The virtual fields method: Extracting constitutive mechanical parameters from full-field deformation measurements

The Virtual Fields Method: Extracting Constitutive Mechanical Parameters from Full-field Deformation Measurements

Volumn 9781461418245, Issue , 2012, Pages 1-517

  Pierron, Fabrice ^a   Grediac, Michel ^b  

^a ARTS ET MÉTIERS PARISTECH   (France)

^b UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMATERIALS; DEFORMATION; MATLAB; STRAIN RATE;

FIELD DEFORMATIONS; FULL-FIELD MEASUREMENT; GENERAL SITUATION; HIGH STRAIN RATES; MATLAB PROGRAM; MECHANICAL PARAMETERS; VIRTUAL FIELDS METHOD;

PARAMETER ESTIMATION;

EID: 84949176955     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4614-1824-5     Document Type: Book

References (182)

1. Grédiac M(1989) Principle of virtual work and identification. Comptes rendus de l'Académie des Sciences, série II 309(1):1-5
2. Grédiac M, Vautrin A (1990) A new method for determination of bending rigidities of thin anisotropic plates. J Appl Mech 57:964-968. Transactions of the American Society of Mechanical Engineers
3. Grédiac M, Vautrin A (1993) Mechanical characterization of anisotropic plates: experiments and results. Eur J Mech/A Solids 12(6):819-838
4. Grédiac M, Pierron F, Vautrin A (1994) The Iosipescu in-plane shear test applied to composites: a new approach based on displacement field processing. Compos Sci Technol 51(3):409-417
5. Grédiac M, Fournier N, Paris P-A, Surrel Y (1998) Direct identification of elastic constants of anisotropic plates by modal analysis: experiments and results. J Sound Vibration 210(5):645-659
6. Surrel Y, Fournier N, Grédiac M, Paris P-A (1999) Phase-stepped deflectometry applied to shape measurement of bent plates. Exp Mech 39(1):66-70
7. Grédiac M, Pierron F, Surrel Y (1999) Novel procedure for complete in-plane composite characterization using a single T-shaped specimen. Exp Mech 39(2):142-149
8. 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
9. 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
10. 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
11. 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
12. 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
13. Daly S, Rittel D, Bhattacharya K, Ravichandran G (2009) Large deformation of nitinol under shear dominant loading. Exp Mech 49:225-233
14. 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
15. Carlsson LA, Pipes RB (1997) Experimental characterization of advanced composite materials. Technomic Publishing Company, Lancaster PA, USA
16. Kavanagh KT, Clough RW(1971) Finite element applications in the characterization of elastic solids. Int J Solids Struct 7(1):11-23
17. Hendricks MAN (1991) Identification of the mechanical properties of solid materials. Doctoral dissertation, Eindhoven University of Technology
18. 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
19. 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
20. 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
21. 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
22. Genovese K, Lamberti L, Pappalettere C (2006) Mechanical characterization of hyperelastic materials with fringe projection and optimization techniques. Opt Lasers Eng 44:423-442
23. Ladevèze P, Leguillon D (1983) Error estimate procedure in the finite element method and applications. SIAM J Numer Anal 20:485-509
24. Latourte F, Chrysochoos A, Pagano S, Wattrisse B (2008) Elastoplastic behavior identification for heterogeneous loadings and materials. Exp Mech 48:435-449
25. Avril S, BonnetM, 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
26. Ikehata M (1993) An inverse problem for the plate in the Love-Kirchhoff theory. SIAM J Numer Anal 53:942-970
27. Dym L, Shames H (1973) Solid mechanics: a variational approach. McGraw-Hill, New York
28. 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
29. 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
30. Timoshenko S, Woinowsky-Krieger S (1959) Theory of plates and shells, 2nd edn. McGraw-Hill, New York
31. Donell LH (1976) Beams, plates and shells. McGraw-Hill, New York
32. Finlayson BA (1972) The method of weighted residual and variational principle with application in fluid mechanics, heat and mass tranfer, vol 87 of Mathematics in Science and Engineering. Academic, New York
33. Reddy JN (1984) Energy and variational principle in applied mechanics. Wiley, New York
