Estimation of the strain field from full-field displacement noisy data
Comparing finite elements global least squares and polynomial diffuse approximation
DOI:
https://doi.org/10.13052/REMN.17.857-868Keywords:
full-field measurements, numerical differentiation, measurement uncertaintyAbstract
In this study, the issue of reconstructing strain fields from corrupted full-field displacement data is addressed. Two approaches are proposed, a global one based on Finite Element Approximation (FEA) and a local one based on Diffuse Approximation (DA). Both approaches are compared on a case study which is supposed difficult (open-hole tensile test). DA provides more stable results, but is more CPU time consuming. Eventually, it is proposed to monitor locally the filtering effect of both approaches, the prospects being an impending improvement of the reconstruction for both approaches.
Downloads
References
Avril S., Pierron F., “ General framework for the identification of constitutive parameters from
full-field measurements in linear elasticity”, International Journal of Solids and Structures,
vol. 44, p. 4978-5002, 2007.
Balaco de Morais A., “ Open hole tensile strength of quasi-isotropic laminates”, Composites
Science and Technology, vol. 60, p. 1997-2004, 2000.
Cleveland W., Loader C., Smoothing by local regression: principles and methods, Springer,
Feng Z., Rowlands R., “ Smoothing finite-element and experimental hybrid technique for stress
analyzing composites”, Computers and Structures, vol. 6, p. 631-639, 1991.
Geers M., De Borst R., Brekelmans W., “ Computing strain fields from discrete displacement
fields in 2D solids”, International Journal of Solids and Structures, vol. 33, n° 29, p. 4293-
, 1996.
Grédiac M., Pierron F., Avril S., Toussaint E., “ The virtual fields method for extracting constitutive
parameters from full-field measurements: a review”, Strain, vol. 42, p. 233-253,
Hickernell F. J., Hon Y. C., “ Radial basis function approximations as smoothing splines”,
Applied Mathematics and Computation, vol. 102, n° 1, p. 1-24, 1999.
Kobayashi A., Handbook on Experimental Mechanics, Wiley, 1993.
Lira I., Cordero R., François M., Vial-Edwards C., “ The uncertainty of experimental
derivarives: application to strain measurement”, Measurement Science and technology, vol.
, p. 2381-2388, 2004.
Nayroles B., Touzot G., Villon P., “ La méthode des éléments diffus”, Comptes rendus de
l’Académie des Sciences, série 2, Mécanique, Physique, Chimie, Sciences de l’Univers,
Sciences de la Terre, vol. 313, n° 2, p. 133-138, 1991.
Pierron F., Green B.,Wisnom M. R., “ Full-field assessment of the damage process of laminated
composite open-hole tensile specimens. Part I: Methodology”, Composites Part A: Applied
Science and Manufacturing, 2007.
Schreier H., Sutton M., “ Systematic errors in digital image correlation due to undermatched
subset shape functions”, Experimental Mechanics, vol. 42, p. 303-310, 2002.
Surrel Y., “ Moiré and grid methods: a signal processing approach.”, in J. Pryputniewicz,
Ryszard J. et Stupnicki (ed.), Interferometry ’94: Photomechanics, vol. 2342, The International
Society for Optical Engineering, SPIE, p. 213-220, Nov, 1994.
Wei T., Li M., “ High order numerical derivatives for one-dimensional scattered noisy data”,
Applied Mathematics and Computation, vol. 175, p. 1744-1759, 2006.
