A Fourier-series-based virtual fields method for the identification of three-dimensional stiffness distributions and its application to incompressible materials
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.
|Authors||Nguyen, TT, Huntley, JM, Ashcroft, IA, Ruiz, PD and Pierron, F|
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.
|Journal citation||53 (5), pp. e12229-e12229|
|Publisher||London South Bank University|
|Digital Object Identifier (DOI)||doi:10.1111/str.12229|
|29 May 2017|
|Publication process dates|
|Deposited||12 Dec 2017|
|Accepted||09 Apr 2017|
|Accepted author manuscript|
CC BY 4.0
|Editors||Grédiac, M and Pierron, F|
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