2014
DOI: 10.1002/nme.4665
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A Fourier‐series‐based virtual fields method for the identification of 2‐D stiffness distributions

Abstract: The Virtual Fields Method (VFM) is a powerful technique for the calculation of spatial distributions of material properties from experimentally-determined displacement fields. A Fourier-series-based extension to the VFM (the F-VFM) is presented here, in which the unknown stiffness distribution is parameterised in the spatial frequency domain rather than in the spatial domain as used in the classical VFM. We present in this paper the theory of the F-VFM for the case of elastic isotropic thin structures with kno… Show more

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Cited by 17 publications
(40 citation statements)
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“…For a thin 2-D sample made of an isotropic material, subject to known traction distributions around its boundary and negligible volume forces, the fundamental equation underlying the VFM may be written [1,7]: …”
Section: Virtual Fields Methods Formulationmentioning
confidence: 99%
See 2 more Smart Citations
“…For a thin 2-D sample made of an isotropic material, subject to known traction distributions around its boundary and negligible volume forces, the fundamental equation underlying the VFM may be written [1,7]: …”
Section: Virtual Fields Methods Formulationmentioning
confidence: 99%
“…The fact that both the expansion of Q xx and the virtual fields are represented as sine and cosine functions means that the integrals can be e xpressed as 2-D Fourier coefficients of a linear combination of the experimental strain fields. It can be shown [7] that a total of only four 2-D Fast Fourier Transforms (FFTs) are required to assemble all the terms in M. For large matrix sizes, the computational effort becomes essentially independent of the resolution of the experimental strain fields, with a theoretical reduction in computational effort by a factor of N x N y by using the fast algorithm over the direct (i.e., element by element) method of assembling the matrix M.…”
Section: Fast Fourier Vfm Implementationmentioning
confidence: 99%
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“…The F‐VFM was developed originally for 2D geometries and extended to the case of incomplete knowledge of the boundary value distributions. In the current paper, it is extended for the first time to volumetric data resulting from, for example, measurements with digital volume correlation or phase contrast MRI.…”
Section: Introductionmentioning
confidence: 99%
“…where ε f and ε exp correspond to fitted and experimentally computed strains respectively, W i are 44 weighting factors, t f and t exp correspond to predicted and experimental lifetimes, and N t and N e 45 refer to the number of creep curves and the number of points per curve respectively. This cost func- incur high computational expense due to the large number of finite-element analyses required.…”
mentioning
confidence: 99%