×

Characteristics of testing conditions for constitutive models in metal plasticity. (English) Zbl 1359.74048

Summary: We propose a method of identifying constitutive models and material parameters in engineering applications. The presented method is used in the setting of optimal experimental design and is based on successive optimization of a finite set of possible material models. The goal is, for an initially unknown material, to define an optimal test bed based on a given set of constitutive models and a range of possible parameters. As a result of the algorithm, suitable observation operators and external loads are identified. These are then the optimal experimental conditions under which the parameters of the unknown material are tested.

MSC:

74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)

Software:

IGPE
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Tonti, E.; Minati, G. (ed.); Pessa, E. (ed.); Abram, M. (ed.), The origin of analogies in physics, 695-706 (2006), New York · doi:10.1007/0-387-28898-8_49
[2] von Mises R (1928) Mechanik der plastischen Formänderung von Kristallen. Zeitschrift f Angewandte Mathematik u Mechanik 8(3):161-185 · JFM 54.0043.07 · doi:10.1002/zamm.19280080302
[3] Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond A193:281-297 · Zbl 0032.08805 · doi:10.1098/rspa.1948.0045
[4] Barlat F, Yoon J, Cazacu O (2007) On linear transformations of stress tensors for the description of plastic anisotropy. Int J Plast 23:876-896 · Zbl 1359.74014 · doi:10.1016/j.ijplas.2006.10.001
[5] Chaboche J (2008) A review of some plasticity and viscoplasticity constitutive theories. Int J Plast 24:1642-1693 · Zbl 1142.74012 · doi:10.1016/j.ijplas.2008.03.009
[6] Yoshida F, Uemori T (2003) A model of large-strain cyclic plasticity and its application to springback simulation. Int J Mech Sci 45:1687-1702 · Zbl 1049.74014 · doi:10.1016/j.ijmecsci.2003.10.013
[7] Ohno N, Wang J-D (1993) Kinematic hardening rules with critical state of dynamic recovery, Part I: formulation and basic features for ratchetting behavior. Int J Plast 9:375-390 · Zbl 0777.73017 · doi:10.1016/0749-6419(93)90042-O
[8] Kocks U, Mecking H (2003) Physics and phenomenology of strain hardening: the FCC case. Prog Mater Sci 48(3):171-273 · doi:10.1016/S0079-6425(02)00003-8
[9] Atkinson AC, Donev AN, Tobias RD (2007) Optimum experimental designs, with SAS. Vol 34 of Oxford statistical science series. Oxford University Press, Oxford · Zbl 1183.62129
[10] Bates DM, Watts DG (1988) Nonlinear regression analysis and its applications. Wiley, New York · Zbl 0728.62062 · doi:10.1002/9780470316757
[11] Engl HW, Hanke M, Neubauer A (1996) Regularization of inverse problems. Mathematics and its applications, vol 375. Kluwer, Dordrecht · Zbl 0859.65054
[12] Rieder A (2003) Keine Probleme mit inversen Problemen. Eine Einführung in ihre stabile Lösung [An introduction to their stable solution]. Friedrich Vieweg & Sohn, Braunschweig · Zbl 1057.65035
[13] Tarantola A (2005) Inverse problem theory and methods for model parameter estimation. SIAM, Philadelphia · Zbl 1074.65013
[14] Vogel CR (2002) Computational methods for inverse problems. Frontiers in applied mathematics, vol 24. SIAM, Philadelphia · Zbl 1008.65103
[15] Michalik C, Stuckert M, Marquardt W (2010) Optimal experimental design for discriminating numerous model candidates: the AWDC criterion. Ind Eng Chem Res 49(2):913-919 · doi:10.1021/ie900903u
[16] Mahnken R, Stein E (1996) A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Comput Methods Appl Mech Eng 136:225-258 · Zbl 0921.73143 · doi:10.1016/0045-7825(96)00991-7
[17] Han W, Reddy BD (1999) Plasticity. Interdisciplinary applied mathematics. Mathematical theory and numerical analysis, vol 9. Springer, New York · Zbl 0926.74001
[18] Kreißig R, Benedix U, Görke U-J, Lindner M (2007) Identification and estimation of constitutive parameters for material laws in elastoplasticity. GAMM-Mitt 30:458-480 · Zbl 1196.74165 · doi:10.1002/gamm.200790027
