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IssuesArchive of Issues2016-5pp.562-570

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E.I. Shifrin, "Factorization Method in the Geometric Inverse Problem of Static Elasticity," Mech. Solids. 51 (5), 562-570 (2016)
Year 2016 Volume 51 Number 5 Pages 562-570
DOI 10.3103/S0025654416050083
Title Factorization Method in the Geometric Inverse Problem of Static Elasticity
Author(s) E.I. Shifrin (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, shifrin@ipmnet.ru)
Abstract The factorization method, which has previously been used to solve inverse scattering problems, is generalized to geometric inverse problems of static elasticity. We prove that finitely many defects (cavities, cracks, and inclusions) in an isotropic linearly elastic body can be determined uniquely if the operator that takes the forces applied to the body outer boundary to the outer boundary displacements due to these forces is known.
Keywords geometric inverse problems, factorization method, linear elasticity, static problem
References
1.  A. Kirsch, "Characterization of the Shape of a Scattering Obstacle Using Spectral Data of the Far Field Operator," Inv. Probl. 14 (6), 1489-1512 (1998).
2.  A. Kirsch, "Factorization of the Far Field Operator for the Inhomogeneous Medium Case and Application to Inverse Scattering Theory," Inv. Probl. 15, 413-429 (1999).
3.  A. Kirsch, "New Characterizations of Solutions in Inverse Scattering Theory," Appl. Anal. 76, 319-350 (2000).
4.  P. Hahner, "An Inverse Problem in Electrostatics," Inv. Probl. 15 (4), 961-975 (1999).
5.  M. Bruhl and M. Hanke, "Numerical Implementation of Two Non-Iterative Methods for Locating Inclusions by Impedance Tomography," Inv. Probl. 16 (4), 1029-1042 (2000).
6.  I. N. Grinberg, "Obstacle Visualization via the Factorization Method for the Mixed Boundary Value Problem," Inv. Probl. 18 (6), 1687-1704 (2002).
7.  R. Kress and L. Kühn, "Linear Sampling Methods for Inverse Boundary Value Problems in Potential Theory," Appl. Numer. Math. 43, 1-2 (2002).
8.  T. Arens, "Linear Sampling Methods for 2D Inverse Elastic Wave Scattering," Inv. Probl. 17 (5), 1445-1464 (2001).
9.  C. J. S. Alves and R. Kress, "On the Far-Field Operator in Elastic Obstacle Scattering," IMA J. Math. 67 (1), 1-21 (2002).
10.  A. Charalambopoulos, A. Kirsch, K. A. Anagnostopoulos, et al., "The Factorization Method in Inverse Elastic Scattering from Penetrable Bodies," Inv. Probl. 23 (1), 27-51 (2007).
11.  R. Potthast, "A Survey on Sampling and Probe Methods for Inverse Problems," Inv. Probl. 22 (2), R1-R47 (2006).
12.  A. Kirsch, "The Factorization Method for a Class of Inverse Elastic Problems," Mathematische Nachrichten 278 (3), 258-277 (2005).
Received 21 April 2016
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