THE VIRTUAL FIELDS METHOD

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The VFM

Applications: problem type

Applications: materials

Publications

Here is a list of papers relating to the Virtual Fields Method.

Seminal paper by Prof. M. Grédiac

• Grédiac M., Principe des travaux virtuels et identification, Comptes Rendus de l’Académie des Sciences, vol. 309, pp. 1–5, 1989 (In French with abridged English version).

Review papers

• Grédiac M., Pierron F., Avril S., Toussaint E., The virtual fields method for extracting constitutive parameters from full-field measurements: a review Strain: an International Journal for Experimental Mechanics, vol. 42, pp. 233-253, 2006.
  This paper can be downloaded here courtesy of Blackwell publishing.
• Avril S., Bonnet M., Bretelle A.-S., Grédiac M., Hild F., Ienny P., Latourte F., Lemosse D., Pagano S., Pagnacco E., Pierron F., Overview of identification methods of mechanical parameters based on full-field measurements Experimental Mechanics, vol. 48, n° 4, pp. 381-402, 2008.

Theory of the VFM

• Grédiac M., Toussaint E., Pierron F., Special virtual fields for the direct determination of material parameters with the virtual fields method. 1- Principle and definition, International Journal of Solids and Structures, vol. 39, n° 10, pp. 2691-2705, 2002.
• Grédiac M., Toussaint E., Pierron F., Special virtual fields for the direct determination of material parameters with the virtual fields method. 2- Application to in-plane properties, International Journal of Solids and Structures, vol. 39, n° 10, pp. 2707-2730, 2002.
• Grédiac M., Toussaint E., Pierron F., Special virtual fields for the direct determination of material parameters with the virtual fields method. 3- Application to the bending rigidities of anisotropic plates, International Journal of Solids and Structures, vol. 40, n° 10, pp. 2401-2419, 2003.
• Grédiac M., Pierron F., Numerical issues in the virtual fields method, International Journal for Numerical Methods in Engineering, vol. 59, n° 10, pp. 1287-1312, 2004.
• Avril S., Grédiac M., Pierron F., Sensitivity of the virtual fields method to noisy data, Computational Mechanics, vol. 34, n° 6, pp. 439-452, 2004
• Toussaint E., Grédiac M., Pierron F., The virtual fields method with piecewise virtual fields, International Journal of Mechanical Sciences, vol. 48, n° 3, pp. 256-264, 2006.
• Avril S., Pierron F., General framework for the identification of elastic constitutive parameters from full-field measurements, International Journal of Solids and Structures, vol. 44, pp. 4978-5002, 2007.

Anisotropic bending stiffnesses of composites plates

• Grédiac M., Vautrin A., A new method for determination of bending rigidities of thin anisotropic plates, Journal of Applied Mechanics, vol. 57, pp. 964–968 (Transactions of the American Society of Mechanical Engineers).
• Grédiac M., Vautrin A., Mechanical characterization of anisotropic plates: experiments and results, European Journal of Mechanics: A Solids, vol. 12, pp. 819–838, 1993.
• Grédiac M., On the direct determination of invariant parameters governing the bending of anisotropic plates, International Journal of Solids and Structures, vol. 33, pp. 3969–3982, 1996.

Orthotropic in-plane/through-thickness stiffnesses of composites (including non-linearity)

