Experimental Mechanics

, Volume 55, Issue 1, pp 105–119 | Cite as

Estimation of Elastoplastic Parameters via Weighted FEMU and Integrated-DIC



DIC-based identification of the constitutive parameters of an elastoplastic law is addressed both from a general viewpoint, and applied to the particular case of dog-bone sample made of commercially pure titanium and subjected to tensile loading. A two-step procedure (Digital Image Correlation — DIC — followed by weighted Finite Element Method Updating — FEMU) is first presented. These two steps can be merged into a single-step procedure (i.e., Integrated-DIC or I-DIC). In both cases, the elastoplastic computations are performed with a commercial code (i.e., non-intrusive identification). When the suited weighting of FEMU is taken into account, which is based on DIC-processed image noise, both I-DIC and FEMU methods provide similar results. It is shown that the addressed experimental case requires the use of static (load) information to get precise estimates of the sought parameters.


Covariance Digital image correlation Identification Integrated approach Ramberg-Osgood model 



It is a pleasure to acknowledge the support of Région Ile de France (“FRESCORT” and “DICCIT” projects).


  1. 1.
    Allix O, Feissel P, Nguyen H (2005) Identification Strategy in the Presence of Corrupted Measurements. Eng Comput 22(5-6):487–504CrossRefMATHGoogle Scholar
  2. 2.
    Amiot F, Hild F, Roger J (2007) Identification of Elastic Property and Loading Fields from Full-Field Displacement Measurements. Int. J. Solids Struct 44:2863–2887CrossRefMATHGoogle Scholar
  3. 3.
    Andrieux S, Abda A B, Bui H (1999) Reciprocity Principle and Crack Identification. Inv Probl 15:59–65CrossRefMATHGoogle Scholar
  4. 4.
    Andrieux S, Bui H, Constantinescu A (2012) Reciprocity Gap Method. In: Grédiac M, Hild F (eds) Full-Field Measurements and Identification in Solid Mechanics. ISTE/Wiley, London, pp 363–378CrossRefGoogle Scholar
  5. 5.
    Avril S, Grédiac M, Pierron F (2004) Sensitivity of the Virtual Fields Method to Noisy Data. Comput Mech 34(6):439–452CrossRefMATHGoogle Scholar
  6. 6.
    Avril S, Bonnet M, Bretelle A, Grédiac M, Hild F, Ienny P, Latourte F, Lemosse D, Pagano S, Pagnacco E, Pierron F (2008a) Overview of Identification Methods of Mechanical Parameters Based on Full-Field Measurements. Exp Mech 48(4):381–402CrossRefGoogle Scholar
  7. 7.
    Avril S, Pierron F, Pannier Y, Rotinat R (2008b) Stress Reconstruction and Constitutive Parameter Identification in Plane-Stress Elasto-Plastic problems Using Surface Measurements of Deformation Fields. Exp Mech 48(4):403–419CrossRefGoogle Scholar
  8. 8.
    Besnard G, Hild F, Roux S (2006) finite-element Displacement Fields Analysis from Digital Images: Application to Portevin-le Chatelier Bands. Exp Mech 46:789-803Google Scholar
  9. 9.
    Besnard G, Leclerc H, Roux S, Hild F (2012) Analysis of Image Series through Digital Image Correlation. J. Strain Anal 47:214–228CrossRefGoogle Scholar
  10. 10.
    Bonnet M (2012) Introduction to Identification Methods. In: Grédiac M, Hild F (eds) Full-Field Measurements and Identification in Solid Mechanics. Wiley, London, pp 223–246CrossRefGoogle Scholar
  11. 11.
    Bonnet M, Constantinescu A (2005) Inverse Problems in Elasticity. Inv Probl 21:R1–R50CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Bouterf A, Roux S, Hild F, Adrien J, Maire E (2014) Digital Volume Correlation Applied to X-ray Tomography Images from Spherical Indentation Tests on Lightweight Gypsum. Submitted for PublicationGoogle Scholar
  13. 13.
    Boyer R, Welsch G, Collings E W(eds) (1994) Materials Properties Handbook: titanium Alloys, ASM InternationalGoogle Scholar
  14. 14.
    Broggiato G (2004) Adaptive Image Correlation Technique for Full-Field Strain Measurement. In: Pappalettere C (ed) 12th Int Conf Exp Mech McGraw Hill, Bari, pp 420–421Google Scholar
  15. 15.