34. Frazer RA, Jones WP, Skan SW (1937) Approximations fo functions and to the solutions of differential equations. Great Britan Air Ministry Aeronautical Research Committee Technical Report 1:517-549, 1937. Reprinted from Great Britan Aeronautical Research Council, Report and Memo., vol 1799, London
35. Biezeno CB, Koch JJ (1923) Over een nieuwe methode ter berekening van vlakke platen met toepassing op enkele voor de techniek belangrijke belastingsgevallen. Ing Grav 38:25-36
36. Strang G, Fix GJ (1973) An analysis of the finite element method. Automatic computation. Prentice-Hall, Englewood Cliffs, NJ
37. Zienkiewicz OC, Taylor RL (2005) The finite element method for solid and structural mechanics, 6th edn. Elsevier, NY, USA
38. Grédiac M, Pierron F (2004) Numerical issues in the virtual fields method. Int J Numer Meth Eng 59(10):1287-1312
39. Avril S, Grédiac M, Pierron F (2004) Sensitivity of the virtual fields method to noisy data. Comput Mech 34(6):439-452
40. Avril S, Pierron F (2007) General framework for the identification of elastic constitutive parameters from full-field measurements. Int J Solids Struct 44:4978-5002
41. Rossi M, Pierron F (2012) Identification of plastic constitutive parameters at large deformation from three dimensional displacement fields. Comput Mech 49(1):53-71
42. Pierron F, Avril S, Tran VT (2010) Extension of the virtual fields method to elastoplastic material identification with cyclic loads and kinematic hardening. Int J Solids Struct 47:2993-3010
43. SuttonMA, Deng X, Liu J, Yang L (1996) Determination of elastic-plastic stresses and strains from measured surface strain data. Exp Mech 36(2):99-112
44. Voce E (1955) A practical strain-hardening function. Metallurgia 51:219-226
45. Toussaint E, Grédiac M, Pierron F (2006) The virtual fields method with piecewise virtual fields. Int J Mech Sci 48(3):256-264
46. Rossi M, Chiappini G, Sasso M (2010) Characterization of aluminum alloys using a 3D full field measurement. 2010 SEM annual conference and exposition on experimental and applied mechanics, Indianapolis, IN, 7-10 June 2010
47. Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, New York
48. Wu T, Coret M, Combescure A (2011) Strain localisation and damage measurement by full 3D digital image correlation: application to 15-5PH stainless steel. Strain 47(1):49-61
49. Pierron F, McDonald SA, Hollis D, Withers PJ, Alderson A (2011) Assessment of the deformation of low density polymeric auxetic foams by X-ray tomography and digital volume correlation. In: Lucas M, Patterson EA (eds) Applied mechanics and materials VII, vol VII of advances in experimental mechanics. Trans Tech Publications. International conference on advances in experimental mechanics, BSSM/SEM, Edinburgh (UK), 7-9 September 2011
50. Bonet J, Wood RD (1997) Nonlinear continuum mechanics for finite element analysis. Cambridge University Press, Cambridge
51. Truesdell C, Noll W (1965) The non-linear field theories of mechanics. Springer, Berlin, Heidelberg, New York
52. Rivlin RS (1949) Large elastic deformations of isotropic materials. VI. further results in the theory of torsion, shear and flexure. Philos Transact A Math Phys Eng Sci 242(845):173-195
53. Ogden RW (1997) Large deformation isotropic elasticity. on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc London. Series A, Math Phys Sci 326(1567):565-584
54. Treloar LRG (1943) The elasticity of a network of long chain molecules (I and II). Trans Faraday Soc 39:241-246
55. Mooney M (1940) A theory of large elastic deformation. J Appl Phys 11(1567):582-592
56. Yeoh OH (1993) Some forms of the strain energy function for rubber. Rubber Chem Technol 66(5):754-771
57. Promma N, Raka B, Grédiac M, Toussaint E, Le Cam JB, Balandraud X, Hild F (2009) Application of the virtual fields method to mechanical characterization of elastomeric materials. Int J Solids Struct 46:698-715
58. Idlbi A, Karama M, Touratier M (1997) Comparison of various laminated plate theories. Compos Struct 37(2):173-184
59. Reddy JN (1999) Theory and analysis of elastic plates. Taylor and Francis, London
60. Touratier M (1991) An efficient standard plate theory. Int J Eng Sci 29(8):901-916
61. Giraudeau A, Pierron F (2005) Identification of stiffness and damping properties of thin isotropic vibrating plates using the Virtual Fields Method. Theory and simulations. J Sound Vibration 284(3-5):757-781
