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A problem of parameters identification for embedded defects in a linear elastic body using results of static tests is considered. A method, based on the use of invariant integrals is developed for solving this problem. A problem on identification the spherical inclusion parameters is considered as an example of the proposed approach application. It is shown that the radius, elastic moduli and coordinates of a spherical inclusion center are determined from one uniaxial tension (compression) test. The explicit formulae expressing the spherical inclusion parameters by means of the values of corresponding invariant integrals are obtained for the case when a spherical defect is located in an infinite elastic solid. If the defect is located in a bounded elastic body, the formulae can be considered as approximate ones. The values of the invariant integrals can be calculated from the experimental data if both applied loads and displacements are measured on the surface of the body in the static test. A numerical analysis of the obtained explicit formulae is fulfilled. It is shown that the formulae give a good approximation of the spherical inclusion parameters even in the case when the inclusion is located close enough to the surface of the body.

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The elastostatic problem of identification of a spheroidal cavity or inclusion in an elastic solid is considered. It is shown that the parameters of the spheroidal defect (coordinates of its center, the magnitudes of the semiaxes, the direction of the axis of rotation and elastic moduli in the case of elastic inclusion) can be determined using one uniaxial tension (compression) test. The explicit formulas expressing the unknown defect parameters by means of the values of the reciprocity gap functional (RGF) are obtained. The values of the RGF can be calculated from experimental data if both applied loads and displacements are measured on the external surface of the elastic body in the static test. Numerical analysis of the obtained explicit formulas is fulfilled.

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