• Grédiac M., Pierron F., Vautrin A., The Iosipescu in-plane shear test applied to composites: a new approach based on displacement field processing, Composites Science and Technology, vol. 51, n° 3, pp. 409-417, 1994.
• Grédiac M., Pierron F., A T-shaped specimen for the direct characterization of orthotropic materials, International Journal for Numerical Methods in Engineering, vol. 41, pp. 293-309, 1998.
• Grédiac M., Pierron F., Surrel Y., Novel procedure for complete in-plane composite characterization using a single T-shaped specimen, Experimental Mechanics, vol. 39, n° 2, pp. 142-149, 1999.
• Pierron F., Zhavoronok S., Grédiac M., Identification of the through-thickness properties of thick laminated tubes using the virtual fields method, International Journal of Solids and Structures, vol. 37, n° 32, pp 4437-4453, 2000.
• Pierron F., Grédiac M., Identification of the through-thickness moduli of thick composites from whole-field measurements using the Iosipescu fixture Composites Part A: Applied Science and Manufacturing, vol. 31, n° 4, pp 309-318, 2000.
• Grédiac M., Auslender F., Pierron F., Using the virtual fields method to identify the through-thickness moduli of thick composites with a nonlinear shear response, Composites Part A: Applied Science and Manufacturing, vol. 32, n° 12, pp. 1713-1725, 2001.
• Chalal H., Meraghni F., Pierron F., Grédiac M., Direct identification of the damage behaviour of composite materials using the virtual fields method, Composites Part A: Applied Science and Manufacturing, vol. 35, n° 7-8, pp. 841-848, 2004.
• Moulart R., Avril S., Pierron F., Identification of the through-thickness rigidities of a thick laminated composite tube, Composites Part A: Applied Science and Manufacturing, vol. 37, n° 2, pp. 326-336, 2006.
• Chalal H., Avril S., Pierron F., Meraghni F., Experimental identification of a nonlinear model for composites using the grid technique coupled to the virtual fields method, Composites Part A: Applied Science and Manufacturing, vol. 37, n° 2, pp. 315-325, 2006.
• Pierron F., Vert G., Burguete R., Avril S., Rotinat R., Wisnom M., Identification of the orthotropic elastic stiffnesses of composites with the virtual fields method: sensitivity study and experimental validation, Strain: an International Journal for Experimental Mechanics, vol. 43, n° 3, pp. 250-259, 2007.
• Pierron F., A novel method for measuring the through-thickness shear moduli of anisotropic plates from surface deformation measurements, Composites Part A: Applied Science and Manufacturing, vol. 40, n°12, pp. 1815-1825, 2009.

Impact damage of composite plates

• Kim J.-H., Pierron F., Wisnom M., Syed-Muhamad K., Identification of the local stiffness reduction of a damaged composite plate using the virtual fields method, Composites Part A: Applied Science and Manufacturing, vol. 38, n° 9, pp. 2065-2075, 2007.
• Kim J.H., Pierron F., Wisnom M., Avril S., Local stiffness reduction in impacted composite plates from full-field measurements, Composites Part A: Applied Science and Manufacturing, vol. 40, n°12, pp. 1961-1974, 2009.

Vibrating bending properties of polymeric and composites plates

• Grédiac M., Paris P.-A., Direct identification of elastic constants of anisotropic plates by modal analysis: theoretical and numerical aspects, Journal of Sound and Vibration, vol. 195, pp. 401–415, 1996.
• Grédiac M., Fournier N., Paris P.-A., Surrel Y., Direct identification of elastic constants of anisotropic plates by modal analysis: experiments and results, Journal of Sound and Vibration, vol. 210, pp. 645–659, 1998.
• Grédiac M., Fournier N., Paris P.-A., Surrel Y., Direct measurement of invariant parameters of composite plates, Journal of Composite Materials, vol. 33, pp. 1939–1965, 1999.
• Giraudeau A., Pierron F., Simultaneous identification of stiffness and damping properties of isotropic materials from forced vibrating plates, Comptes rendus Mécanique, vol. 331, n° 4, pp. 259-264, 2003.
• Giraudeau A., Pierron F., Identification of stiffness and damping properties of thin isotropic vibrating plates using the Virtual Fields Method. Theory and simulations, Journal of Sound and Vibration, vol. 284, n° 3-5, pp. 757-781, 2005.
• Giraudeau A., Guo B., Pierron F., Stiffness and damping identification from full field measurements on vibrating plates, Experimental Mechanics, vol. 46, n° 6, pp. 777-787, 2006.
• Giraudeau A., Pierron F., Guo B., An alternative to modal analysis for material stiffness and damping identification from vibrating plates, Journal of Sound and Vibration, vol. 329, n° 10, pp. 1653-1672, 2010.

Elasto-plasticity

Small deformation elasto-plasticity, static

• Grédiac M., Pierron F., Applying the Virtual Fields Method to the identification of elasto-plastic constitutive parameters, International Journal of Plasticity, vol. 22, pp. 602-627, 2006.
• Pannier Y., Avril S., Rotinat R., Pierron F., Identification of elasto-plastic constitutive parameters from statically undetermined tests using the virtual fields method, Experimental Mechanics, vol. 46, n° 6, pp. 735-755, 2006.
• Avril S., Pierron F., Pannier Y., Rotinat R., Stress reconstruction and constitutive parameter identification in elastoplasticity using measurements of deformation fields, Experimental Mechanics, vol. 48, n° 4, pp. 403-420, 2008.
• Pierron F., Avril S., Tran T.V., Extension of the virtual fields method to elasto-plastic material identification with cyclic loads and kinematic hardening, International Journal of Solids and Structures, vol. 47, pp. 2993–3010, 2010.

