A Fourier‐series‐based virtual fields method for the identification of three‐dimensional stiffness distributions and its application to incompressible materials Article Swipe
T.T. Nguyen
,
J. M. Huntley
,
Ian Ashcroft
,
Pablo D. Ruiz
,
Fabrice Pierron
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1111/str.12229
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1111/str.12229
We present an inverse method to identify the spatially varying stiffness distributions in 3 dimensions. The method is an extension of the classical Virtual Fields Method—a numerical technique that exploits information from full‐field deformation measurements to deduce unknown material properties—in the spatial frequency domain, which we name the Fourier‐series‐based virtual fields method (F‐VFM). Three‐dimensional stiffness distributions, parameterised by a Fourier series expansion, are recovered after a single matrix inversion. A numerically efficient version of the technique is developed, based on the Fast Fourier Transform. The proposed F‐VFM is also adapted to deal with the challenging situation of limited or even non‐existent knowledge of boundary conditions. The three‐dimensional F‐VFM is validated with both numerical and experimental data. The latter came from a phase contrast magnetic resonance imaging experiment containing material with Poisson's ratio close to 0.5; such a case requires a slightly different interpretation of the F‐VFM equations, to enable the application of the technique to incompressible materials.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1111/str.12229
- OA Status
- green
- Cited By
- 16
- References
- 33
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2618005891
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https://openalex.org/W2618005891Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1111/str.12229Digital Object Identifier
- Title
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A Fourier‐series‐based virtual fields method for the identification of three‐dimensional stiffness distributions and its application to incompressible materialsWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2017Year of publication
- Publication date
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2017-05-29Full publication date if available
- Authors
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T.T. Nguyen, J. M. Huntley, Ian Ashcroft, Pablo D. Ruiz, Fabrice PierronList of authors in order
- Landing page
-
https://doi.org/10.1111/str.12229Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://dspace.lboro.ac.uk/2134/24774Direct OA link when available
- Concepts
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Fourier series, Fourier transform, Compressibility, Inversion (geology), Series (stratigraphy), Inverse, Stiffness, Mathematical analysis, Computer science, Algorithm, Geometry, Mathematics, Physics, Mechanics, Structural engineering, Geology, Engineering, Structural basin, PaleontologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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16Total citation count in OpenAlex
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2025: 4, 2024: 2, 2023: 1, 2022: 1, 2021: 1Per-year citation counts (last 5 years)
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33Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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