62. ISO 527-4:1997. Plastics-determination of tensile properties-part 4: Test conditions for isotropic and orthotropic fibre-reinforced plastic composites. International Standards Organization
63. ISO 527-5:2009. Plastics-determination of tensile properties-part 5: Test conditions for unidirectional fibre-reinforced plastic composites. International Standards Organization
64. ISO 14129:1997. Fibre-reinforced plastic composites-determination of the in-plane shear stress/shear strain response, including the in-plane shear modulus and strength, by the plus or minus 45 degree tension test method. International Standards Organization
65. ISO 15310:1999. Fibre-reinforced plastic composites-determination of the in-plane shear modulus by the plate twist method. International Standards Organization
66. Lecompte D, Smits A, Sol H, Vantomme J, Van Hemelrijck D (2007) Mixed numericalexperimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens. Int J Solids Struct 44(5):1643-1656
67. Pierron F, Vautrin A (1994) Accurate comparative determination of the in-plane shear modulus of T300/914 using the Iosipescu and 45? off-axis tests. Compos Sci Technol 52 (1):61-72
68. Pierron F (1998) Saint-Venant effects in the Iosipescu specimen. J Compos Mater 32(22): 1986-2015
69. Prabhakaran R, Sawyer W(1986) A photoelastic investigation of asymmetric four point bend shear test for composite materials. Compos Struct 5(3):217-231
70. Romano AJ, Shirron JJ, Bucaro JA (1998) On the noninvasive determination of material parameters from a knowledge of elastic displacements: Theory and numerical simulation. IEEE Trans Ultrasonics, Ferroelectrics Freq Control 45(3):751-759
71. Romano AJ, Bucaro JA, Ehman RL, Shirron JJ (2000) Evaluation of a material parameter extraction algorithm using MRI-based displacement measurements. IEEE Trans Ultrasonics, Ferroelectrics Freq Control 47(6):1575-1581
72. Pierron F, Grédiac M (2000) Identification of the through-thickness moduli of thick composites from whole-field measurements using the Iosipescu fixture. Compos Part A: Appl Sci Manufac 31(4):309-318
73. 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):2691-2705
74. Grédiac M, Toussaint E, Pierron F (2002) Special virtual fields for the direct determination of material parameters with the virtual fields method. 2-Application to in-plane properties. Int J Solids Struct 39(10):2707-2730
75. Chalal H, Meraghni F, Pierron F, Grédiac M (2004) Direct identification of the damage behaviour of composite materials using the virtual fields method. Compos Part A: Appl Sci Manuf 35(7-8):841-848
76. Chalal H, Avril S, Pierron F, Meraghni F (2006) Experimental identification of a nonlinear model for composites using the grid technique coupled to the virtual fields method. Compos Part A: Appl Sci Manuf 37(2):315-325
77. Surrel Y (1994) Moiré and grid methods: a signal-processing approach. In: Pryputniewicz RJ, Stupnicki J (eds) Interferometry '94: Photomechanics, vol 2342, pp 213-220 Proc Soc Photo-Opt Instrum Eng
78. Moulart R, Rotinat R, Pierron F, Lerondel G (2007) On the realization of microscopic grids for local strain measurement by direct interferometric photolithography. Opt Lasers Eng 45 (12):1131-1147
79. Piro J-L, Grédiac M (2004) Producing and transferring low-spatial-frequency grids for measuring displacement fields with moiré and grid methods. Exp Tech 28(4):23-26
80. Chalal H (2005) Identification numérique et expérimentale de lois de comportement non lineaíres de matériaux composites à partir de mesures de champs cinématiques (Numerical and experimental identification of a non-linear behaviour law for composite materials from full-field measurements). PhD thesis, Ecole Nationale Supérieure d'Arts et Métiers (ENSAM), 2005. http://www.lmpf.net/FR/centre telechargement/client/download.php?id=6
81. Pierron F, Vert G, Burguete R, Avril S, Rotinat R, Wisnom M (2007) Identification of the orthotropic elastic stiffnesses of composites with the Virtual Fields Method: sensitivity study and experimental validation. Strain 43(3):250-259
82. ASTM D2344/D2344M 00(2006). Standard test method for short-beam strength of polymer matrix composite materials and their laminates. ASTM International, West Conshohocken, PA, 2003, 2006. DOI: 10.1520/D2344 D2344M-00R06.
