From strain to stress using full-field data: Computationally efficient stress reconstruction

From strain to stress using full-field data: Computationally efficient stress reconstruction


download PDF

Abstract. Conventional stress reconstruction based on full-field strain measurements presents a major computational burden, especially when using standard implicit stress integration methods. This presents a notable challenge for inverse identification methods used to characterize the plasticity of metallic materials, particularly those reliant on stress reconstruction, such as the nonlinear sensitivity-based Virtual Fields Method (VFM). To reduce the computational effort, the full-field strain data are usually spatially and temporally down-sampled. However, for metals subject to nonlinear strain paths, this practice can lead to errors in the resulting stress states and compromise the accuracy of the nonlinear VFM. In this work, we introduce a highly efficient explicit stress reconstruction algorithm to reduce the computational challenges of repeated stress reconstruction which can be utilized in inverse identification methods such as nonlinear VFM.

Stress Reconstruction, Plasticity, Digital Image Correlation, Virtual Field Method

Published online 4/24/2024, 10 pages
Copyright © 2024 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: HALILOVIČ Miroslav, STARMAN Bojan, COPPIETERS Sam, From strain to stress using full-field data: Computationally efficient stress reconstruction, Materials Research Proceedings, Vol. 41, pp 1089-1098, 2024


The article was published as article 120 of the book Material Forming

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

[1] M. Grédiac, F. Pierron, S. Avril, E. Toussaint, and M. Rossi, “Virtual Fields Method,” in Full-Field Measurements and Identification in Solid Mechanics, John Wiley & Sons, Ltd, 2012, pp. 301–330.
[2] D. Claire, F. Hild, and S. Roux, “A finite element formulation to identify damage fields: the equilibrium gap method,” Int. J. Numer. Methods Eng., vol. 61, no. 2, pp. 189–208.
[3] E. Pagnacco, A. Moreau, and D. Lemosse, “Inverse strategies for the identification of elastic and viscoelastic material parameters using full-field measurements,” Mater. Sci. Eng. A, vol. 452–453, pp. 737–745.
[4] H. D. Bui, A. Constantinescu, and H. Maigre, “Numerical identification of linear cracks in 2D elastodynamics using the instantaneous reciprocity gap,” Inverse Probl., vol. 20, no. 4, p. 993.
[5] F. Mathieu, H. Leclerc, F. Hild, and S. Roux, “Estimation of Elastoplastic Parameters via Weighted FEMU and Integrated-DIC,” Exp. Mech., vol. 55, no. 1, pp. 105–119.
[6] J. Réthoré, Muhibullah, T. Elguedj, M. Coret, P. Chaudet, and A. Combescure, “Robust identification of elasto-plastic constitutive law parameters from digital images using 3D kinematics,” Int. J. Solids Struct., vol. 50, no. 1, pp. 73–85.
[7] A. P. Ruybalid, J. P. M. Hoefnagels, O. van der Sluis, and M. G. D. Geers, “Comparison of the identification performance of conventional FEM updating and integrated DIC,” Int. J. Numer. Methods Eng., vol. 106, no. 4, pp. 298–320.
[8] S. Coppieters and T. Kuwabara, “Identification of Post-Necking Hardening Phenomena in Ductile Sheet Metal,” Exp. Mech., vol. 54, no. 8, pp. 1355–1371.
[9] S. Coppieters, S. Cooreman, H. Sol, P. Van Houtte, and D. Debruyne, “Identification of the post-necking hardening behaviour of sheet metal by comparison of the internal and external work in the necking zone,” J. Mater. Process. Technol., vol. 211, no. 3, pp. 545–552.
[10] D. Lecompte, S. Cooreman, S. Coppieters, J. Vantomme, H. Sol, and D. Debruyne, “Parameter identification for anisotropic plasticity model using digital image correlation,” Eur. J. Comput. Mech., vol. 18, no. 3–4, pp. 393–418.
[11] A. Maček, B. Starman, N. Mole, and M. Halilovič, “Calibration of Advanced Yield Criteria Using Uniaxial and Heterogeneous Tensile Test Data,” Metals, vol. 10, no. 4, p. 542.
