 | | 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
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| In English (Mech. Solids): | | 3212 |
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| E.I. Shifrin and P.S. Shushpannikov, "Identification of Finitely Many Small Defects in an Anisotropic Linearly Elastic Body from a Single Static Test," Mech. Solids. 50 (4), 421-431 (2015) |
| Year |
2015 |
Volume |
50 |
Number |
4 |
Pages |
421-431 |
| DOI |
10.3103/S0025654415040081 |
| Title |
Identification of Finitely Many Small Defects in an Anisotropic Linearly Elastic Body from a Single Static Test |
| Author(s) |
E.I. Shifrin (A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, shifrin@ipmnet.ru)
P.S. Shushpannikov (A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, shushpan@ipmnet.ru) |
| Abstract |
The problem of identification of finitely many small defects (inclusions, cavities, cracks) clearly separated from each other in the arbitrarily anisotropic linearly elastic space is considered. It is assumed that the forces and displacements are measured on the outer boundary of the body in a single static experiment. A method for determining the number of defects and their center position from the available data is developed. The geometric parameters (dimensions and orientations) of defects are determined if they have ellipsoidal shapes. |
| Keywords |
theory of elasticity, anisotropy, inverse problem, multiple defects, reciprocity functional |
| References |
| 1. | L. M. Bezerra and A. S. Saigal,
"A Boundary Element Formulation for the Inverse Elastostatics Problems (IESP)
of Flaw Detection,"
Int. J. Num. Meth. Engng
36, 2189-2202 (1993). |
| 2. | S.-C. Hsieh and T. Mura,
"Nondestructive Cavity Identification in Structures,"
Int. J. Solids Struct.
30 (12), 1579-1587 (1993). |
| 3. | W. D. Keat, M. C. Larson, and M. A. Verges,
"Inverse Method of Identification for Three-Dimensional Subsurfaces Cracks in a Half-Space,"
Int. J. Fract.
92, 253-270 (1998). |
| 4. | M. Engelhardt, M. Schanz, G. E. Stavroulakis, and H. Antes,
"Defect Identification in 3-D Elastostatics Using a Genetic Algorithm,"
Optimizat. Engng
7, 63-79 (2006). |
| 5. | H. Ben Ameur, M. Burger, and B. Hackl,
"Level Set Methods for Geometric Inverse Problems in Linear Elasticity,"
Inv. Probl.
20, 673-696 (2004). |
| 6. | H. Ben Ameur, M. Burger, and B. Hackl,
"Cavity Identification in Linear Elasticity and Thermoelasticity,"
Math. Meth. Appl. Sci.
30, 625-647 (2007). |
| 7. | C. J. S. Alves and N. F. M. Martins,
"The Direct Method of Fundamental Solutions and the Inverse Kirch-Kress Method
for the Reconstruction of Elastic Inclusions or Cavities,"
J. Int. Equations Appl.
21, 153-178 (2009). |
| 8. | M. Khoddad and M. Dashti Ardakani,
"Investigation of Effect of Different Boundary Conditions
on the Identification of a Cavity inside Solid Bodies,"
Int. J. Adv. Des. Manufact. Tech.
4, 9-17 (2011). |
| 9. | H. Ammari, H. Kang, G. Nakamura, and K. Tanuma,
"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. Elasticity
67, 97-129 (2002). |
| 10. | H. Kang, E. Kim, and J.-Y. Lee,
"Identification of Elastic Inclusions and Elastic Moment Tensors by Boundary Measurements,"
Inv. Probl.
19, 703-724 (2003). |
| 11. | H. Ammari and H. Kang,
Reconstruction of Small Inhomogeneities from Boundary Measurements,
in Lecture Notes in Mathematics, Vol. 1846
(Springer-Verlag, Berlin, 2004). |
| 12. | H. Ammari and H. Kang,
Polarization and Moment Tensors: With Applications to Inverse Problems and Effective Medium Theory,
in Applied Mathematical Sciences, Vol. 162
(Springer-Verlag, New York, 2007). |
| 13. | A. Morassi and E. Rosset,
"Detecting Rigid Inclusions, or Cavities, in an Elastic Body,"
J. Elasticity
73, 101-126 (2003). |
| 14. | G. Alessandrini, A. Bilotta, G. Formica, et al.,
"Evaluation of the Volume of a Hidden Inclusion in an Elastic Body,"
J. Comp. Appl. Math.
198, 288-306 (2007). |
| 15. | S. Andrieux, A. Ben Abda, and H. Bui,
"Reciprocity Principle and Crack Identification,"
Inv. Probl.
