×

Robust identification of elastic properties using the modified constitutive relation error. (English) Zbl 1423.74090

Summary: The present study concerns the identification of linear elastic material properties based on inhomogeneous tests and the use of full-field measurements, often based upon inverse approaches. This study presents the formulation of the so-called Modified Constitutive Relation Error (MCRE) method in the context of elastostatics when dealing with uncertain data. Such an approach addresses the concept of the reliability of information and mainly consists in the partitioning of all the available mechanical quantities into a reliable set and a less reliable one, so as to take into account the measurement uncertainties and the error made on the constitutive equation into the formulation, and then allows to identify the sought material properties. The method is split in two steps: the first one consists in defining admissible mechanical fields from all the theoretical and experimental data, for a fixed set of mechanical properties. This is made by the minimization of a criterion allowing a compromise between the constitutive equation and the measurements adequacy. Then, the second step consists in the identification of the sought material properties and takes the form of minimizing a cost function defined by using the above admissible mechanical fields. A comparison with the Finite Element Model Updating (FEMU) method was performed on some numerical examples where realistic perturbations were added. This comparison showed that the MCRE method is more robust towards perturbations for similar input data. Moreover, the proposed method only deals with the available information and does not need additional hypotheses to calculate the mechanical quantities. Eventually, the method was applied to the identification of the shear modulus of an organic matrix composite from experimental data.

MSC:

74B05 Classical linear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs

Software:

