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Factorization method in the geometric inverse problem of static elasticity

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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.

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526, Russia

    E. I. Shifrin

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  1. E. I. Shifrin
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Correspondence to E. I. Shifrin.

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Original Russian Text © E.I. Shifrin, 2016, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2016, No. 5, pp. 68–78.

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Shifrin, E.I. Factorization method in the geometric inverse problem of static elasticity. Mech. Solids 51, 562–570 (2016). https://doi.org/10.3103/S0025654416050083

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  • DOI: https://doi.org/10.3103/S0025654416050083

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