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Effective Elasticity Tensors in Context of Random Errors

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Abstract

We introduce the effective elasticity tensor of a chosen material-symmetry class to represent a measured generally anisotropic elasticity tensor by minimizing the weighted Frobenius distance from the given tensor to its symmetric counterpart, where the weights are determined by the experimental errors. The resulting effective tensor is the highest-likelihood estimate within the specified symmetry class. Given two material-symmetry classes, with one included in the other, the weighted Frobenius distance from the given tensor to the two effective tensors can be used to decide between the two models—one with higher and one with lower symmetry—by means of the likelihood ratio test.

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Acknowledgements

We wish to acknowledge discussions with Johann Guilleminot, Luke Mifflen-Mitchell, Michael Rochester and Sergey Sadov as well as the graphic and editorial support of Elena Patarini and David Dalton, respectively.

This research was performed in the context of The Geomechanics Project supported by Husky Energy. Also, this research was supported partially by the Natural Sciences and Engineering Research Council of Canada, Discovery Grants 341792-2013 and 238416-2013, and by the Polish National Science Center under Grant No. UMO-2013/11/B/ST10/04742.

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Authors and Affiliations

  1. Department of Geoinformatics and Applied Computer Science, AGH—University of Science and Technology, Kraków, Poland

    Tomasz Danek

  2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada

    Mikhail Kochetov

  3. Department of Earth Sciences, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada

    Michael A. Slawinski

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  1. Tomasz Danek
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  2. Mikhail Kochetov
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  3. Michael A. Slawinski
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Correspondence to Michael A. Slawinski.

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Danek, T., Kochetov, M. & Slawinski, M.A. Effective Elasticity Tensors in Context of Random Errors. J Elast 121, 55–67 (2015). https://doi.org/10.1007/s10659-015-9519-4

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  • DOI: https://doi.org/10.1007/s10659-015-9519-4

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