83. Genovese K, Lamberti L, Pappalettere C (2004) A new hybrid technique for in-plane characterization of orthotropic materials. Exp Mech 44(6):584-592
84. Grédiac M, Pierron F (1998) A T-shaped specimen for the direct characterization of orthotropic materials. Int J Numer Meth Eng 41:293-309
85. Broughton WR, Sims GD (1994) An overview of through-thickness test methods for polymer matrix composites. Technical report, DMMA(A) 148, National Physics Laboratory, UK, 1994
86. Mespoulet S (1998) Through-thickness test methods for laminated composite materials. PhD thesis, Imperial College of Science, Technology and Medecine
87. Broughton WR (2000) Mechanical testing of advanced fibre composites. Hodgkinson JM (ed) chapter 8. Through-thickness testing, pp 143-170. Woodhead Publishing, Delhi, India
88. Pierron F, Zhavoronok S, Grédiac M (2000) Identification of the through-thickness properties of thick laminates using the virtual fields method. Int J Solids Struct 37(32):4437-4453
89. Moulart R, Avril S, Pierron F (2006) Identification of the through-thickness rigidities of a thick laminated composite tube. Compos Part A: Appl Sci Manuf 37(2):326-336
90. Pierron F (1998) Saint-Venant effects in the Iosipescu specimen. J Compos Mater 32(22): 1986-2015
91. 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):735-755
92. Nunio F, Aubert G, Berriaud C, Schild T, Védrine P (2008) Full resolution structural finite element analysis of the CEA/Iseult 11.75T MRI coil. IEEE Trans Appl Superconduct 18(2):916-919. art. no. 4497225
93. Nunio F, Aubert G, Berriaud C, Schild T, Védrine P (2010) Mechanical design of the Iseult 11.7 T whole body MRI magnet. IEEE Trans Appl Superconduct 20(3):916-919. art. no. 5422888.
94. Kim J-H, Nunio F, Pierron F, Védrine P (2010) Identification of the mechanical properties of superconducting windings using the Virtual Fields Method. IEEE Trans Appl Superconduct 20(3):1993-1997
95. Pierron F (2009) A novel method for measuring the through-thickness shear moduli of anisotropic plates from surface deformation measurements. Compos Part A: Appl Sci Manuf 40(12):1815-1825
96. Avril S, Feissel P, Pierron F, Villon P (2010) Comparison of two approaches for controlling the uncertainty in data differentiation: application to full-field measurements in solid mechanics. Meas Sci Technol 21(015703):11
97. Kim J-H, Pierron F, Grédiac M, Wisnom M (2007) A procedure for producing reflective coatings on plates to be used for full-field slope measurements by a deflectometry technique. Strain 43(2):138-144
98. Kim J-H, Pierron F, Wisnom M, Syed-Muhammad K (2007) Identification of the local stiffness reduction of a damaged composite plate using the virtual fields method. Compos Part A: Appl Sci Manuf 38(9):2065-2075
99. Lekhnitskii SG (1968) Anisotropic plates. Gordon and Breach Science, New York. Translated from the second Russian edition by Tsai SW and Cheron T
100. Tsai SW, Hahn HT (1980) Introduction to composite materials. Technomic Publishing
