Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alves CJS and Ha-Duong T (1999). Inverse scattering for elastic plane cracks. Inverse Probl 15: 91–97
Ammari H, Kang H, Nakamura G and Tanuma K (2002). Complete asymptotic expansions of solutions of the system of elastostatics in the presence of an inclusion of small diameter and detection of an inclusion. J Elast 67: 97–129
Andrieux S, Ben Abda A and Bui H (1999). Reciprocity principle and crack identification. Inverse Probl 15: 59–65
Bonnet M and Constantinescu A (2005). Inverse problems in elasticity. Inverse Probl 21: R1–R50
Bostrom A and Wirdelius H (1995). Ultrasonic probe modeling and nondestructive crack detection. J Acoust Soc Am 97(5 Pt.1): 2836–2848
Engelhardt M, Schanz M, Stavroulakis G and Antes H (2006). Defect identification in 3-D elastostatics using a genetic algorithm. Optim Eng 7: 63–79
Glushkov EV, Glushkova NV and Ehlakov AV (2002). Mathematical model of the ultrasonic defectoscopy of spatial cracks. Appl Math Mech (PMM) 66(1): 147–156, (in Russian)
Goodier JN (1933) Concentration of stress around spherical and cylindrical inclusions and flaws. J Appl Mech APM-55-7 39–44
Guzina B, Nintcu Fata S and Bonnet M (2003). On the stress-wave imaging of cavities in a semi-infinite solid. Int J Solids Struct 40: 1505–1523
Keat W, Larson M and Verges M (1998). Inverse method of identification for three-dimensional subsurface cracks in a half-space. Int J Fract 92: 253–270
Knowles JK and Sternberg E (1972). On a class of conservation laws in linearized and finite elastostatics. Arch Rational Mech Anal 44(3): 187–211
Vatuliyan AO (2004). On the determination of crack configuration in anisotropic medium. Appl Math Mech (PMM) 68(1): 180–188, (in Russian)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media B.V.
About this paper
Cite this paper
Goldstein, R.V., Shifrin, E.I., Shushpannikov, P.S. (2007). Application of invariant integrals to the problems of defect identification. In: Dascalu, C., Maugin, G.A., Stolz, C. (eds) Defect and Material Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6929-1_6
Download citation
DOI: https://doi.org/10.1007/978-1-4020-6929-1_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-6928-4
Online ISBN: 978-1-4020-6929-1
eBook Packages: EngineeringEngineering (R0)