A Fourier‐series‐based virtual fields method for the identification of three‐dimensional stiffness distributions and its application to incompressible materials
posted on 2017-04-21, 13:31authored byTho Nguyen, Jonathan Huntley, Ian A. Ashcroft, Pablo RuizPablo Ruiz, Fabrice Pierron
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.
History
School
Mechanical, Electrical and Manufacturing Engineering
Published in
Strain
Volume
53
Issue
5
Citation
NGUYEN, T.T. ...et al., 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.
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
Acceptance date
2017-04-09
Publication date
2017-05-29
Notes
This is the peer reviewed version of the following article: NGUYEN, T.T. ...et al., 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, which has been published in final form at https://doi.org//10.1111/str.12229. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.