101. Grédiac M, Vautrin A, Verchery G (1993) A general method for data averaging of anisotropic elastic constants. J Appl Mech 60:614-618. Trans Am Soc Mech Eng
102. Grédiac M (1996) On the direct determination of invariant parameters governing the bending of anisotropic plates. Int J Solids Struct 33(27):3969-3982
103. Bruno L, Furgiuele FM, Pagnotta L, Poggialini A (2002) A full-field approach for the elastic characterization of anisotropic materials. Opt Lasers Eng 37(4):417-431
104. Avril S, Grédiac M, Pierron F, Surrel Y, Toussaint E (2004) Deflectometry and virtual fields for identification of static plate bending stiffnesses. In: Xth International Congress of the Society for Experimental Mechanics, Costa Mesa
105. Grédiac M, Toussaint E, Pierron F (2003) Special virtual fields for the direct determination of material parameters with the virtual fields method. 3-Application to the bending rigidities of anisotropic plates. Int J Solids Struct 40:2401-2419
106. Syed Muhammad K, Toussaint E, Grédiac M, Avril S, Kim JH (2008) Characterization of composite plates using the Virtual Fields Method using optimized loading conditions. Compos Struct 85(1):70-82
107. Kim J-H, Pierron F, Wisnom M, Avril S (2009) Local stiffness reduction in impacted composite plates from full-field measurements. Compos Part A: Appl Sci Manuf 40(12):1961-1974
108. Grédiac M, Paris P-A (1996) Direct identification of elastic constants of anisotropic plates by modal analysis: theoretical and numerical aspects. J Sound Vibration 195(3):401-415
109. Swanson SR, Messick M, Toombes GR (1985) Comparison of torsion tube and Iosipescu in-plane shear test results for a carbon epoxy composite. Composites 16(3):220-224
110. Ho H, Morton J, Farley GL (1993) Nonlinear numerical analysis of the Iosipescu specimen for composite materials. Compos Sci Technol 50(3):355-65
111. Ladevèze P, Le Dantec E (1992) Damage modeling of the elementary ply for laminated composites. Compos Sci Technol 43(3):257-267
112. Grédiac M, Auslender F, Pierron F (2001) Using the virtual fields method to identify the through-thickness moduli of thick composites with a nonlinear shear response. Compos Part A: Appl Sci Manuf 32(12):1713-1725
113. Périé JN, Leclerq H, Roux S, Hild F (2009) Digital image correlation and biawial test on composite material for anisotropic damage law identification. Int J Solids Struct 46:2388-2396
114. Claire D, Hild F, Roux S (2007) Identification of a damage law by using full-field displacement measurements. Int J Damage Mech 16(2):179-197
115. Crouzeix L, Périé JN, Collombet F, Douchin B (2009) An orthotropic variant of the equilibrium gap method applied to the analysis of a biaxial test on a composite material. Compos Part A: Appl Sci Manuf 40(11):1732-1740
116. Kim J-H (2008) Identification of the local stiffness reduction of damaged composite plates using the virtual fields method. PhD thesis, Arts et Métiers ParisTech, 2008. www.lmpf.net.
