Identification from measurements of mechanical fields by finite element model updating strategies
DOI:
https://doi.org/10.13052/EJCM.18.353-376Keywords:
finite elements, parameter identification, inverse problems, full-field measurementsAbstract
Inverse problem resolution methods are widely used in the determination of material behaviour. The optimisation of the parameters, as inputs into a well-defined system, is obtained from observed outputs such as kinematic field measurements. The aim of this paper is to summarize the research concerning one inverse method, Finite Element Modelling Updating, based on the use of these field measurements. This method is based on a combination of three components, described in the following three sections. First we present the optical field measurements applied to multi-axially loaded objects, together with their performances. Then we outline the use of Finite Element Modelling for achieving a correlation between numerical fields and their experimental counterparts. Finally we describe the identification process, together with cost functions, minimisation procedure and model validation analysis.
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References
Bathe K., Finite Element Procedures, Prentice Hall, 1996.
Bruno L., Furgiuele F. M., Pagnotta L., Poggialini A., Stigliano G., “ Elastic Characterization
of Orthotropic Plates of Any Shape via Static Testing”, International journal of Solids and
Structures, In Press.
Bruno L., Furgiuele F., Pagnotta L., Poggialini A., “ A full-field approach for the elastic characterization
of anisotropic materials”, Optics and Lasers in Engineering, vol. 37, p. 417-431,
Bui H. D., Constantinescu A., Maigre H., “ Numerical identification of linear crack in 2D
elastodynamics using the instantaneous reciprocity gap”, Inverse Problems, vol. 20, p. 993,
Burczynski T., “ Evolutionary Computation in Mechanics”, , IACM Expressions, Bull. for The
Int. Assoc. for Comp. Mech., October, 2003. p. 4-9.
Burczynski T., Ku´s W., Dugosz A., Orantek P., “ Optimization and defect identification using
distributed evolutionary algorithms”, Engineering Applications of Artificial Intelligence,
vol. 17, p. 337-344, June, 2004.
Cardenas-Garcia J., Preidikman S., “ Solution of the moire hole drilling method using a finiteelement-
method-based approach”, International Journal of Solids and Structures, vol. 43,
n° 22-23, p. 6751-6766, November, 2006.
Claire D., Hild F., Roux S., “ A finite element formulation to identify damage fields: the equilibrium
gap method.”, International Journal for Numerical Methods in Engineering, vol. 2,
p. 189-208, 2004.
Collins J., Hart G., Kennedy B., “ Statistical identification of structures”, AIAA Journal, vol.
, n° 2, p. 185-190, 1974.
Cottin N., Felgenhauer H., Natke H., “ On the parameter identification of elastomechanical
systems using input and ouput residuals”, Ingenieur-Archiv, vol. 54, p. 378-387, 1984.
Cugnoni J., Botsis J., Sivasubramaniam V., Janczak-Rusch J., “ Experimental and numerical
studies on size and constraining effects in lead-free solder joints”, Fatigue Fract. Engng.
Mater. Struct., vol. 30, n° 2, p. 387-399, 2006.
Cugnoni J., Gmur T., Schorderet A., “ Inverse method based on modal analysis for characterizing
the constitutive properties of thick composite plates”, Computers and Structures, 2007.
In Press.
Dascotte E., “ Model Updating for Structural Dynamics: Past, Present and Future Outlook”,
International Conference on Engineering Dynamics (ICED), Carvoeiro, Algarve, Portugal,
April 16-18, 2007. cdrom, 12 pages.
Forestier R., Massoni E., Chastel Y., “ Estimation of constitutive parameters using an inverse
method coupled to a 3D finite element software”, Journal of Materials Processing Technology,
vol. 125-126, p. 594-601, 2002.
Friswell M., Mottershead J., Finite element Model Updating in Structural Dynamics, Kluwer
Academic Publishers, 1995.
Genovese K., Lamberti L., C. P., “ Mechanical characterization of hyperelastic materials with
fringe projection and optimization techniques”, Optics and Lasers in Engineering, vol. 44,
n° 5, p. 423-442, May, 2006a.
Genovese K., Lamberti L., Pappalettere C., “ Identification of mechanical properties of bovine
bones by combining PS-ESPI and global optimization”, Speckle06, Nîmes, p. 634108.1-
7, 2006b.