[12] S. Avril and F. Pierron, “General framework for the identification of constitutive parameters from full-field measurements in linear elasticity,” Int. J. Solids Struct., vol. 44, no. 14, pp. 4978–5002.
[13] M. Grédiac and F. Pierron, “Applying the Virtual Fields Method to the identification of elasto-plastic constitutive parameters,” Int. J. Plast., vol. 22, no. 4, pp. 602–627.
[14] M. Rossi and F. Pierron, “Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields,” Comput. Mech., vol. 49, no. 1, pp. 53–71.
[15] A. Lattanzi, F. Barlat, F. Pierron, A. Marek, and M. Rossi, “Inverse identification strategies for the characterization of transformation-based anisotropic plasticity models with the non-linear VFM,” Int. J. Mech. Sci., p. 105422.
[16] B. Rahmani, I. Villemure, and M. Levesque, “Regularized virtual fields method for mechanical properties identification of composite materials,” Comput. Methods Appl. Mech. Eng., vol. 278, pp. 543–566.
[17] L. Zhang et al., “Verification of a virtual fields method to extract the mechanical properties of human optic nerve head tissues in vivo,” Biomech. Model. Mechanobiol., vol. 16, no. 3, pp. 871–887.
[18] A. Marek, F. M. Davis, and F. Pierron, “Sensitivity-based virtual fields for the non-linear virtual fields method,” Comput. Mech., vol. 60, no. 3, pp. 409–431.
[19] M. Rossi, F. Pierron, and M. Štamborská, “Application of the virtual fields method to large strain anisotropic plasticity,” Int. J. Solids Struct., vol. 97–98, pp. 322–335.
[20] A. Marek, F. M. Davis, J.-H. Kim, and F. Pierron, “Experimental Validation of the Sensitivity-Based Virtual Fields for Identification of Anisotropic Plasticity Models,” Exp. Mech., vol. 60, no. 5, pp. 639–664.
[21] M. Rossi, A. Lattanzi, L. Cortese, and D. Amodio, “An approximated computational method for fast stress reconstruction in large strain plasticity,” Int. J. Numer. Methods Eng., vol. 121, no. 14, pp. 3048–3065.
[22] H. Takizawa et al., “Development of the User Subroutine Library ‘Unified Material Model Driver for Plasticity (UMMDp)’ for Various Anisotropic Yield Functions,” J. Phys. Conf. Ser., vol. 1063, no. 1, p. 012099.
[23] M. Halilovič, M. Vrh, and B. Štok, “NICE—An explicit numerical scheme for efficient integration of nonlinear constitutive equations,” Math. Comput. Simul., vol. 80, no. 294–313.
[24] M. Vrh, M. Halilovič, and B. Štok, “Improved explicit integration in plasticity,” Int. J. Numer. Methods Eng., vol. 81, no. 7, pp. 910–938.
[25] M. Halilovič, M. Vrh, and B. Štok, “NICE h: a higher-order explicit numerical scheme for integration of constitutive models in plasticity,” Eng. Comput., vol. 29, no. 1, pp. 55–70.
[26] M. Halilovic, B. Starman, M. Vrh, and B. Stok, “A robust explicit integration of elasto-plastic constitutive models, based on simple subincrement size estimation,” Eng. Comput.
[27] T. J. R. Hughes and J. Winget, “Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis,” Int. J. Numer. Methods Eng., vol. 15, no. 12, pp. 1862–1867.
[28] Y. Yamada, N. Yoshimura, and T. Sakurai, “Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method,” Int. J. Mech. Sci., vol. 10, no. 5, pp. 343–354.
[29] M. C. Oliveira, J. L. Alves, B. M. Chaparro, and L. F. Menezes, “Study on the influence of work-hardening modeling in springback prediction,” Int. J. Plast., vol. 23, no. 3, pp. 516–543.
[30] S. Yoon and F. Barlat, “Non-iterative stress integration method for anisotropic materials,” Int. J. Mech. Sci., vol. 242, p. 108003.
[31] S. Bossuyt, “Optimized Patterns for Digital Image Correlation,” in Imaging Methods for Novel Materials and Challenging Applications, Volume 3, H. Jin, C. Sciammarella, C. Furlong, and S. Yoshida, Eds., in Conference Proceedings of the Society for Experimental Mechanics Series. New York, NY: Springer, 2013, pp. 239–248.