Small deformation visco-plasticity, dynamic

• Avril S., Pierron F., Yan J., Sutton M.,
  Identification of viscoplastic parameters and characterization of Lüders behaviour using Digital Image Correlation and the Virtual Fields Method Mechanics of Materials, vol. 40, pp. 729-742, 2008.

Large deformation plasticity, static

• Rossi M., Pierron F., Identification of plastic constitutive parameters at large deformation from three dimensional displacement fields
  Computational Mechanics, available online, 2011.

Welds

• Sutton M.A., Yan J., Avril S., Pierron F., Adeeb S.M., Identification of heterogeneous parameters in a welded specimen: constant stress and virtual fields method for material property estimation Experimental Mechanics, vol. 48, n° 4, pp. 451-464, 2008.

Wood

• Xavier J., Avril S., Pierron F., Morais J.L., Novel experimental approach for the characterisation of the LR stiffness parameters of clear wood using a single specimen Holzforschung, vol. 61, pp. 573-581, 2007.
• Xavier J., Avril S., Pierron F., Morais J., Lousada J., Evaluation of the stiffness radial variability of P. pinaster within the stem Composites Part A: Applied Science and Manufacturing, vol. 40, n°12, pp. 1953-1960, 2009.

Soft materials

• Promma N., Raka B., Grédiac M., Toussaint E., Le Cam J.-B., Balandraud X., Hild F., Application of the virtual fields method to mechanical characterization of elastomeric materials International Journal of Solids and Structures, vol. 46, pp. 698-715, 2009.
• Guélon T., Toussaint E., Le Cam J.-B., Promma N., Grédiac M., A new characterization method for rubber Polymer testing, vol. 28, n° 7, pp. 715-723, 2009.
• Pierron F., Identification of Poisson's ratios of standard and auxetic low density polymeric foams from full-field measurements Journal of Strain Analysis for Engineering Design, vol. 45, n° 4, pp. 233-253, 2010.
  2010 SAGE Best Paper Award for Journal of Strain Analysis for Engineering Design

Biomaterials

• Avril S., Huntley J.M., Pierron F., Steele D.D., 3D heterogeneous stiffness identification using MRI and the virtual fields method Experimental Mechanics, vol. 48, n° 4, pp. 479-494, 2008.
• Avril S., Badel P., Duprey A., Anisotropic and hyperelastic identification of in vitro human arteries from full-field optical measurements Journal of Biomechanics, vol. 43, pp. 2978-2985, 2010.

Industrial applications

• Kim J.-H., Nunio F., Pierron F., Védrine P., Identification of the mechanical properties of superconducting windings using the Virtual Fields Method IEEE Transactions on Applied Superconductivity, vol. 20, n° 3, pp. 1993–1997, 2010.
• Kim J.-H, Pierron F., Nunio F., Védrine P.,
  Characterizing elastic properties of superconducting windings by simulations and experiments
  Superconductor Science and Technology, in press, 2011.

High strain rate testing

• Pierron F., Sutton M.A., Tiwari V., Ultra high speed DIC and Virtual Fields Method analysis of a three point bending impact test on an aluminium bar Experimental Mechanics, vol. 51, n° 4, pp. 537-563, 2011.
• Moulart R., Pierron F., Hallett S.R., Wisnom M.R., Full-field strain measurement and identification of mechanical properties at high strain rate Experimental Mechanics, vol. 51, n° 4, pp. 509-536, 2011.

Identification simulator / test design and optilization

• Syed Muhammad K., Toussaint E., Grédiac M., Avril S., Kim J.-H., Characterization of composite plates using the virtual fields method using optimized loading conditions Composite Structures, vol. 85, n° 1, pp. 70-82, 2008.
• Syed Muhammad K., Toussaint E., Grédiac M., Optimization of a mechanical test on composite plates with the Virtual Fields Method Structural and Multidisciplinary Optimization, vol. 38, n° 1, pp. 71-82, 2009.
• Rossi M., Pierron F.,
  On the use of simulated experiments in designing tests for material characterization from full-field measurements
  International Journal of Solids and Structures, in press, 2011.