VIC-2D; Gmsh; VIC
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chu, T. C.; Ranson, W. F.; Sutton, M. A., Applications of digital-image-correlation techniques to experimental mechanics, Exp. Mech., 25, 3, 232-244 (1985)
[2] Hild, F.; Roux, S., Digital image correlation: from displacement measurement to identification of elastic properties—a review, Strain, 42, 69-80 (2006)
[3] Kobayashi, A. S., Handbook on Experimental Mechanics (1987), Wiley: Wiley New York
[4] Kavanagh, K. T.; Clough, R. W., Finite element applications in the characterization of elastic solids, Int. J. Solids Struct., 7, 1, 11-23 (1971) · Zbl 0205.55303
[5] Collins, J. D.; Hart, G. C.; Haselman, T. K.; Kennedy, B., Statistical identification of structures, Am. Inst. Aeronaut. Atronaut. J., 12, 2, 185-190 (1974) · Zbl 0274.73051
[6] Passieux, J.-C.; Bugarin, F.; David, C.; Périé, J.-N.; Robert, L., Multiscale displacement field measurement using digital image correlation: Application to the identification of elastic properties, Exp. Mech., 1-17 (2014)
[7] Grédiac, M.; Pierron, F.; Avril, S.; Toussaint, E., The virtual fields method for extracting constitutive parameters from full-field measurements: a review, Strain, 42, 233-253 (2006)
[8] Claire, D.; Hild, F.; Roux, S., A finite element formulation to identify damage fields: The equilibrium gap method, Internat. J. Numer. Methods Engrg., 61, 2, 189-208 (2004) · Zbl 1075.74641
[9] Roux, S.; Hild, F., Digital image mechanical identification, Exp. Mech., 48, 495-508 (2008)
[10] Ben Azzouna, M.; Périé, J.-N.; Guimard, J.-M.; Hild, F.; Roux, S., On the identification and validation of an anisotropic damage model using full-field measurements, Int. J. Damage Mech., 20, 8, 1130-1150 (2011)
[11] Bui, H. D.; Constantinescu, A.; Maigre, H., Numerical identification of linear cracks in 2D elastodynamics using the instantaneous reciprocity gap, Inverse Problems, 20, 4, 993 (2004) · Zbl 1061.74029
[12] Ladevèze, P.; Reynier, M.; Maya, N., Error on the constitutive relation in dynamics, (Tanaka, Bui; etal., Inverse Problems in Engineering (1994)), 251-256
[13] Feissel, P.; Allix, O., Modified constitutive relation error identification strategy for transient dynamics with corrupted data: The elastic case, Comput. Methods Appl. Mech. Engrg., 196, 1968-1983 (2007) · Zbl 1173.74415
[14] Avril, S.; Bonnet, M.; Bretelle, A.-S.; Grédiac, M.; Hild, F.; Ienny, P.; Latourte, F.; Lemosse, D.; Pagano, S.; Pagnacco, E.; Pierron, F., Identification from measurements of mechanical fields, Exp. Mech., 48, 381-402 (2008)
[15] Grédiac, M.; Hild, F., Full-Field Measurements and Identification in Solid Mechanics (2012), Wiley
[16] Reynier, M., Sur le contrôle de modélisations éléments finis : recalage à partir d’essais dynamiques (1990), Université Pierre et Marie Curie, (Ph.D. thesis)
[17] Deraemaeker, A.; Ladevèze, P.; Romeuf, T., Model validation in the presence of uncertain experimental data, Eng. Comput., 21, 8, 808-833 (2004) · Zbl 1134.65304
[18] Decouvreur, V., Updating acoustic models: a constitutive relation error approach (2008), Université Libre de Bruxelles, (Ph.D. thesis)
[19] Calloch, S.; Dureisseix, D.; Hild, F., Identification de modèles de comportement de matériaux solides : utilisation d’essais et de calculs, Technol. Form., 100, 36-41 (2002)
[20] Nguyen, H. M.; Allix, O.; Feissel, P., A robust identification strategy for rate-dependent models in dynamics, Inverse Problems, 24, 065006 (2008) · Zbl 1387.74052
[21] Banerjee, B.; Walsh, T. F.; Aquino, W.; Bonnet, M., Large scale parameter estimation problems in frequency-domain elastodynamics using an error in constitutive equation functional, Comput. Methods Appl. Mech. Engrg., 253, 60-72 (2012) · Zbl 1297.74052
[22] Florentin, E.; Lubineau, G., Identification of the parameters of an elastic material model using the constitutive equation gap method, Comput. Mech., 46, 521-531 (2010) · Zbl 1358.74058
[23] Ben Azzouna, M.; Feissel, P.; Villon, P., Identification of elastic properties from full-field measurements: a numerical study of the effect of filtering on the identification results, Meas. Sci. Technol., 24, 5, 055603 (2013)
[24] Calvettia, D.; Morigib, S.; Reichelc, L.; Sgallarid, F., Tikhonov regularization and the L-curve for large discrete ill-posed problems, J. Comput. Appl. Math., 123, 423-446 (2000) · Zbl 0977.65030
[25] Morozov, V. A., Methods for Solving Incorrectly Posed Problems (1984), Springer: Springer New York · Zbl 0549.65031
[26] Latourte, F.; Chrysochoos, A.; Pagano, S.; Wattrisse, B., Elastoplastic behavior identification for heterogeneous loadings and materials, Exp. Mech., 48, 435-449 (2008)
[27] Ben Azzouna, M., Identification à partir de mesures de champs. Application de l’erreur en relation de comportement modifiée (2013), Université de Technologie de Compiègne, (Ph.D. thesis)
[28] Bonnet, M.; Burczyski, T.; Nowakowski, M., Sensitivity analysis for shape perturbation of cavity or internal crack using bie and adjoint variable approach, Int. J. Solids Struct., 39, 9, 2365-2385 (2002) · Zbl 1087.74645
[29] Geuzaine, C.; Remacle, J.-F., Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities, Internat. J. Numer. Methods Engrg., 79, 11, 1309-1331 (2009) · Zbl 1176.74181
[30] Zhang, X., Contribution à l’étude de l’apport des coutures sur les performances mécaniques des structures composites cousues (2012), Université de Technologie de Compiègne, (Ph.D. thesis)
[32] Hild, F.; Roux, S., Comparison of local and global approaches to digital image correlation, Exp. Mech., 52, 9, 1503-1519 (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.