 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 45, Issue 3 / 2010 | Next article >> |
| E.I. Shifrin, "Ellipsoidal Defect Identification in an Elastic Body from the Results of a Uniaxial Tension (Compression) Test," Mech. Solids. 45 (3), 417-426 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
3 |
Pages |
417-426 |
| DOI |
10.3103/S002565441003012X |
| Title |
Ellipsoidal Defect Identification in an Elastic Body from the Results of a Uniaxial Tension (Compression) Test |
| Author(s) |
E.I. Shifrin (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, shifrin@ipmnet.ru) |
| Abstract |
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. |
| Keywords |
linear elasticity, inverse problem, reciprocity principle, ellipsoidal defect identification |
| References |
| 1. | S. Andrieux, A. Ben Abda, and H. Bui,
"Reciprocity Principle and Crack Identification,"
Inverse Probl.
15, 59-65 (1999). |
| 2. | J. K. Knowles and E. Sternberg,
"On a Class of Conservation Laws in Linearized and Finite Elastostatics,"
Arch. Ration. Mech. Anal.
44 (3), 187-211 (1972). |
| 3. | F. H. K. Chen and R. T. Shield,
"Conservation Laws in Elasticity of the J-Integral Type,"
ZAMP
28, 1-22 (1977). |
| 4. | R. V. Goldstein, E. I. Shifrin, and P. S. Shupannikov,
"Application of Invariant Integrals to the Problems of Defect Identification,"
Int. J. Fract.
147 (1-4), 45-54 (2007). |
| 5. | R. V. Goldstein, E. I. Shifrin, and P. S. Shupannikov,
"Application of Invariant Integrals to Elastostatic Inverse Problems,"
C. r. Acad. Sci. Ser. Mecanique
336, 108-117 (2008). |
| 6. | E. I. Shifrin,
"The Relation between Invariant Integrals of the Linear Isotropic Theory of Elasticity and Integrals Defined by the Duality Principle,"
Prikl. Mat. Mekh.
73 (2), 325-334 (2009)
[J. Appl. Math. Mech. (Engl. Transl.)
73 (2), 237-243 (2009)]. |
| 7. | E. I. Shifrin,
"Symmetry Properties of the Reciprocity Gap Functional in the Linear Elasticity,"
Int. J. Fract.
159, 209-218 (2009). |
| 8. | E. I. Shifrin and P. S. Shushpannikov,
"Identification of a Spheroidal Defect in an Elastic Solid Using Reciprocity Gap Functional,"
Inverse Probl.
26, 055001 (2010). |
| 9. | J. D. Eshelby,
"The Determination of the Elastic Field on an Ellipsoidal Inclusion and Related Problems,"
Proc. Roy. Soc. London. Ser. A
241 (1226), 376-396 (1957). |
|
| Received |
21 December 2009 |
| Link to Fulltext |
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