A Fourier-series-based virtual fields method for the identification of three-dimensional stiffness distributions and its application to incompressible materials

Journal article


Nguyen, TT, Huntley, JM, Ashcroft, IA, Ruiz, PD and Pierron, F (2017). A Fourier-series-based virtual fields method for the identification of three-dimensional stiffness distributions and its application to incompressible materials. Strain. 53 (5), pp. e12229-e12229.
AuthorsNguyen, TT, Huntley, JM, Ashcroft, IA, Ruiz, PD and Pierron, F
Abstract

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.

Year2017
JournalStrain
Journal citation53 (5), pp. e12229-e12229
PublisherLondon South Bank University
ISSN0039-2103
Digital Object Identifier (DOI)doi:10.1111/str.12229
Publication dates
Print29 May 2017
Publication process dates
Deposited12 Dec 2017
Accepted09 Apr 2017
Accepted author manuscript
License
CC BY 4.0
EditorsGrédiac, M and Pierron, F
Permalink -

https://openresearch.lsbu.ac.uk/item/86z42

  • 4
    total views
  • 41
    total downloads
  • 0
    views this month
  • 5
    downloads this month

Related outputs

Estimation of damage location in advanced composite materials
Nguyen, TT (2010). Estimation of damage location in advanced composite materials. Engineering Conference. Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, UK 2010 Loughborough University.
Three-dimensional self-calibrating surface reconstruction using digital photogrammetry
Nguyen, TT (2008). Three-dimensional self-calibrating surface reconstruction using digital photogrammetry. AUN/SEED-Net Workshop on Mechanical and Aerospace Engineering. Bandung Institute of Technology, Bandung, Indonesia 23 - 24 Jul 2008 London South Bank University.
A Fourier-series-based Virtual Fields Method for the identification of modulus distributions
Nguyen, TT, Huntley, JM, Ashcroft, IA, Ruiz, PD and Pierron, F (2013). A Fourier-series-based Virtual Fields Method for the identification of modulus distributions. BSSM Seminar on Tomographic Imaging of Displacement and Strain Fields. Loughborough University, Loughborough, UK 10 Apr 2013 London South Bank University.
3D embedded freeform electrical circuitry in metal componentry
Nguyen, TT, Li, J and Harris, RA (2016). 3D embedded freeform electrical circuitry in metal componentry. Solid Freeform Fabrication (SFF) Conference. Texas, United States 01 Aug 2016 London South Bank University.
Challenges in designing a localisation system suitable for hazardous environments
Nguyen, TT, Kaur, A and Howlader, MOF (2017). Challenges in designing a localisation system suitable for hazardous environments. Michal Lyons Poster Competition. London South Bank University, London 01 Jul 2017 London South Bank University.
Fourier-series-based Virtual Fields Method for the identification of 2-D stiffness distributions
Nguyen, TT, Huntley, JM, Ashcroft, IA, Ruiz, PD and Pierron, F (2013). Fourier-series-based Virtual Fields Method for the identification of 2-D stiffness distributions. International conference on full-field measurement techniques and their applications in experimental solid mechanics (PhotoMechanics 2013). Montpellier 27 - 29 May 2013 London South Bank University.
Fast Fourier Virtual Fields Method for determination of modulus distributions from full-field optical strain data
Nguyen, TT, Huntley, JM, Ashcroft, IA, Ruiz, PD and Pierron, F (2013). Fast Fourier Virtual Fields Method for determination of modulus distributions from full-field optical strain data. in: Osten, W (ed.) Fringe 2013 Berlin Springer. pp. 161-166
Fourier-series-based Virtual Fields Method for the identification of 3-D stiffness distributions
Nguyen, TT, Huntley, JM, Ashcroft, IA, Ruiz, PD and Pierron, F (2014). Fourier-series-based Virtual Fields Method for the identification of 3-D stiffness distributions. 16th International Conference on Experimental Mechanics (ICEM16). Cambridge 07 - 11 Jul 2014 London South Bank University.
Three-dimensional surface reconstruction of aircraft component using digital photogrammetry
Nguyen, TT, Suada, MG, Dirgantara, T and Putra, IS (2007). Three-dimensional surface reconstruction of aircraft component using digital photogrammetry. 2nd Regional Conference on Aerospace Science, Technology and Industry. Bandung, Indonesia 01 - 02 Jul 2007 London South Bank University.
Monocular three-dimensional self-calibrating surface reconstruction using digital photogrammetry
Nguyen, TT, Suada, MG, Dirgantara, G and Putra, IS (2008). Monocular three-dimensional self-calibrating surface reconstruction using digital photogrammetry. AUN/SEED-Net Regional Workshop on Mechanical and Aerospace Engineering. Bandung, Indonesia 23 - 24 Jul 2008 London South Bank University.
A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions
Nguyen, TT, Huntley, JM, Ashcroft, IA, Ruiz, PD and Pierron, F (2014). A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions. International Journal for Numerical Methods in Engineering. 98 (12), pp. 917-936.
A Fourier-series-based Virtual Fields Method for the Identification of 2-D Stiffness and Traction Distributions
Nguyen, TT, Huntley, JM, Ashcroft, IA, Ruiz, PD and Pierron, F (2014). A Fourier-series-based Virtual Fields Method for the Identification of 2-D Stiffness and Traction Distributions. Strain. 50 (5), pp. 454-468.
Hybrid additive manufacturing of 3D electronic systems
Li, J, Wasley, T, Nguyen, TT, Ta, VD, Shephard, JD, Stringer, J, Smith, P, Esenturk, E, Connaughton, C and Kay, R (2016). Hybrid additive manufacturing of 3D electronic systems. Journal of Micromechanics and Microengineering. 26 (10), pp. 105005-105005.
Multifunctional metal matrix composites with embedded printed electrical materials fabricated by ultrasonic additive manufacturing
Li, J, Monaghan, T, Nguyen, TT, Kay, RW, Friel, RJ and Harris, RA (2017). Multifunctional metal matrix composites with embedded printed electrical materials fabricated by ultrasonic additive manufacturing. Composites Part B: Engineering. 113, pp. 342-354.