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Strain Measurements Through Optimized Particle Tracking in Volumetric Images: Methodology and Error Assessment

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Abstract

An optimized particle tracking methodology using rigid spherical markers embedded within a material is developed for use with volumetric images. Using synthetic volumetric images with additive Gaussian intensity pattern noise in both the undeformed and deformed states, numerical simulations are performed to quantify the positional errors that accumulate at each marker position during the optimal tracking process. To quantify the positional errors, Monte Carlo simulations are performed to obtain the marker position variability for a range of key parameters including marker radius, image intensity noise level and marker spacing. Using theoretical analyses to quantify strain metric variability, results show that (a) without intensity noise, there is a “sinusoidal” bias trend for sub-voxel displacement that is maximum at 0.4 and 0.6 sub-voxel positions; (b) with intensity noise up to 10 %, the standard deviation range is a non-linear function of marker radius, decreasing to 0.03 voxels when the marker radius is 9 voxels and rising to 0.25 voxels for markers with a radius of 1 voxel; (c) standard deviation in the line strain is approximately 2σC /L where σC is the standard deviation in marker centroid position and L is the distance between markers; and (d) the standard deviation in shear strain is approximately 8σC /L.

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Notes

  1. Other convex shaped markers can be used since the centroid position is the only measured metric for the followed analysis and the centroid position is computed by integration. Even so, the spherical steel or silica markers are conveniently available in the market, and have been adopted by some industry researchers since injection techniques were developed for post-manufacturing insertion into softer materials (e.g. rubber).

  2. It is assumed that visual inspection of each volumetric image has been performed so that the region occupied by the particles in each image has been identified and separated from the remainder of the image for further image analysis of the particle region.

  3. Prior baseline volumetric simulation studies by the authors showed that consistent statistical results were obtained by Monte-Carlo simulation when using more than 200 images. Thus, the authors chose 211 images since this is the first prime number exceeding 200.

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Acknowledgments

Technical and computer support provided by the Department of Mechanical Engineering at the University of South Carolina is gratefully acknowledged. In addition, the financial support provided through NASA Cooperative Agreement NNX13AD43A and by the State of South Carolina NASA EPSCoR program office are deeply appreciated.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Columbia, SC, 29208, USA

    N. Li & M. A. Sutton

  2. Correlated Solutions Incorporated, 121 Dutchman Blvd, Irmo, SC, 29063, USA

    H. W. Schreier

  3. Bridgestone Americas LLC, 1200 Firestone Parkway, Akron, OH, 44317-0001, USA

    J. L. Turner & N. Mani

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  1. N. Li
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  2. M. A. Sutton
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  3. H. W. Schreier
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  4. J. L. Turner
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  5. N. Mani
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Correspondence to M. A. Sutton.

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Li, N., Sutton, M.A., Schreier, H.W. et al. Strain Measurements Through Optimized Particle Tracking in Volumetric Images: Methodology and Error Assessment. Exp Mech 56, 1281–1291 (2016). https://doi.org/10.1007/s11340-016-0146-1

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  • DOI: https://doi.org/10.1007/s11340-016-0146-1

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