Geymonat G., Pagano S., “ Identification of mechanical properties by displacement field measurement:
a variational approach”, Meccanica, vol. 38, p. 535-545, 2003.
Gill P. E., Murray W., Wright M. H., Practical Optimization, Elsevier Academic Press, 84
Theobald’s Road, London WC1X 8RR, UK, 2006.
Giton M., Caro-Bretelle A. S., Ienny P., “ Hyperelastic Behaviour Identification by a Forward
Problem Resolution: Application to a Tear Test of a Silicone-Rubber”, Strain, vol. 42, n° 4,
p. 291-297, Nov., 2006.
Grédiac M., “ Principe des travaux virtuels et identification”, Compte Rendu de l’Academie des
Sciences, vol. 309, p. 1-5, 1989.
Hendricks M., Identification of the mechanical properties of solid materials, PhD thesis, Eindhoven
University of Technology, 1991.
Hoc T., Gélébart L., Crépin J., Zaoui A., “ A procedure for identifying the plastic behavior of
single crystals from the local response of polycrystals”, Acta Materialia, vol. 51, p. 5477-
, 2003.
Kajberg J., Lindkvist G., “ Characterization of materials subjected to large strains by inverse
modelling based on in-plane displacement fields”, International Journal of Solids and
Structures, vol. 41, p. 3439-3459, 2004a.
Kajberg J., Sundin K., Melin L., Ståhle P., “ High strain rate tensile and viscoplastic parameter
identification using micoscopic high-speed photography”, International Journal of Plasticity,
vol. 20, p. 561-575, 2004b.
Kavanagh K., Clough R., “ Finite element applications in the characterization of elastic solids”,
International Journal of Solids and Structures, vol. 7, p. 11-23, 1971.
Latourte F., Chrysochoos A., Pagano S., Watrisse B., “ Elastoplastic behavior identification
for heterogeneous loading and materials”, Experimental Mechanics, Special Issue: Inverse
Problems, In Press.
Lecompte D., Smits A., Bossuyt S., Sol H., Vantomme J., Van Hemelrijck D., Habraken A.,
“ Quality assessment of Speckle Patterns for Digital Image Correlation”, Optics and Lasers
in Engineering, vol. 44, p. 1132-1145, November, 2006.
Lecompte D., Smits A., Sol H., Vantomme J., Van Hemelrijck D., “ Mixed numericalexperimental
technique for orthotropic parameter identification using biaxial tensile tests
on cruciform specimens”, International Journal of Solids and Structures, vol. 44, n° 5,
p. 1643-1656, March, 2007.
Le Magorou L., Bos F., Rouger F., “ Identification of constitutive laws for wood-based panels by
means of an inverse method”, Composite Science and Technology, vol. 62(4), p. 591-596,
Lemosse D., Pagnacco E., “ Identification de propriétés matériaux à partir de mesures de
champs de déplacements statiques et en présence d’une distribution d’efforts inconnue”,
Colloque National en Calcul des Structures de Giens, Giens, 2003. cdrom, 15 p.
Linet V., Lepage A., Sol A., Bohineust X., “ Validation and Improvement of Body Panels Fe
Models From 3d-Shape and Vibration Measurements By Optical Methods”, SAE Noise &
Vibration Conference & Exposition, n° 2001-01-1536, Grand Traverse, MI, USA, April,
cdrom, 8 p.
Mahnken R., “ Aspects on the finite-element implementation of the Gurson model including
parameter identification”, International Journal of Plasticity, vol. 15, n° 3-4, p. 1111-1137,
September, 1999.
Mahnken R., “ A comprehensive study of a multiplicative elastoplasticity model coupled to
damage including parameter identification”, Computers and Structures, vol. 74, n° 3-4,
p. 179-200, September, 2000.
Mahnken R., Stein E., “ A unified approach for parameter identification of inelastic material
models in the frame of the finite element method”, Computer Methods in Applied Mechanics
and Engineering, vol. 136, n° 3-4, p. 225-258, September, 1996.
Mahnken R., Stein E., “ Parameter identification for finite deformation elasto-plasticity in principal
directions”, Computer Methods in Applied Mechanics and Engineering, vol. 147, n° 3-
, p. 17-39, September, 1997.
