3D Heterogeneous Stiffness Reconstruction Using MRI and the Virtual Fields Method

Avril, Stéphane; Huntley, Jonathan M.; Pierron, Fabrice; Steele, D. D.

doi:10.1007/s11340-008-9128-2

Cited by 49 publications

(72 citation statements)

References 25 publications

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“…the lower limit on n in Eqn. (7) was -N rather than 0. Ripples are visible at the inclusion/matrix boundary which can -as for the layered material in Section 3.1 -be regarded as an example of Gibb's phenomenon, resulting from the sharp change in modulus between the two phases.…”

Section: Stiffness Distribution With An Elastic Square Inclusionmentioning

confidence: 91%

“…As a result, it is necessary for the general case to explicitly include the negative frequencies in the summation of Eqn. (7). However, due to the even/odd symmetry of the cosine/sine functions, only one of the two indices m and n needs to take negative values.…”

Section: Parameterisation Of the Stiffness Distribution By A 2-d Fourmentioning

confidence: 99%

“…); and (iv) the sensitivity of the method to noisy data. A state-of-the-art review of the FEMU, together with several of other inverse methods, can be read in [7].…”

Section: Introductionmentioning

confidence: 99%

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A Fourier‐series‐based virtual fields method for the identification of 2‐D stiffness distributions

Nguyen

Huntley

Ashcroft

et al. 2014

Numerical Meth Engineering

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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 known boundary conditions. An efficient numerical algorithm based on the 2-D fast Fourier transform is presented, which reduces the computation time by 3-4 orders of magnitude compared to a direct implementation of the F-VFM for typical experimental dataset sizes. Artefacts specific to the F-VFM (ringing at the highest spatial frequency near to modulus discontinuities) can be largely removed through the use of appropriate filtering strategies. Reconstruction of stiffness distributions with the F-VFM has been validated on three stiffness distribution scenarios under varying levels of noise in the input displacement fields. Robust reconstructions are achieved even when the displacement noise is higher than in typical experimental fields.

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Section: Stiffness Distribution With An Elastic Square Inclusionmentioning

confidence: 91%

Section: Parameterisation Of the Stiffness Distribution By A 2-d Fourmentioning

confidence: 99%

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A Fourier‐series‐based virtual fields method for the identification of 2‐D stiffness distributions

Nguyen

Huntley

Ashcroft

et al. 2014

Numerical Meth Engineering

Self Cite

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“…In works that do not use iterative process, natural frequencies and mode shapes, or operational frequencies and modes, are input data of an algorithm based on the differential equation that governs the transversal vibration of sample in a specific direction and under specific boundary conditions (Gibson, 2000;Alfano & Pagnotta, 2007). In this methodology, it can be included the use of Virtual Fields Method, VFM (Grédia, 1996(Grédia, , 2004Grédiac & Paris, 1996;Grédiac & Pierron, 1998Pierron et al, , 2007Grédiac et al, 1999aGrédiac et al, , 1999bGrédiac et al, , 2001Giraudeau & Pierron, 2003Chalal et al, 2006;Toussaint et al, 2006;Pierron et al, 2007;Avril et al, 2008;Giraudeau et al, 2006). For VFM, weighting functions are the called virtual fields.…”

Section: Wwwintechopencom Techniques For Identification Of Bendingamentioning

confidence: 99%

Techniques for Identification of Bending and Extensional Elastic Stiffness Matrices on Thin Composite Material Plates Based on Virtual Field Method (VFM): Theoretical and Numerical Aspects

Batista¹,

Albuquerque²

2011

Nanocomposites With Unique Properties and Applications in Medicine and Industry

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“…Joint projects between medical and engineering groups should be established in the near future to help solve these very important and challenging problems. A first application of the VFM in this area was published recently [25] and a project is presently underway with Loughborough University on the measurement of the stiffness variation of cornea in the throughthickness direction using optical coherence tomography-based techniques [26].…”

Section: Stiffness Reductionmentioning

confidence: 99%

Identification of Materials Mechanical Properties from Full-Field Measurements: Latest Advances in the Virtual Fields Method

Pierron

2008

AMM

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Abstract. This paper presents a short overview of the state of the art and future challenges of the use of full-field measurements and inverse procedures to identify the constitutive mechanical parameters of a wide range of materials. It concentrates on the so-called Virtual Fields Method (VFM) which is a tool fully dedicated to the processing of full-field measurements. Some of the future challenges are briefly covered here, namely the design of test configurations and the application to damage assessment, high strain rate testing and biomaterials. Some examples are given and the main scientific issues briefly discussed.

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3D Heterogeneous Stiffness Reconstruction Using MRI and the Virtual Fields Method

Cited by 49 publications

References 25 publications

A Fourier‐series‐based virtual fields method for the identification of 2‐D stiffness distributions

A Fourier‐series‐based virtual fields method for the identification of 2‐D stiffness distributions

Techniques for Identification of Bending and Extensional Elastic Stiffness Matrices on Thin Composite Material Plates Based on Virtual Field Method (VFM): Theoretical and Numerical Aspects

Identification of Materials Mechanical Properties from Full-Field Measurements: Latest Advances in the Virtual Fields Method

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