15, 59-65 (1999). |
| 16. | P. Steinhorst and A.-M. Sandig,
"Reciprocity Principle for the Detection of Planar Cracks in Anisotropic Elastic Material,"
Inv. Probl.
28, 085910 (2012). |
| 17. | E. I. Shifrin and P. S. Shushpannikov,
"Identification of a Spheroidal Defect in an Elastic Solid Using a Reciprocity Gap Functional,"
Inv. Probl.
26, 055001 (2010). |
| 18. | E. I. Shifrin,
"Ellipsoidal Defect Identification in an Elastic Body
from the Results of a Uniaxial Tension (Compression) Test,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 131-142 (2010)
[Mech. Solids (Engl. Transl.)
45 (3), 417-426 (2010)]. |
| 19. | E. I. Shifrin and P. S. Shushpannikov,
"Identification of an Ellipsoidal Defect in an Elastic Solid Using Boundary Measurements,"
Int. J. Solids Struct.
48 (7-8), 1154-1163 (2011). |
| 20. | E. I. Shifrin and P. S. Shushpannikov,
"Reconstruction of an Ellipsoidal Defect in Anisotropic Elastic Solid Using Results
of One Static Test,"
Inv. Probl. Sci. Engng
21 (5), 781-800 (2013). |
| 21. | H. Ammari, H. Kang, E. Kim, and M. Lim,
"Reconstruction of Closely Spaced Small Inclusions,"
SIAM J. Num. Anal.
42, 2408-2428 (2005). |
| 22. | H. Kang, E. Kim, and J.-Y. Lee,
"Numerical Recognition of a Cluster of Small Elliptic Inclusions,"
Inv. Probl.
23, 2311-2314 (2007). |
| 23. | L. Batatchart, A. Ben Abda, E. Ben Hassen, and J. Leblond,
"Recovery of Pointwise Sources and Small Inclusions in 2D Domains and Rational Approximation,"
Inv. Probl.
21, 51-74 (2005). |
| 24. | K. Bryan, R. Krieger, and N. Trainor,
"Imaging of Multiple Linear Cracks Using Impedance Data,"
J. Comp. Appl. Math.
200, 388-407 (2007). |
| 25. | M. Hanke and W. Rundell,
"On Rational Approximation Methods for Inverse Source Problems,"
Inv. Probl. Imaging
5, 185-202 (2011). |
| 26. | A. Karageorghis, D. Lesnic, and L. Marin,
"The Method of Fundamental Solutions for the Detection of Rigid Inclusions and Cavities
in Plane Inverse Elastic Bodies,"
Comp. Struct.
106-107, 176-188 (2012). |
| 27. | A. Karageorghis, D. Lesnic, and L. Marin,
"A Moving Pseudo-Boundary MFS for Void Detection in Two-Dimensional Thermoelasticity,"
Int. J. Mech. Sci.
88, 276-288 (2014). |
| 28. | E. I. Shifrin and P. S. Shushpannikov,
"Identification of Small Well-Separated Defects in an Isotropic Elastic Body
Using Boundary Measurements,"
Int. J. Solids Struct.
50, 3707-3716 (2013). |
| 29. | 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). |
| 30. | R. J. Asaro,
"Somigliana Dislocations and Internal Stresses: with Applications to Second Phase Hardening,"
Int. J. Engng Sci.
13, 271-286 (1975). |
| 31. | S. G. Lekhnitskii,
Theory of Elasticity of Anisotropic Bodies
(Nauka, Moscow, 1977)
[in Russian]. |
| 32. | A. El Badia and T. Ha-Duong,
"An Inverse Source Problem in Potential Analysis,"
Inv. Probl.
16, 651-663 (2000). |
| 33. | H. Kang and J.-Y. Lee,
"Identification of Simple Poles via Boundary Measurements and an Application of EIT,"
Inv. Probl.
20, 1853-1863 (2004). |
| 34. | O. L. Anderson,
"Determination and Some Uses of Isotropic Elastic Constants of Polycrystalline Aggregates
Using Simple Crystal Data,"
in Physical Acoustic: Principles and Methods,
Ed. by W. Mason
(Academic Press, New York, 1965). |
|
| Received |
15 April 2015 |
| Link to Fulltext |
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