Meijer R., Douven L., Oomens C., “ Characterisation of anisotropic and non-linear behaviour
of human skin in-vivo”, Comput. Methods in Biomechanics and Biomedical Engineering,
vol. 1, p. 13-27, 1997.
Meuwissen M., An inverse method for the mechanical characterisation of metals, PhD thesis,
TU Eindhoven, 1998.
Meuwissen M. H. H., Oomens C.W. J., Baaijens F. P. T., Petterson R., Janssen J. D., “ Determination
of the elasto-plastic properties of aluminium using a mixed numerical-experimental
method”, Journal of Materials Processing Technology, vol. 75, n° 1-3, p. 204-211, March,
Michot S., Cogan S., Foltête E., Raynaud J., Piranda J., “ Apports des techniques de mesures
holographiques dans le domaine de la localisation de défauts en dynamique des structures”,
ème Colloque d’Analyse Vibratoire Expérimentale, Blois, 13-14 Novembre, 2001. cdrom,
pages.
Molimard J., Le Riche R., Vautrin A., Lee J., “ Identification of the four orthotropic plate
stiffnesses using a single open-hole tensile test”, Journal of SEM, vol. 45, n° 5, p. 404-411,
Montay G., Fran¸cois M., Tourneix M., Guelorget B., Vial-Edwards C., Lira I., “ Strain and
strain rate measurement during the bulge test by elestronic speckle pattern interferometry”,
Journal of Materials Processing Technology, vol. 184, n° 1-3, p. 428-435, April, 2007.
Moreau A., Pagnacco E., Borza D., Lemosse D., “ An evaluation of different mixed experimental/
numerical procedures using FRF for the identification of viscoelastic materials”,
International Conference on Noise and Vibration Engineering, ISMA 2006, Leuven, 2006.
cdrom, 15 p.
Oomens C., Van Ratingen M., Janssen J., Kok J., Hendriks M., “ A numerical-experimental
for a mechanical characterization of biological materials”, Journal of Biomechanics, vol.
(4/5), p. 617-621, 1993.
Padmanabhan S., Hubner J., Kumar A., Ifju P., “ Load and Boundary Conditions Calibration
using Full-Field Strain Measurement”, Experimental Mechanics, vol. 46, n° 5, p. 569-578,
Pagano S., “ A review of identification methods based on full fields measurements”, Photomechanics
, Int. conf. on full-field measurements techniques and their applications in
experimental solid mechanics, 2006.
Pagnacco E., Lemosse D., Borza D., “ A coupled FE based inverse strategy from displacement
field measurement subject to an unknown distribution of forces”, Photomechanics 2006,
Int. conf. on full-field measurements techniques and their applications in experimental solid
mechanics, Clermont-Ferrand, France, July 10-12, 2006.
Pagnacco E., Lemosse D., Hild F., Amiot F., “ Inverse strategy from displacement field measurement
and distributed forces using FEA”, SEM Annual Conference and Exposition on
Experimental and Applied Mechanics, June 07-09, 2005. cdrom, 7 p.
Pagnacco E., Moreau A., Lemosse D., “ Inverse strategies for the identification of elastic and
viscoelastic material parameters using full-field measurements”, Materials Science and Engineering:
A, vol. 452-453, p. 737-745, April, 2007.
Piranda J., Foltête E., Raynaud J. L., Michot S., Lepage A., Linet V., “ New trends in modal
analysis and model updating using electronic speckle pattern interferometry”, in P. Kurka,
A. Fleury (eds), X Diname, Ubatuba - SP - Brazil, p. 107-117, 10-14th March, 2003.
Silva G., Le Riche R., Molimard J., Vautrin A., “ Exact and Efficient Interpolation using Finite
Element Shape Functions”, European Journal of Computational Mechanicsp. to appear,
October, 2007.
Simon D., Golinval J. C., “ Use of whole-field displacement measurements for model updating
of blades”, IMAC XXI, n° 131, Feb. 3-6, 2003. cdrom, 10 p.
Surell Y., “ Les techniques optiques de mesure de champs: essai de classification”, I2M, vol.
/3-4, p. 11-42, 2004.
Van Ratingen M., Mechanical identification of inhomogeneous solids: a mixed numerical experimental
approach, PhD thesis, Eindhoven University of Technology, 1994.
