Tomographic reconstruction of stress from photoelastic measurements using elastic regularization.

Szotten, David and Lionheart, William RB and Tomlinson, Rachel A (2006) Tomographic reconstruction of stress from photoelastic measurements using elastic regularization. [MIMS Preprint]

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Abstract

In this paper we consider the problem of recovering the stress tensor field of a three dimensional object from measurements of the polarization state of transmitted light. In contrast to the ray transform approach suggested by Sharafutdinov, which uses the inversion of planar Radon transforms to recover a single component of the deviatoric stress normal to a plane, we study the simultaneous reconstruction of all components of the deviatoric stress in each voxel using a matrix approximation to the truncated transverse ray transform. This approach allows us to employ partial differential operators related to linear elasticity in a regularizing penalty term resulting in a well posed problem. We note that the hydrostatic stress is determined by the deviatoric stress (up to an additive constant) from the equilibrium equation, and that our numerical results confirm that the full stress tensor can be recovered using elastic regularization.

Item Type: MIMS Preprint
Uncontrolled Keywords: Photoelasticity inverse problems tensor tomography
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry
MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
MSC 2010, the AMS's Mathematics Subject Classification > 78 Optics, electromagnetic theory
Depositing User: Prof WRB Lionheart
Date Deposited: 08 Jul 2006
Last Modified: 20 Oct 2017 14:12
URI: https://eprints.maths.manchester.ac.uk/id/eprint/369

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