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

This is the peer reviewed version of the following article: Nguyen, TT and Huntley, JM and Ashcroft, IA and 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). e12229-e12229 which has been published in final form at 10.1111/str.12229 This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."

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
PublisherWiley
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
File Access Level
Open
EditorsGrédiac, M and Pierron, F
Permalink -

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

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Accepted author manuscript
ttn_3dfvfm_Strain_revised_V3_6_marked.pdf
License: CC BY 4.0
File access level: Open

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