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Defect detection using Cauchy data on a part of outer boundary of an elastic body

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Abstract

An inverse elastostatic problem is considered. It is assumed that as a result of static test one type of boundary data (Dirichlet or Neumann) is measured on the whole external boundary of an elastic body and both types of boundary data are measured only on a part of the external boundary. A method for defect (inclusion, cavity or a crack) detection and localization by means of the measured data is developed. The idea of the method is to construct a set of subdomains, continuously depending on a parameter. The set must have the following properties. The subdomains increase with increasing parameter, eventually reaching the entire domain occupied by the body. As the parameter tends to the minimal value, the subdomains tend to the part of the boundary on which the Cauchy data are specified. A functional that depends on a subdomain of the set is constructed. The value of the functional is equal zero if intersection of the subdomain with the defect is empty. The value of the functional is not zero if the subdomain contains the defect inside. Thus, we obtain a criterion for the defect detection. The proposed approach enables also to evaluate approximately the position of the defect. In case when the shape of the defect is a convex polygon, the developed method enables to determine its vertices. Numerical examples are considered that illustrate the effectiveness of the proposed method.

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Acknowledgements

The support of Russian Ministry of Science and Higher Education (Project Reg. No AAAA-A20- 120011690132-4) and RFBR (Project No 19-01-00100) is gratefully acknowledged.

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  1. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences (IPMech RAS), Pr. Vernadskogo 101-1, Moscow, Russia, 119526

    Efim I. Shifrin & Elena A. Kasparova

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  1. Efim I. Shifrin
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Correspondence to Efim I. Shifrin.

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Shifrin, E.I., Kasparova, E.A. Defect detection using Cauchy data on a part of outer boundary of an elastic body. Z. Angew. Math. Phys. 73, 134 (2022). https://doi.org/10.1007/s00033-022-01765-1

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  • DOI: https://doi.org/10.1007/s00033-022-01765-1

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