117. Moulart R, Pierron F, Hallett SR, Wisnom MR (2011) Full-field strain measurement and identification of mechanical properties at high strain rate. Exp Mech 51(4):509-536
118. Pierron F, Green B, Wisnom MR, Hallett SR (2007) Full-field assessment of the damage process of laminated composite open-hole tensile specimens. Part II: experimental results. Compos Part A: Appl Sci Manuf 38:2321-2332
119. Grédiac M, Pierron F (2006) Applying the virtual fields method to the identification of elastoplastic constitutive parameters. Int J Plasticity 22:602-627
120. Avril S, Pierron F, Pannier Y, Rotinat R (2008) Stress reconstruction and constitutive parameter identification in elastoplasticity using measurements of deformation fields. Exp Mech 48(4):403-420
121. Meuwissen MHH (1998) An inverse method for the echanical characterisation of metals. PhD thesis, Eindhoven Technical University, 1998
122. Pannier Y (2006) Identification de paramètres élastoplastiques par des essais statiquement indéterminés: mise en oeuvre expérimentale et validation de la méthode des champs virtuels (Identification of elasto-plastic parameters from statically-undetermined tests: experimental application and validation of the virtual field method.). PhD thesis, Ecole Nationale Supérieure d'Arts et Métiers (ENSAM), 2006. http://www.lmpf.net/FR/centre telechargement/client/download.php?id=9
123. Tran VT (2008) Identification du comportement des matériaux métalliques au del de leur limite d'élasticité par la méthode des champs virtuels (thorough study to identify elastoplastic constitutive parameters of metallic materials by the virtual fields method). PhD thesis, Université de Technologie de Troyes (UTT), 2008. http://www.lmpf.net/FR/centre telechargement/client/download.php?id=16
124. Avril S, Pierron F, Yan J, Sutton M. A (2008) Identification of viscoplastic parameters and characterization of Lüders behavior using Digital Image Correlation and the Virtual Fields Method. Mech Mater 40(9):729-742
125. Lemâ?tre J, Chaboche J-L (1990) Mechanics of solid materials. Springer, New York
126. Yoshida FA (2000) A constitutive model of cyclic plasticity. Int J Plasticity 16:359-380
127. Perzyna P (1963) The constitutive equations for rate-sensitive plastic materials. Q Appl Math 20:321-332
128. Kajberg J, Sundin KG, Melin LG, St°ahle P (2004) High strain rate tensile and viscoplastic parameter identification using micoscopic high-speed photography. Int J Plasticity 20:561-575
129. Graff S, Forest S, Strudel J-L, Prioul C, Pilvin P, Bechade J-L (2004) Strain localization phenomena associated with static and dynamic strain ageing in notched specimens: experiments and finite element simulations. Mater Sci Eng A 387-389:181-185
130. Sutton M. A, Yan J, Avril S, Pierron F, Adeeb S (2008) Identification of heterogeneous constitutive parameters in a welded specimen: Uniform stress and virtual fields methods for material property estimation. Exp Mech 48(4):451-464
131. Casavola C, Pappalettere C, Tattoli F (2009) Experimental and numerical study of static and fatigue properties of titanium alloy welded joints. Mech Mater 41(3):231-243
132. Tattoli F, Pierron F, Rotinat R, Casavola C, Pappalettere C (2010) Full-field strain measurement on titanium welds and local elasto-plastic identification with the virtual fields method. In: El Mansori M, Chinesta F, Chastel Y (eds) International conference on advances in materials and processing technologies (AMPT2010), vol 1315 of AIP conference proceedings. American Institute of Physics, 2010
133. Le Louëdec G, Sutton M. A, Pierron F, Reynolds AP (2011) Dynamic local elasto-plastic identification of the behaviour of aluminium FSW welds with the virtual fields method. In: Annual conference of the British society for experimental mechanics (BSSM), 2011. 7-9 September 2011, Edinburgh, UK
134. Guélon T, Toussaint E, Le Cam J-B, Promma N, Grédiac M (2009) A new characterization method for rubber. Polym Testing 28(7):715-723
