  Mechanics of Solids A Journal of Russian Academy of Sciences   Founded
in January 1966
Issued 6 times a year
Print ISSN 00256544 Online ISSN 19347936 
Archive of Issues
Total articles in the database:   10864 
In Russian (Èçâ. ÐÀÍ. ÌÒÒ):   8009

In English (Mech. Solids):   2855 

<< Previous article  Volume 47, Issue 4 / 2012  Next article >> 
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), 433447 (2012) 
Year 
2012 
Volume 
47 
Number 
4 
Pages 
433447 
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, prt Vernadskogo 101, str. 1, Moscow, 119526 Russia, kaptsov@ipmnet.ru)
E.I. Shifrin (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, prt Vernadskogo 101, str. 1, Moscow, 119526 Russia, shifrin@ipmnet.ru)
P.S. Shushpannikov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, prt 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 nonelliptic 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 
1.  S. Andrieux and A. Ben Abda,
"Identification of Planar Cracks by Complete Overdetermined Data: Inversion Formula,"
Inverse Probl.
12 (5), 553563 (1996). 
2.  T. Bannur, A. Ben Abda, and M. A. Jaoua,
"A SemiExplicit Algorithm for the Reconstruction of 3D Planar Cracks,"
Inverse Probl.
13 (4), 899917 (1997). 
3.  A. El Badia and T. HaDuong,
"An Inverse Source Problem in Potential Analysis,"
Inverse Probl.
16 (4), 651663 (2000). 
4.  C. J. S. Aves, J. Ben Abdallah, and M. A. Jaoua,
"Recovery of Cracks Using PointSource Reciprocity Gap Function,"
Inverse Probl. Sci. Engng
12 (5), 519534 (2004). 
5.  A. El Badia,
"Inverse Source Problem in an Anisotropic Medium by Boundary Measurements,"
Inverse Probl.
21 (5), 14871506 (2005). 
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, 14311438 (1997). 
7.  S. Andrieux, A. Ben Abda, and H. Bui,
"Reciprocity Principle and Crack Identification,"
Inverse Probl.
15 (1), 5965 (1999). 
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 (14), 4554 (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, 131142 (2010)
[Mech. Solids (Engl. Transl.)
45 (3), 417426 (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 (78), 11541163 (2011). 
12.  A. Morassi and E. Rosset,
"Detecting Rigid Inclusions, or Cavities, in an Elastic Body,"
J. Elasticity
73 (13), 101126 (2003). 
13.  G. Alessandrini, A. Bilotta, G. Formica, et al.,
"Evaluating the Volume of a Hidden Inclusion in an Elastic Body,"
J. Comput. Appl. Math.
198 (2), 288306 (2007). 
14.  E. I. Shifrin,
"Symmetry Properties of the Reciprocity Gap Functional in the Linear Elasticity,"
Int. J. Fract.
159 (2), 209218 (2009). 
15.  V. Ph. Zhuravlev,
Fundamentals of Theoretical Mechanics
(Fizmatlit, Moscow, 2001)
[in Russian]. 

Received 
09 February 2011 
Link to Fulltext 

<< Previous article  Volume 47, Issue 4 / 2012  Next article >> 

If you find a misprint on a webpage, please help us correct it promptly  just highlight and press Ctrl+Enter

