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General Reconstruction of Elastic Strain Fields from their Longitudinal Ray Transform Full article

Journal SIAM Journal on Applied Mathematics
ISSN: 0036-1399 , E-ISSN: 1095-712X
Output data Year: 2025, Volume: 85, Number: 2, Pages: 945-960 Pages count : 16 DOI: 10.1137/24m1684852
Tags strain tomography, longitudinal ray transform, Bragg-edge, neutron transmission
Authors Wensrich C.M. 1 , Holman S. 2 , Lionheart W.R.B. 2 , Courdurier M. 3 , Polyakova A. 4 , Svetov I. 4 , Doubikin T. 1
Affiliations
1 School of Engineering, University of Newcastle, University Drive, Callaghan NSW, 2308 Australia.
2 School of Mathematics, University of Manchester, Manchester, M21 8TD, UK.
3 Department of Mathematics, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna, 4860 Macul, Santiago, Chile.
4 Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia.

Funding (2)

1 Sobolev Institute of Mathematics FWNF-2022-0009
2 Russian Science Foundation 24-21-00200

Abstract: We develop an algorithm for reconstruction of elastic strain fields from their longitudinal ray transform (LRT) in either two or three dimensions. In general, the LRT only determines the solenoidal part of a symmetric tensor field, but elastic strain fields additionally satisfy mechanical equilibrium; an extra condition that allows for full reconstruction in many cases. Our method provides full reconstruction for general elastic strain fields in connected objects whose boundary only contains one component, while previous results included other requirements such as no residual stress, or zero boundary traction. This allows for full reconstruction in energy resolved neutron transmission imaging for simple objects. Along the way, we prove that the LRT of a potential rank-2 tensor restricted to a bounded set determines the potential on the boundary of the set up to infinitesimal rigid motions on each component of the boundary. The method is demonstrated with numerical examples in two dimensions.
Cite: Wensrich C.M. , Holman S. , Lionheart W.R.B. , Courdurier M. , Polyakova A. , Svetov I. , Doubikin T.
General Reconstruction of Elastic Strain Fields from their Longitudinal Ray Transform
SIAM Journal on Applied Mathematics. 2025. V.85. N2. P.945-960. DOI: 10.1137/24m1684852 WOS Scopus OpenAlex
Dates:
Published print: May 5, 2025
Published online: May 5, 2025
Identifiers:
Web of science: WOS:001504754200003
Scopus: 2-s2.0-105004394452
OpenAlex: W4409820141
Citing:
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OpenAlex 1
Scopus 1
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