135. Heuillet P, Dugautier L (1997) Génie mécanique des caoutchoucs et des élastomères thermoplastiques, chapter Modélisation du comportement élastique des élastomères compacts, pages 67-103. Apollor, 1997 (in French)
136. Mullins L (1948) Effect of stretching on the properties of rubber. Rubber Chem Technol 21:281-300
137. SuttonMA, Orteu J-J, Schreier H (2009) Image correlation for shape, motion and deformation measurements. Springer, New York
138. Bergonnier S, Hild F, Roux S (2005) Digital image correlation used for mechanical tests on crimped glass wool samples. J Strain Anal Eng Des 40:185-197
139. Scarpa F, Pastorino P, Garelli A, Patsias S, Ruzzene M (2005) Auxetic compliant flexible PU foams static and dynamic properties. Phys Status Solid B 242(3):681-694
140. Bianchi M, Scarpa FL, Smith CW (2008) Stiffness and energy dissipation in polyurethane auxetic foams. J Mater Sci 43(17):5851-5860
141. Bezazi A, Scarpa F (2007) Mechanical behaviour of conventional and negative Poisson's ratio thermoplastic polyurethane foams under compressive cyclic loading. Int J Fatigue 29: 922-930
142. Pierron F (2010) Identification of Poisson's ratios of standard and auxetic low density polymeric foams from full-field measurements. J Strain Anal Eng Des 45(4):233-253
143. El-Ratal WH, Mallick PK (1996) Elastic response of flexible polyurethane foams in uniaxial tension. J Eng Mater Technol 118:157-161
144. Widdle RD, Bajaj AK, Davies P (2008) Measurement of the Poisson's ratio of flexible polyurethane foam and its influence on a uniaxial compression model. Int J Eng Sci 46:31-49
145. Zhang D, Zhang X, Cheng G (1999) Compression strain measurement by digital speckle correlation. Exp Mech 39(1):62-65
146. Chiang FP, Uzer G (2008) Mapping full-field deformation of auxetic foams using digital speckle photography. Physica Status Solidi B 245(11):2391-2394
147. Smith CW, Wootton RJ, Evans KE (1999) Interpretation of experimental data for Poisson's ratio of highly nonlinear materials. Exp Mech 39(4):356-362
148. Samani A, Zubovits J, Plewes DB (2007) Elastic moduli of normal and pathological human breast tissues: an inversion-technique-based investigation of 169 samples. Phys Med Biol 52:1565-1576
149. Venkatesh SK, Yin M, Glockner JF, Takahashi N, Araoz PA, Talwalkar JA, Ehman RL (2008) MR elastography of liver tumors: preliminary results. Am J Roentgenol 52(6):1534-1540
150. Atay S, Kroenke CD, Sabet A, Bayly PV (2008) Measurement of the dynamic shear modulus of mouse brain tissue in-vivo by magnetic resonance elastography. J Biomech Eng 130:021013
151. Muthupillai R, Lomas DJ, Rossman PJ, Greenleaf JF, Manduca A, Ehman RL (1995) Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. Science 269:1854-1857
152. Steele DD, Chevenert TL, Skovoroda AR, Emelianov SY (2000) Three dimensional static displacement stimulated echo nmr elasticity imaging. Phys Med Biol 45:1633-1648
153. Sinkus R, Tanter M, Xydeas T, Catheline S, Bercoff J, Fink M (2005) Viscoelastic shear properties of in vivo breast lesions measured by mr elastography. Mag Resonance Imag 23:159-165
154. Pierron F, Bayly PV, Namani R (2010) Application of the virtual fields method to magnetic resonance elastography data. 2010 SEM annual conference and exposition on experimental and applied mechanics, Indianapolis, IN, 7-10 June 2010
155. Avril S, Huntley JM, Pierron F, Steele DD (2008) 3D heterogeneous stiffness reconstruction using MRI and the Virtual Fields Method. Exp Mech 48(4):479-494
156. Avril S, Badel P, Duprey A (2010) Anisotropic and hyperelastic identification of in vitro human arteries from full-field optical measurements. J Biomech 43:2978-2985
157. Genovese K (2009) A video-optical system for time-resolved whole-body measurement on vascular segments. Opt Lasers Eng 47:995-1008
158. Machado J, Cruz H (2005) Within stem variation of maritime pine timber mechanical properties. Holz als Roh-und Werkstoff 63(2):154-159
159. Xavier J, Avril S, Pierron F, Morais J (2007) Novel experimental approach for the characterisation of the LR stiffness parameters of clear wood using a single specimen. Holzforschung 61:573-581
