Skip to main content
Log in

Sensitivity of the virtual fields method to noisy data

  • Published:
Computational Mechanics Aims and scope Submit manuscript


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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Author information

Authors and Affiliations


Corresponding author

Correspondence to S. Avril.

Additional information

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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avril, S., Grédiac, M. & Pierron, F. Sensitivity of the virtual fields method to noisy data. Computational Mechanics 34, 439–452 (2004).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: