Abstract
We study a parameter identification problem associated with a two-dimensional mechanical problem. In the first part, the experimental technique of determining the displacement field is briefly presented. The variational method proposed herein is based on the minimization of either a separately convex functional or a convex functional that leads to the reconstruction of the elastic tensor and the stress field. These two reconstructed fields are continuous and piecewise linear on a triangulation of the two-dimensional domain. Some numerical and experimental examples are presented to test the performance of the algorithms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bell, J.F., ‘The experimental foundations of solid mechanics’, in: Flügge, S. (ed.), Handbuch der Physik, Vol. VIa/1, Springer, Berlin, 1973.
Brezzi, F., Douglas Jr., J. and Marini, L.D., ‘Two families of mixed finite elements for second order elliptic problems’, Numer. Math. 47 (1985) 217-235.
Chevalier, L., Calloch, S., Hild, F. and Marco, Y., ‘Digital image correlation used to analyze the multiaxial behavior of rubber-like materials’, Eur. J. Mech. A/Solids 20 (2001) 169-187.
François, M., Geymonat, G. and Berthaud, Y., ‘Determination of the symmetries of an experimentally determined stiffness tensor: application to acoustic measurements’, Int. J. Solids Struct. 35 (1998) 4091-4106.
Geymonat, G., Hild, F. and Pagano, S., ‘Identification of elastic parameters by displacement field measurement’, C.R. Mécanique 330 (2002) 403-408.
Grediac, M., Toussaint, E. and Pierron, F., ‘L'identification des propriétés mécaniques de matériaux avec la méthode des champs virtuels, une alternative au recalage par éléments finis’, C.R. Mécanique 330 (2002) 107-112.
Hild, F., Amar, E. and Marquis, D., ‘Stress heterogeneity effect on the strength of silicon nitride’, J. Am. Ceram. Soc. 75 (1992) 700-702.
Holst, G., CCD Arrays, Cameras and Displays, SPIE Engineering Press, 1998.
Kohn, R.V. and Lowe, B.D., ‘A variational method for parameter identification’, Math. Mod. and Numer. Anal. 22 (1988) 119-158.
Ladevèze, P., Nedjar, D. and Reynier, M., ‘Updating of finite element models using vibration tests’, AIAA J. 32 (1994) 1485-1491. See also: Calloch, S., Dureisseix, D. and Hild, F., ‘Identification de modèles de comportement de matériaux solides: utilisation d'essais et de calculs’, Technologies et Formations 100 (2002) 36–41.
Lemaitre, J. and Chaboche, J.-L., Mécanique des Matériaux Solides, Dunod, 1985. English translation: Mechanics of Solid Materials, Cambridge University Press, Cambridge, 1990.
Renaud, P., Comportement d'un Matériau Composite Carbone/Carbone 3D Sous Chargement Uniaxial, MSc Report, ENS de Cachan, 2000.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Geymonat, G., Pagano, S. Identification of Mechanical Properties by Displacement Field Measurement: A Variational Approach. Meccanica 38, 535–545 (2003). https://doi.org/10.1023/A:1024766911435
Issue Date:
DOI: https://doi.org/10.1023/A:1024766911435