-separated defects in an isotropic elastic body using boundary measurements

Abstract

An inverse problem of identification of a finite number of small, well-separated defects in an isotropic linear elastic body is considered. It is supposed that the defects are cavities or inclusions (rigid or linear elastic). If the defects are cavities then their boundaries are supposed unloaded. If the defects are inclusions it is supposed complete bonding between the matrix and inclusions. It is assumed also that as a result of static test the loads and displacements are measured on the external boundary of the body. A method for determination of centers of the defects projections on an arbitrary plane is developed. If the defects are ellipsoids their geometrical parameters (directions and magnitudes of the ellipsoids axes) are determined also. Numerical examples illustrating efficiency of the developed method are considered.