Ellipsoidal defect identification in an elastic body from the results of a uniaxial tension (compression) test

We consider the problem of identification of an ellipsoidal cavity or ellipsoidal inclusion (rigid or elastic) in an isotropic linearly elastic body. We solve the problem by a method based on the use of a reciprocity functional. We propose a constructive procedure which allows us to express the defect geometric parameters in terms of the values of the reciprocity functional. These values can be calculated by measuring the displacements on the external surface of the body in a static uniaxial tension (compression) test. The proposed procedure permits exact identification of the parameters of the ellipsoidal defect if it is located in an infinite space. In the case of a bounded elastic body, it can be considered as an approximate procedure.