Experimental Mechanics

, Volume 54, Issue 7, pp 1189–1204 | Cite as

Determination of Anisotropic Plastic Constitutive Parameters Using the Virtual Fields Method

  • J.-H. Kim
  • F. Barlat
  • F. Pierron
  • M.-G. LeeEmail author


The aim of the present study is to retrieve all the anisotropic plastic constitutive parameters from uniaxial loading. A complex geometry which can provide very heterogeneous stress states in a uniaxial tensile test was chosen for steel sheet specimens. A digital image correlation technique was used for the full-field heterogeneous strain measurement. The orthotropic Hill1948 yield criterion with Swift isotropic hardening was adopted as an elasto-plastic constitutive model. The virtual fields method (VFM) was employed as an inverse analytical tool to determine the constitutive parameters. All the parameters were successfully identified using the VFM by combining two tensile test results obtained in rolling and transverse directions.


Full-field measurements Virtual fields method Plasticity Anisotropy Advanced high strength steel 



The authors appreciate the support by POSCO. This work was supported by the NRF grant funded by the Korea government(MSIP) (No. 2012R1A5A1048294) and by the grants from the Industrial Source Technology Development Program (#10040078) of MKE.


  1. 1.
    Wu PD, Jain M, Savoie J, MacEwen SR, Tuğcu P, Neale KW (2003) Evaluation of anisotropic yield functions for aluminum sheets. Int J Plasticity 19(1):121–138CrossRefGoogle Scholar
  2. 2.
    Banabic D (2010) Sheet metal forming processes: constitutive modelling and numerical simulation. SpringerGoogle Scholar
  3. 3.
    Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc Roy Soc Lond Math Phys Sci 193(1033):281–297CrossRefzbMATHGoogle Scholar
  4. 4.
    Barlat F, Brem JC, Yoon JW, Chung K, Dick RE, Lege DJ, Pourboghrat F, Choi S-H, Chu E (2003) Plane stress yield function for aluminum alloy sheets - part 1: theory. Iny J Plasticity 19(9):1297–1319CrossRefzbMATHGoogle Scholar
  5. 5.
    Grédiac M (2004) The use of full-field measurement methods in composite material characterization: interest and limitations. Compos Part A-Appl S 35(7):751–761CrossRefGoogle Scholar
  6. 6.
    Avril S, Pierron F (2007) General framework for the identification of constitutive parameters from full-field measurements in linear elasticity. Int J Solids Struct 44(14):4978–5002CrossRefzbMATHGoogle Scholar
  7. 7.
    Meuwissen MHH, Oomens CWJ, Baaijens FPT, Petterson R, Janssen JD (1998) Determination of the elasto-plastic properties of aluminium using a mixed numerical–experimental method. J Mater Process Tech 75(1):204–211CrossRefGoogle Scholar
  8. 8.
    Khalfallah A, Bel Hadj Salah H, Dogui A (2002) Anisotropic parameter identification using inhomogeneous tensile test. Eur J Mech A-Solid 21(6):927–942CrossRefzbMATHGoogle Scholar
  9. 9.
    Kajberg J, Lindkvist G (2004) Characterisation of materials subjected to large strains by inverse modelling based on in-plane displacement fields. Int J Solids Struct 41(13):3439–3459CrossRefzbMATHGoogle Scholar
  10. 10.
    Belhabib S, Haddadi H, Gaspérini M, Vacher P (2008) Heterogeneous tensile test on elastoplastic metallic sheets: Comparison between FEM simulations and full-field strain measurements. Int J Mech Sci 50(1):14–21CrossRefzbMATHGoogle Scholar
  11. 11.
    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-Solid 30(3):373–382CrossRefzbMATHGoogle Scholar
  12. 12.
    Güner A, Soyarslan C, Brosius A, Tekkaya AE (2012) Characterization of anisotropy of sheet metals employing inhomogeneous strain fields for Yld2000-2D yield function. Int J Solids Struct 49(25):3517–3527CrossRefGoogle Scholar
  13. 13.
    Lecompte D, Smits A, Sol H, Vantomme J, Van 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
  14. 14.
    Cooreman S, Lecompte D, Sol H, Vantomme J, Debruyne D (2008) Identification of mechanical material behavior through inverse modeling and DIC. Exp Mech 48(4):421–433CrossRefGoogle Scholar
  15. 15.
    Teaca M, Charpentier I, Martiny M, Ferron G (2010) Identification of sheet metal plastic anisotropy using heterogeneous biaxial tensile tests. Int J Mech Sci 52(4):572–580CrossRefGoogle Scholar
  16. 16.
    Pottier T, Vacher P, Toussaint F, Louche H, Coudert T (2012) Out-of-plane testing procedure for inverse identification purpose: application in sheet metal plasticity. Exp Mech 52(7):951–963CrossRefGoogle Scholar
  17. 17.
    Rastogi PK (ed) (2000) Photomechanics, topics in applied physics, vol 77. Springer, Berlin (Germany)Google Scholar
