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A Fourier-series-based virtual fields method for the identification of 3-D stiffness distributions and its application to incompressible materials

A Fourier-series-based virtual fields method for the identification of 3-D stiffness distributions and its application to incompressible materials
A Fourier-series-based virtual fields method for the identification of 3-D stiffness distributions and its application to incompressible materials
We present an inverse method to identify the spatially-varying stiffness distributions in three-dimensions (3-D). The method is an extension of the classical Virtual Fields Method (VFM) – a numerical technique which 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 3-D F-VFM is validated with both numerical and experimental data. The latter came from a phase contrast MRI 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.
1475-1305
1-22
Nguyen, Tho
221bbf09-88d0-47bc-9af1-16222a3bbe95
Huntley, Jonathan M.
941d0f5a-42f7-4506-88de-ae7c4f34c6f9
Ashcroft, Ian
c23904fe-3fd0-4c5c-b852-d82d8b3d2ddc
Ruiz, Pablo D.
dd7e72d7-ff20-472b-b129-39fd84602174
Pierron, Fabrice
a1fb4a70-6f34-4625-bc23-fcb6996b79b4
Nguyen, Tho
221bbf09-88d0-47bc-9af1-16222a3bbe95
Huntley, Jonathan M.
941d0f5a-42f7-4506-88de-ae7c4f34c6f9
Ashcroft, Ian
c23904fe-3fd0-4c5c-b852-d82d8b3d2ddc
Ruiz, Pablo D.
dd7e72d7-ff20-472b-b129-39fd84602174
Pierron, Fabrice
a1fb4a70-6f34-4625-bc23-fcb6996b79b4

Nguyen, Tho, Huntley, Jonathan M., Ashcroft, Ian, Ruiz, Pablo D. and Pierron, Fabrice (2017) A Fourier-series-based virtual fields method for the identification of 3-D stiffness distributions and its application to incompressible materials. Strain, 53 (5), 1-22, [e12229]. (doi:10.1111/str.12229).

Record type: Review

Abstract

We present an inverse method to identify the spatially-varying stiffness distributions in three-dimensions (3-D). The method is an extension of the classical Virtual Fields Method (VFM) – a numerical technique which 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 3-D F-VFM is validated with both numerical and experimental data. The latter came from a phase contrast MRI 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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ttn_3dfvfm_Strain_revised_V3_6 - Accepted Manuscript
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More information

Accepted/In Press date: 9 April 2017
e-pub ahead of print date: 29 May 2017
Published date: October 2017
Organisations: Engineering Mats & Surface Engineerg Gp

Identifiers

Local EPrints ID: 408456
URI: http://eprints.soton.ac.uk/id/eprint/408456
ISSN: 1475-1305
PURE UUID: eceadc85-5207-427f-94ed-c1eef9044850
ORCID for Fabrice Pierron: ORCID iD orcid.org/0000-0003-2813-4994

Catalogue record

Date deposited: 20 May 2017 04:05
Last modified: 22 Nov 2021 05:22

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Contributors

Author: Tho Nguyen
Author: Jonathan M. Huntley
Author: Ian Ashcroft
Author: Pablo D. Ruiz
Author: Fabrice Pierron ORCID iD

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