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Introduction, Main Equations and Notations

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The Virtual Fields Method

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Abstract

After a general introduction, the objective of this chapter is to present some notations used in this book, to recall the main equations involved in mechanics of deformable solids and to introduce the problem that is tackled in this book: retrieving constitutive parameters by processing kinematical full-field measurements. This problem is also compared with the classical problem to be solved in mechanics of deformable solids: calculating the displacement, strain and stress distributions within a solid subjected to a given load.

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References

  1. Grédiac M (1989) Principle of virtual work and identification. Comptes rendus de l’Académie des Sciences, série II 309(1):1–5

    MATH  Google Scholar 

  2. Pierron F, Alloba E, Surrel Y, Vautrin A (1998) Whole-field assessment of the effects of boundary conditions on the strain field in off-axis tensile testing of unidirectional composite. Compos Sci Technol 58(12):1939–1947

    Article  Google Scholar 

  3. ASTM D5379 / D5379M 05. Standard test method for shear properties of composite materials by the V-notched beam method. ASTM International, West Conshohocken, PA, 2003, 2005. DOI: 10.1520/D5379_D5379M-05

    Google Scholar 

  4. Chrysochoos A, Louche H (2000) An infrared image processing to analyse the calorific effects accompanying strain localisation. Int J Eng Sci 38(16):1759–1788

    Article  Google Scholar 

  5. Saai A, Louche H, Tabourot L, Chang HJ (2010) Experimental and numerical study of the thermo-mechanical behavior of Al bi-crystal in tension using full-field measurements and micromechanical modeling. Mech Mater 42:275–292

    Article  Google Scholar 

  6. Badulescu C, Grédiac M, Haddadi H, Mathias J-D, Balandraud X, Tran H-S (2011) Applying the grid method and infrared thermography to investigate plastic deformation in aluminium multicrystal. Mech Mater 43(11):36–53

    Article  Google Scholar 

  7. Daly S, Rittel D, Bhattacharya K, Ravichandran G (2009) Large deformation of nitinol under shear dominant loading. Exp Mech 49:225–233

    Article  Google Scholar 

  8. Delpueyo D, Grédiac M, Balandraud X, Badulescu C (2012) Investigation of martensitic microstructures in a monocrystalline Cu-Al-Be shape-memory alloy with the grid method and infrared thermography. Mech Mater 45:34–51

    Article  Google Scholar 

  9. Carlsson LA, Pipes RB (1997) Experimental characterization of advanced composite materials. Technomic Publishing Company, Lancaster PA, USA

    Google Scholar 

  10. Kavanagh KT, Clough RW (1971) Finite element applications in the characterization of elastic solids. Int J Solids Struct 7(1):11–23

    Article  MATH  Google Scholar 

  11. Hendricks MAN (1991) Identification of the mechanical properties of solid materials. Doctoral dissertation, Eindhoven University of Technology

    Google Scholar 

  12. LeMagorou L, Bos F, Rouger F (2002) Identification of constitutive laws for wood-based panels by means of an inverse method. Compos Sci Technol 62(4):591–596

    Article  Google Scholar 

  13. 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 Technol 75(1–3):204–211

    Article  Google Scholar 

  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):421–433

    Article  Google Scholar 

  15. Kajberg J, Wikman B (2007) Viscoplastic parameter estimation by high strain-rate experiments and inverse modelling – speckle measurements and high-speed photography. Int J Solids Struct 44:145–164

    Article  Google Scholar 

  16. Genovese K, Lamberti L, Pappalettere C (2006) Mechanical characterization of hyperelastic materials with fringe projection and optimization techniques. Opt Lasers Eng 44:423–442

    Article  Google Scholar 

  17. Ladevèze P, Leguillon D (1983) Error estimate procedure in the finite element method and applications. SIAM J Numer Anal 20:485–509

    Article  MathSciNet  MATH  Google Scholar 

  18. Latourte F, Chrysochoos A, Pagano S, Wattrisse B (2008) Elastoplastic behavior identification for heterogeneous loadings and materials. Exp Mech 48:435–449

    Article  Google Scholar 

  19. Avril S, Bonnet M, Bretelle AS, Grédiac M, Hild F, Ienny P, Latourte F, Lemosse D, Pagano S, Pagnacco S, Pierron F (2008) Overview of identification methods of mechanical parameters based on full-field measurements. Exp Mech 48(4):381–402

    Article  Google Scholar 

  20. Ikehata M (1993) An inverse problem for the plate in the Love-Kirchhoff theory. SIAM J Numer Anal 53:942–970

    MathSciNet  MATH  Google Scholar 

  21. Dym L, Shames H (1973) Solid mechanics: a variational approach. McGraw-Hill, New York

    Google Scholar 

  22. Claire D, Hild F, Roux S (2004) A finite element formulation to identify damage fields: The equilibrium gap method. Int J Numer Meth Eng 61(2):189–208

    Article  MATH  Google Scholar 

  23. Grédiac M, Pierron F, Avril S, Toussaint E (2006) The Virtual Fields Method for extracting constitutive parameters from full-field measurements: a review. Strain 42:233–253

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Ecole Nationale Superieure d’Arts et Métiers (ENSAM), Rue Saint Dominique, 51006, Châlons en Champagne, France

    Prof. Fabrice Pierron

  2. Institut Pascal, Université Clermont-Ferrand II and CNRS, Campus de Clermont-Ferrand les Cézeaux, 63175, Aubière Cedex, France

    Michel Grédiac

Authors
  1. Prof. Fabrice Pierron
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  2. Michel Grédiac
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Pierron, F., Grédiac, M. (2012). Introduction, Main Equations and Notations. In: The Virtual Fields Method. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1824-5_1

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  • DOI: https://doi.org/10.1007/978-1-4614-1824-5_1

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-1823-8

  • Online ISBN: 978-1-4614-1824-5

  • eBook Packages: EngineeringEngineering (R0)

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