    Calloch S, Dureisseix D, Hild F (2002) Identification de modèles de comportement de matériaux solides : Utilisation d’essais et de CalculsTechnol Form 100:36–41Google Scholar
  16. 16.
    Claire D, Hild F, Roux S (2004) A finite element formulation to identify damage fields: the equilibrium gap method. Int J Num Meth Engng 61(2):189–208CrossRefMATHGoogle Scholar
  17. 17.
    Collins J, Hart G, Kennedy B (1974) Statistical identification of structures. AIAA J 12(2):185–190CrossRefMATHGoogle Scholar
  18. 18.
    Conrad H, Jones R (1970) The Science, Technology and Application of Titanium. Pergamon Press, OxfordGoogle Scholar
  19. 19.
    Cooreman S, Lecompte D, Sol H, Vantomme J, Debruyne D (2007) Elasto-plastic material parameter identification by inverse methods: calculation of the sensitivity matrix. Int J Solids Struct 44(13):4329–4341CrossRefMATHGoogle Scholar
  20. 20.
    Fagerholt E, Børvik T, Hopperstad OS (2013) Measuring discontinuous displacement fields in cracked specimens using digital image correlation with mesh adaptation and crack-path optimization. Opt Lasers Eng 51(3):299–310CrossRefGoogle Scholar
  21. 21.
    Feissel P, Allix O (2007) Modified constitutive relation error identification strategy for transient dynamics with corrupted data: the elastic case. Comput Meth Appl Mech Eng 196(13/16):1968–1983CrossRefMATHGoogle Scholar
  22. 22.
    Geymonat G, Hild F, Pagano S (2002) Identification of elastic parameters by displacement field measurement. C R Mécanique 330:403–408CrossRefMATHGoogle Scholar
  23. 23.
    Gras R, Leclerc H, Roux S, Otin S, Schneider J, Périé J (2013b) Identification of the out-of-plane shear modulus of a 3d woven composite. Exp Mech 53:719–730CrossRefGoogle Scholar
  24. 24.
    Gras R, Leclerc H, Hild F, Roux S, Schneider J (2013) Identification of a set of macroscopic elastic parameters in a 3d woven composite: uncertainty analysis and regularization. Int J Solids Struct. doi: 10.1016/j.ijsolstr.2013.12.023
  25. 25.
    Grédiac M (1989) Principe des travaux virtuels et identification. C R Acad Sci Paris 309 (Série II):1–5MATHGoogle Scholar
  26. 26.
    Grédiac M, Hild F(eds) (2012) Full-Field Measurements and Identification in Solid Mechanics, ISTE/Wiley, LondonGoogle Scholar
  27. 27.
    Hamam R, Hild F, Roux S (2007) Stress intensity factor gauging by digital image correlation: application in cyclic fatigue. Strain 43:181–192CrossRefGoogle Scholar
  28. 28.
    Héripré E, Dexet M, Crépin J, Gélébart L, Roos A, Bornert M, Caldemaison D (2007) Coupling between experimental measurements and polycrystal finite element calculations for micromechanical study of metallic materials. Int J Plast 23(9):1512–1539CrossRefMATHGoogle Scholar
  29. 29.
    Hermez F, Farhat C (1993) Updating finite element dynamic models using element-by-element sensitivity methodology. AIAA J 31(9):1702–1711CrossRefGoogle Scholar
  30. 30.
    Hild F, Roux S (2006) Digital image correlation: from measurement to identification of elastic properties - A revision. Strain 42:69–80CrossRefGoogle Scholar
  31. 31.
    Hild F, Roux S (2012a) Comparison of local and global approaches to digital image correlation. Exp Mech 52(9):1503–1519CrossRefGoogle Scholar
  32. 32.
    Hild F, Roux S (2012b) Digital Image Correlation. In: Rastogi P, Hack E (eds) (2012) Optical Methods for Solid Mechanics. A Full-Field Approach. Wiley-VCH, Weinheim, pp 183–228Google Scholar
  33. 33.
    Kavanagh K (1972) Extension of classical experimental techniques for characterizing the composite-material behavior. Exp Mech 12(1):50–56CrossRefGoogle Scholar
  34. 34.
    Kavanagh K, Clough R (1971) Finite element applications in the characterization of elastic solids. Int J Solids Struct 7:11–23CrossRefMATHGoogle Scholar
  35. 35.
    Kim J-H, Serpantié A, Barlat F, Pierron F, Lee M-G (2013) Characterization of the post-necking strain hardening behavior using the virtual fields method. Int J Solids Struct 50:3829–3842CrossRefGoogle Scholar
  36. 36.