160. Xavier J (2007) Characterisation of the wood stiffness variability within the stem by the virtual fields method: application to P. Pinaster in the LR plane. (Identification de la variabilité des rigidités du bois à l'intérieur de l'arbre par la méthode des champs virtuels: application au P. Pinaster dans le plan LR.). PhD thesis, Ecole Nationale Supérieure d'Arts et Métiers (ENSAM). http://www.lmpf.net/FR/centre telechargement/client/download.php?id=12
161. Pereira J (2005) Comportamento mecânico da madeira em tracç aõ nas direcç ões de simetria material. PhD thesis, Universidade de Traás-os-Montes e Alto Douro, Vila Real (in Portuguese)
162. Xavier J, Garrido NM, Oliveira M, Morais JL, Camanho PP, Pierron F (2004) A comparison between the Iosipescu and off-axis shear test methods for the characterization of Pinus Pinaster Ait. Compos Part A 35(7-8):827-840
163. Xavier J, Avril S, Pierron F, Morais J, Lousada J (2009) Evaluation of the stiffness radial variability of P. Pinaster within the stem. Compos Part A 40:1953-1960
164. Barnett JR, Bonham VA (2004) Cellulose microfibril angle in the cell wall of wood fibres. Biol Rev 79(2):461-472
165. Thuvander F, Jernkvist L, Gunnars J (2000) Influence of repetitive stiffness variation on crack growth behaviour in wood. J Mater Sci 35(24):6259-6266
166. Tschoegl NW, Knauss WG, Emri I (2002) Poisson's ratio in linear viscoelasticity-a critical review. Mech Time-Dependent Mater 6:3-51
167. Giraudeau A, Pierron F (2003) Simultaneous identification of stiffness and damping properties of isotropic materials from forced vibrating plates. Comptes Rendus Mécanique 331(4): 259-264
168. Giraudeau A, Pierron F, Guo B (2010) An alternative to modal analysis for material stiffness and damping identification from vibrating plates. J Sound Vibration 329(10):1653-1672
169. Giraudeau A, Guo B, Pierron F (2006) Stiffness and damping identification from full field measurements on vibrating plates. Exp Mech 46(6):777-787
170. Erzar B, Forquin P (2010) An experimental method to determine the tensile strength of concrete at high rates of strain. Exp Mech 50:941-955
171. Etoh TG, Vo Le C, Hashishin Y, Otsuka N, Takehara K, Ohtake H, Hayashida T, Maruyama H (2007) Evolution of ultra-high-speed ccd imagers. Plasma Fusion Res 2:S1021
172. Pierron F, Forquin P (2011) Ultra high speed full-field strain measurements on spalling tests on concrete materials. 2011 SEM annual conference and exposition on experimental and applied mechanics, Mohegan Sun, CT, 13-16 June 2011
173. Syed-Muhammad K, Toussaint E, Grédiac M (2009) Optimization of a mechanical test on composite plates with the Virtual Fields Method. Struct Multidiscip Optim 38(1):71-82
174. Bornert M, Brémand F, Doumalin P, Dupré J-C, Fazzini M, Grédiac M, Hild F, Mistou S, Molimard J, Orteu J-J, Robert L, Surrel Y, Vacher P, Wattrisse B (2009) Assessment of digital image correlation measurement errors: Methodology and results. Exp Mech 49(3):353-370
175. 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(3-4):420-435
176. Chen WW, Song B (2011) Split Hopkinson (Kolsky) bar. Springer, Berlin, Heidelberg, New York
177. Othman R, Aloui S, Poitou A (2010) Identification of non-homogeneous stress fields in dynamic experiments with a non-parametric method. Polym Testing 29(5):616-623
178. Pierron F, Sutton M. A, Tiwari V (2011) Ultra high speed DIC and Virtual Fields Method analysis of a three point bending impact test on an aluminium bar. Exp Mech 51(4):537-563
179. Tiwari V, Sutton M. A, McNeill SR (2007) Assessment of high speed imaging systems for 2D and 3D deformation measurements: methodology development and validation. Exp Mech 47(4):561-579
180. Golub GH, Van Loan CF (1973) Matrix computations. Johns Hopkins University Press, Baltimore, MD
181. The MathWorks Inc. Reference Guide, 1994
182. KumosaM, Han Y (1997) Non-linear finite-element analysis of Iosipescu specimens. Compos Sci Technol 59(4):561-573