[19] Herzog R, Meyer C (2011) Optimal control of static plasticity with linear kinematic hardening. J Appl Math Mech 91(10):777-794 · Zbl 1284.49026
[20] Harth T, Lehn J (2007) Identification of material parameters for inelastic constitutive models using stochastic methods. GAMM-Mitt 30(2):409-429 · Zbl 1196.74016 · doi:10.1002/gamm.200790025
[21] Andrade-Campos A, Thulier S, Pilvin P, Teixeira-Dias F (2007) On the determination of material parameters for internal variable thermoelastic viscoplastic constitutive models. Int J Plast 23:1349-1379 · Zbl 1134.74325 · doi:10.1016/j.ijplas.2006.09.002
[22] Schnur DS, Zabaras N (1992) An inverse method for determining elastic material properties and a material interface. Int J Numer Methods Eng 33:2039-2057 · Zbl 0767.73078 · doi:10.1002/nme.1620331004
[23] Pukelsheim F (2006) Optimal design of experiments, vol 50 of Classics in applied mathematics. SIAM, Philadelphia. Reprint of the 1993 original · Zbl 0834.62068
[24] Uciński D (2005) Optimal measurement methods for distributed parameter system identification. CRC Press, Boca Raton · Zbl 1155.93003
[25] Atkinson AC, Fedorov VV (1975) The design of experiments for discriminating between two rival models. Biometrika 62:57-70 · Zbl 0308.62071 · doi:10.1093/biomet/62.1.57
[26] Atkinson AC, Fedorov VV (1975) Optimal design: experiments for discriminating between several models. Biometrika 62:289-303 · Zbl 0321.62085
[27] Box GEP, Hill WJ (1967) Discrimination among mechanistic models. Technometrics 9:57-71 · doi:10.1080/00401706.1967.10490441
[28] Buzzi-Ferraris G, Forzatti P (1983) A new sequential experimental design procedure for discriminating among rival models. Chem Eng Sci 38(2):225-232 · doi:10.1016/0009-2509(83)85004-0
[29] Froment G (1975) Model discrimination and parameter estimation in heterogenous catalysis. AICheE J 21:1041-1056 · doi:10.1002/aic.690210602
[30] Hunter WG, Reiner AM (1965) Design for discriminating between two rival models. Technometrics 7:307-323 · doi:10.1080/00401706.1965.10490265
[31] Akaike H (1974) A new look at statistical model identification. Autom Control 19:716-722 · Zbl 0314.62039 · doi:10.1109/TAC.1974.1100705
[32] Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach. Springer, New York · Zbl 1005.62007
[33] Bambach M, Heinkenschloss M, Herty M (2013) A method for model identification and parameter identification. Inverse Probl 29(2):025009 · Zbl 1334.65187 · doi:10.1088/0266-5611/29/2/025009
[34] Gill PE, Murray W, Wright MH (1981) Practical optimization. Academic Press, New York · Zbl 0503.90062
[35] Dennis JE Jr, Schnabel RB (1983) Numerical methods for unconstrained optimization and nonlinear equations. Prentice-Hall, Englewood Cliffs · Zbl 0579.65058
[36] Fletcher R (1987) Practical methods of optimization, 2nd edn. Wiley, New York · Zbl 0905.65002
[37] Nocedal J, Wright SJ (2006) Numerical optimization, 2nd edn. Springer, New York · Zbl 1104.65059
[38] Kelly CT (1999) Iterative methods for optimization. SIAM, Philadelphia · Zbl 0934.90082 · doi:10.1137/1.9781611970920
[39] Rall LB (1981) Automatic differentiation: techniques and applications. Lecture notes in computer science, vol 120. Springer, Berlin · Zbl 0473.68025
[40] Griewank A, Walther A (2008) Evaluating derivatives: principles and techniques of algorithmic differentiation, 2nd edn. No. 105 in Other titles in applied mathematics. SIAM, Philadelphia · Zbl 1159.65026
[41] Vladimirov IN, Pietryga MP, Reese S (2008) On the modeling of nonlinear kinematic hardening at finite strains with application to springback—comparison of time integration algorithms. Int J Numer Methods Eng 75:1-28 · Zbl 1195.74019 · doi:10.1002/nme.2234
[42] Vladimirov IN, Pietryga MP, Reese S (2009) Prediction of springback in sheet forming by a new finite strain model with nonlinear kinematic and isotropic hardening. J Mater Process Technol 209:4062-4075 · doi:10.1016/j.jmatprotec.2008.09.027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.