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Sensitivity of the virtual fields method to noisy data

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Abstract

This paper deals with the application of the virtual fields method (VFM) to the identification of constants governing anisotropic constitutive equations. After a short recalling of the main features of the VFM, its sensitivity to noisy data is addressed. The study focuses on the random component of the noise which always adds to the actual fields in experimental full-field measurements. The uncertainty of the identified constants due to this random component is derived analytically. The obtained closed-form expression is set as a criterion for grading virtual fields. The least sensitivity to noise leads to the best identification. The grading procedure is implemented directly in the VFM algorithm, providing systematically the virtual field which minimizes the sensitivity to random noises. Examples are provided for validating the approach with numerically simulated noisy data. Finally, the grading procedure is applied for adjusting the geometry which leads to an optimal use of the three-point bending test for identifying the elastic constants of a composite material. It shows that the criterion “sensitivity to noise” characterizes quantitatively the identifiability of one or several parameters. Future applications appear quite promising within the design of novel test methods for composites using the VFM.

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Correspondence to S. Avril.

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The authors would like to express deep gratitude to Professor Michel Fogli whose help was crucial for formulating rigorously the mathematical approach of this paper.

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Avril, S., Grédiac, M. & Pierron, F. Sensitivity of the virtual fields method to noisy data. Computational Mechanics 34, 439–452 (2004). https://doi.org/10.1007/s00466-004-0589-6

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  • DOI: https://doi.org/10.1007/s00466-004-0589-6

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