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Identification of material parameters for inelastic constitutive models using stochastic methods. (English) Zbl 1196.74016

Summary: The parameters of a constitutive model are usually identified by minimization of the distance between model response and experimental data. However, measurement failures and differences in the specimens lead to deviations in the determined parameters. In this article we present our results of a study of these uncertainties for two constitutive models of Chaboche-type. The models differ only by a kinematic hardening variable. It turns out, that the kinematic hardening variable proposed by Haupt, Kamlah, and Tsakmakis yields a better description quality than the one of Armstrong and Frederick. For the parameter optimization as well as for the study of the deviations of the fitted parameters we apply stochastic methods. The available test data result from creep tests, tension-relaxation tests and cyclic tests performed on AINSI SS316 stainless steel at 600OC. Since the amount of test data is too small for a proper statistical analysis we apply a stochastic simulation technique to generate artificial data which exhibit the same stochastic behaviour as the experimental data.

MSC:

74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74P99 Optimization problems in solid mechanics
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[1] Materials with Memory: Initial-Boundary Value Problems for Constitutive Equations with Internal Variables, series: Lecture Notes in Mathematics Vol. 1682 (Springer Verlag, Berlin, 1998).
[2] and , A Mathematical Representation of the Multiaxial Bauschinger Effect, CEGB report RD/B/N731 (1966).
[3] , , , Quantitative Assessment of the Accuracy of Constitutive Laws for Plasticity with an Emphasis on Cyclic Deformation, Technical Note BN-1146, University of Maryland, College Park (1993).
[4] Nonlinear Parameter Estimation (Academic Press, Inc., New York, 1974).
[5] Bodner, Journal of Applied Mechanics 42 pp 385– (1975)
[6] Unified Plasticity for Engineering Applications, Mathematical Concepts and Methods in Science and Engineering 47 (Kluwer Academic / Plenum Publishers, New York, 2002).
[7] Analysis of Scattering Material Behaviour in Constitutive Models, Bericht Nr. 93- 75, Institut für Statik der Technischen Universität Braunschweig, 1–14 (1993).
[8] Brokate, Int. Ser. Numer. Math. 126 pp 67– (1998)
[9] Bruhns, Int. J. Plasticity 15 pp 1311– (1999)
[10] Chaboche, Bulletin de l’Academie Polonaise des Sciences, Série Sc. et Techn. 15 pp 33– (1977)
[11] Chaboche, Int. J. Plasticity 5 pp 283– (1989) · Zbl 0695.73001
[12] Chaboche, Journal of Pressure Vessel Technology 105 pp 153– (1983)
[13] Chelminski, Cont. Mech. Thermodyn. 15 pp 221– (2003)
[14] Chan, Journal of Engineering Materials and Technology 110 pp 1– (1988)
[15] Untersuchungen zur Parameteridentifikation für das phänomenologische Modell nach Nouailhas et al. und das kristallographische Modell nach Méric et al. am Beispiel der einkristallinen Nickel-Basis-Legierung CMSX-4, Dissertation, Technische Universität Darmstadt (1999).
[16] Stochastic Analysis of Multivariate Systems in Computational Mechanics and Engineering, (CIMNE, Barcelona, 1999). · Zbl 0959.00016
[17] Eichenauer, Statistical Papers 27 pp 315– (1986)
[18] Eichenauer-Herrmann, Math. Comp. 60 pp 375– (1993)
[19] , and , Solving Ordinary Differential Equations I, (Springer Verlag, Heidelberg, 1987).
[20] Identification of Material Parameters for Inelastic Constitutive Models: Stochastic Simulation and Design of Experiments, Dissertation, Technische Universität Darmstadt (2003).
[21] Harth, Identification of Material Parameters for Inelastic Constitutive Models: Stochastic Simulation, in: Deformation and Failure in Metallic Materials, edited by K. Hutter and H. Baaser, Lecture Notes in Applied and Computational Mechanics · Zbl 1037.74002
[22] Harth, Int. J. Plasticity 20 pp 1403– (2004)
[23] Hartmann, Acta Mechan. 69 pp 139– (1987)
[24] Haupt, Nuclear Engineering and Design 162 pp 13– (1996)
[25] Haupt, Int. J. Plasticity 8 pp 803– (1992)
[26] Anwendung Neuronaler Netze bei nichtlinearen Problemen der Mechanik, Habilitationsschrift, Wissenschaftliche Berichte FZKA 6504 (2000).
[27] Krempl, Mechanics of Materials 5 pp 35– (1986) · Zbl 0611.73045
[28] Kunkel, Acta Mechan. 124 pp 27– (1997)
[29] and , Mechanics of Solid Materials (Cambridge University Press, 1990).
[30] Mahnken, Int. J. Plasticity 12 pp 451– (1996)
[31] Mahnken, Engineering Computations 15 pp 925– (1998)
[32] Mücke, Technische Mechanik 20 pp 61– (2000)
[33] , and , Stochastische Suchverfahren (Verlag Harry Deutsch, Thun u. Frankfurt/Main, 1986).
[34] , , and , Numerical Recipes in C - The Art of Scientific Computing, Second Edition (Univ. Press, Cambridge, 1994).
[35] A Controlled Random Search Procedure for Global Optimization, in: Towards Global Optimization 2, edited by L.C.W. Dixon and G.P. Szegö (North-Holland Publishing Company, Amsterdam, 1978), pp. 71–84.
[36] and , Achieving Design Targets through Stochastic Simulation, Madymo User’s Conference, Paris (2000).
[37] Identifikation der Parameter inelastischer Werkstoffmodelle: Statistische Analyse und Versuchsplanung, Dissertation, Technische Universität Darmstadt (2000).
[38] Simulationstechniken zur Untersuchung der Streuungen bei der Identifikation der Parameter inelastischerWerkstoffmodelle, Dissertation, FachbereichMathematik der Technischen Hochschule Darmstadt (1996).
[39] Seibert, Continuum Mechanics and Thermodynamics 12 pp 95– (2000)
[40] Steck, Int. J. Plasticity 1 pp 243– (1985)
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