# Fourier-series-based Virtual Fields Method for the identification of 3-D stiffness distributions

Conference paper

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 European Association for Experimental Mechanics.
Authors Nguyen, TT, Huntley, JM, Ashcroft, IA, Ruiz, PD and Pierron, F Conference paper The virtual fields method (VFM) is a powerful technique for determining stiffness distributions of a sample, based onmeasured full-field strain data. The advantage of the VFM over many other methods is its ability to solve inverseproblems of this type without any iteration. A key step in any application of the VFM is the selection of the virtualfields. Several techniques are based on the use of polynomials of spatial variables (either on the whole domain or in apiecewise form), and the material properties are considered as having single values (homogeneous) within the domain.The first attempt to parameterise the material properties as a function of spatial variables was proposed in forreconstruction of the stiffness map of a plate with impact damage.In this paper, we retain the basic concepts underlying the VFM but approach the parameterisation of the materialproperties in the spatial frequency, rather than spatial, domain by performing a 3-D Fourier series expansion of thestiffness distribution over the region of interest. Furthermore, the virtual fields are not selected as polynomials of spatialvariables as in the previous VFM literature, but from a set of simple cosine or sine functions of different spatialfrequencies. The abbreviation F-VFM will be used to denote the VFM in which both a Fourier series is used for thematerial property parameterization, and cosine/sine functions for the virtual fields. The F-VFM was developedoriginally for 2-D geometries; here it is extended to volumetric datasets resulting, for example, from measurementswith Digital Volume Correlation or Phase Contrast Magnetic Resonance Imaging. 2014 European Association for Experimental Mechanics Nguyen et al V2.pdfLicenseCC BY 4.0File Access LevelOpen 07 Jul 2014 19 Dec 2017 14 Feb 2014

https://openresearch.lsbu.ac.uk/item/877z9

###### Accepted author manuscript
 Nguyen et al V2.pdf License: CC BY 4.0 File access level: Open

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