    Leclerc H, Périé J, Roux S, Hild F (2009) Integrated digital image correlation for the identification of mechanical properties, LNCS, vol 5496. Springer, Berlin, pp 161–171Google Scholar
  37. 37.
    Lecompte D, Smits A, Sol H, Vantomme J, Hemelrijck D (2007) Mixed numerical-experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens. Int J Solids Struct 44(5):1643–1656CrossRefGoogle Scholar
  38. 38.
    Mathieu F, Hild F, Roux S (2012) Identification of a crack propagation law by digital image correlation. Int J Fat 36:146–154CrossRefGoogle Scholar
  39. 39.
    Mathieu F, Aimedieu P, Guimard J, Hild F (2013a) Identication of interlaminar fracture properties of a composite laminate using local full-field kinematic measurements and finite element simulations. Comp Part A 49:203–213CrossRefGoogle Scholar
  40. 40.
    Mathieu F, Hild F, Roux S (2013b) Image-based identification procedure of a crack propagation law. Eng Fract Mech 103:48–59CrossRefGoogle Scholar
  41. 41.
    Passieux J C, Périé J N (2012) Digital image correlation using proper generalized decomposition: PGD-DIC. Int J Num Meth Eng 92:531–550CrossRefGoogle Scholar
  42. 42.
    Pagnacco E, Caro-Bretelle A, Ienny P (2012) Parameter Identification from Mechanical Field Measurements using Finite Element Model Updating Strategies. In: Grédiac M, Hild F (eds) (2012) Full-Field Measurements and Identification in Solid Mechanics. ISTE/Wiley, London, pp 247–274CrossRefGoogle Scholar
  43. 43.
    Pierron F, Grédiac M (2012) The Virtual Fields Method. SpringerGoogle Scholar
  44. 44.
    Pottier T, Toussaint F, Vacher P (2011) Contribution of heterogeneous strain field measurements and boundary conditions modelling in inverse identification of material parameters. Eur J Mech A/Solids 30(3):373–382CrossRefMATHGoogle Scholar
  45. 45.
    Ramberg W, Osgood W R (1943) Description of stress-strain curves by three parameters. Tech rep., National Advisory Committee For Aeronautics, Washington DC (USA)Google Scholar
  46. 46.
    Réthoré J (2010) A fully integrated noise robust strategy for the identification of constitutive laws from digital images. Int J Num Meth Eng 84(6):631–660CrossRefMATHGoogle Scholar
  47. 47.
    Roux S, Hild F (2006) Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches. Int J Fract 140(1-4):141–157CrossRefMATHGoogle Scholar
  48. 48.
    Roux S, Hild F (2008) Digital image mechanical identification (DIMI). Exp Mech 48(4):495–508CrossRefGoogle Scholar
  49. 49.
    Simoncelli E P (1999) Bayesian Multi-Scale Differential Optical Flow. In: Jähne B, Haussecker H, Geissler P (eds) Handbook of Computer Vision and Applications, vol 2. Academic Press, pp 297–422Google Scholar
  50. 50.
    Simulia (2009) Abaqus Analysis User’s Manual, 19.1.1. Inelastic behavior. Dassault Systèmes, Providence, RI (USA)Google Scholar
  51. 51.
    Sun Y, Pang J, Wong C, Su F (2005) Finite-element formulation for a digital image correlation method. Appl Optics 44(34):7357–7363CrossRefGoogle Scholar
  52. 52.
    Sutton M, Orteu J, Schreier H (2009) Image correlation for shape, motion and deformation measurements: Basic Concepts, Theory and Applications. Springer, New YorkGoogle Scholar
  53. 53.
    Tarigopula V, Hopperstad O, Langseth M, Clausen A, Hild F (2008a) A study of localisation in dual phase high-strength steels under dynamic loading using digital image correlation and fe analysis. Int J Solids Struct 45(2):601–619CrossRefMATHGoogle Scholar
  54. 54.
    Tarigopula V, Hopperstad O, Langseth M, Clausen A, Hild F, Lademo O, Eriksson M (2008b) A study of large plastic deformations in dual phase steel using digital image correlation and fe analysis. Exp Mech 48(2):181–196CrossRefGoogle Scholar
  55. 55.
    Tomicevic Z, Hild F, Roux S (2013) Mechanics-aided digital image correlation. J Strain Anal 48:330–343CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2014

Authors and Affiliations

  1. 1.Laboratoire de Mécanique et Technologie (LMT-Cachan)ENS Cachan CNRS PRES UniverSud ParisCachan CedexFrance

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