  18. 18.
    Grédiac M, Toussaint E, Pierron F (2002) Special virtual fields for the direct determination of material parameters with the virtual fields method. 1–Principle and definition. Int J Solids Struct 39(10):2691–2705CrossRefzbMATHGoogle Scholar
  19. 19.
    Grédiac M, Pierron F (2006) Applying the virtual fields method to the identification of elasto-plastic constitutive parameters. Iny J Plasticity 22(4):602–627CrossRefzbMATHGoogle Scholar
  20. 20.
    Pannier Y, Avril S, Rotinat R, Pierron F (2006) Identification of elasto-plastic constitutive parameters from statically undetermined tests using the virtual fields method. Exp Mech 46(6):735–755CrossRefGoogle Scholar
  21. 21.
    Avril S, Pierron F, Pannier Y, Rotinat R (2008) 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
  22. 22.
    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(24):3829–3842CrossRefGoogle Scholar
  23. 23.
    Pierron F, Avril S, The Tran V (2010) Extension of the virtual fields method to elasto-plastic material identification with cyclic loads and kinematic hardening. Int J Solids Struct 47(22):2993–3010CrossRefzbMATHGoogle Scholar
  24. 24.
    Rossi M, Pierron F (2012) Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields. Comput Mech 49(1):53–71CrossRefzbMATHGoogle Scholar
  25. 25.
    WorldAutoSteel (2009) Advanced high strength steel (AHSS) application guidelines version 4.1.
  26. 26.
    Sutton MA, Orteu J-J, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer Publishing Company, IncorporatedGoogle Scholar
  27. 27.
    Avril S, Badel P, Duprey A (2010) Anisotropic and hyperelastic identification of in vitro human arteries from full-field optical measurements. J Biomech 43(15):2978–2985CrossRefGoogle Scholar
  28. 28.
    Kim J-H, Avril S, Duprey A, Favre J-P (2012) Experimental characterization of rupture in human aortic aneurysms using a full-field measurement technique. Biomech Model Mechan 11(6):841–853CrossRefGoogle Scholar
  29. 29.
    Dunne F, Petrinic N (2005) Introduction to computational plasticity. Oxford University Press, New YorkzbMATHGoogle Scholar
  30. 30.
    Avril S, Feissel P, Pierron F, Villon P (2010) Comparison of two approaches for differentiating full-field data in solid mechanics. Meas Sci Technol 21(1):015703CrossRefGoogle Scholar
  31. 31.
    Feng Z, Rowlands RE (1991) Smoothing finite-element and experimental hybrid technique for stress analyzing composites. Comput Struct 39(6):631–639CrossRefGoogle Scholar
  32. 32.
    Lay DC (2003) Linear algebra and its applications, Addison WesesleyGoogle Scholar
  33. 33.
    Bower AF (2011) Applied mechanics of solids, CRC pressGoogle Scholar
  34. 34.
    Chen W-F (1994) Constitutive equations for engineering materials, Vol. 2 - plasticity and modeling. ElsevierGoogle Scholar
  35. 35.
    Pierron F, Grédiac M (2012) The virtual fields method. Springer, New-YorkCrossRefGoogle Scholar
  36. 36.
    Sutton MA, Deng X, Liu J, Yang L (1996) Determination of elastic-plastic stresses and strains from measured surface strain data. Exp Mech 36(2):99–112CrossRefGoogle Scholar
  37. 37.
    Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM J Optimiz 9(1):112–147CrossRefzbMATHMathSciNetGoogle Scholar
  38. 38.
    Avril S, Feissel P, Pierron F, Villon P (2008) Estimation of the strain field from full-field displacement noisy data: comparing finite elements global least squares and polynomial diffuse approximation. Eur J Comput Mech 17(5-7):857–868zbMATHGoogle Scholar
  39. 39.
    Cleveland WS, Loader C (1996) Smoothing by local regression: Principles and methods. In: Statistical theory and computational aspects of smoothing, pages 10–49. SpringerGoogle Scholar
  40. 40.
    Nayroles B, Touzot G, Villon P (1991) 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 313(2):133–138zbMATHGoogle Scholar
  41. 41.
    Le Louëdec G, Pierron F, Sutton MA, Reynolds AP (2013) Identification of the local elasto-plastic behavior of FSW welds using the virtual fields method. Exp Mech 53(5):849–859CrossRefGoogle Scholar
  42. 42.
    Rossi M, Pierron F (2012) On the use of simulated experiments in designing tests for material characterization from full-field measurements. Int J Solids Struct 49(3):420–435CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2014

Authors and Affiliations

  1. 1.GIFT, Pohang University of Science and TechnologyPohangRepublic of Korea
  2. 2.Faculty of Engineering and the EnvironmentUniversity of SouthamptonSouthamptonUK

Personalised recommendations