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IssuesArchive of Issues2012-4pp.433-447

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A.V. Kaptsov, E.I. Shifrin, and P.S. Shushpannikov, "Identification of Parameters of a Plane Elliptic Crack in an Isotropic Linearly Elastic Body from the Results of a Single Uniaxial Tension Test," Mech. Solids. 47 (4), 433-447 (2012)
Year 2012 Volume 47 Number 4 Pages 433-447
DOI 10.3103/S0025654412040085
Title Identification of Parameters of a Plane Elliptic Crack in an Isotropic Linearly Elastic Body from the Results of a Single Uniaxial Tension Test
Author(s) A.V. Kaptsov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo†101, str.†1, Moscow, 119526 Russia, kaptsov@ipmnet.ru)
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)
P.S. Shushpannikov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo†101, str.†1, Moscow, 119526 Russia, shushpan@ipmnet.ru)
Abstract The method earlier developed by one of the authors for identifying ellipsoidal defects is numerically tested for the applicability to the problem of identification of a degenerate ellipsoidal defect, i.e., an elliptic crack. The method is based on the reciprocity functional and the assumption that the displacements are measured in a uniaxial tension test of an isotropic linearly elastic body. Calculations show that the earlier developed method is also efficient for identification of an elliptic crack and its parameters (the center coordinates, the normal to the crack plane, and the directions and lengths of the semiaxes) can be determined with high accuracy. Some examples where the crack has a non-elliptic shape are also considered. It is discovered that, in many cases, the ellipsoids that were constructed by formulas reconstructing the ellipsoidal crack from the data on the external boundary of the body that correspond to a nonelliptic crack, approximate the actual defect with sufficient accuracy. The method stability was investigated with respect to noise in the initial data.
Keywords linear elasticity, inverse problem, reciprocity principle, elliptic crack
References
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6.  S. Andrieux, A. Ben Abda, and H. Bui, "On the Identification of Planar Cracks in Elasticity via Reciprocity Gap Concept," C. R. Acad. Sci. Ser. I 324, 1431-1438 (1997).
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8.  R. V. Goldstein, E. I. Shifrin, and P. S. Shushpannikov, "Application of Invariant Integrals to the Problems of Defect Identification," Int. J. Fract. 147 (1-4), 45-54 (2007).
9.  E. I. Shifrin and P. S. Shushpannikov, "Identification of a Spheroidal Defect in an Elastic Solid Using a Reciprocity Gap Functional," Inverse Probl. 26 (5), 055001 (2010).
10.  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)].
11.  E. I. Shifrin and P. S. Shushpannikov, "Identification of an Ellipsoical Defect in an Elastic Solid Using Boundary Measurements," Int. J. Solids Struct. 48 (7-8), 1154-1163 (2011).
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15.  V. Ph. Zhuravlev, Fundamentals of Theoretical Mechanics (Fizmatlit, Moscow, 2001) [in Russian].
Received 09 February 2011
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