Abstract
The material parameters of a constitutive model have to be identified by minimization of the distance between the model response and the experimental data using an appropriate optimization algorithm. However, measurement failures and differences in the specimens lead to uncertainties in the determined parameters. Since the amount of test data is not sufficient for a statistical analysis, a method of stochastic simulation is introduced in order to generate artificial data with the same behaviour as the experimental data. The stochastic simulations are validated by comparing the results of the parameter fits from artificial data with the results from experimental data. Furthermore, the results of the parameter identification for different inelastic constitutive models are presented and a principal component analysis is performed to study the correlation structure of the estimated material parameters. The presented simulation method is a suitable tool for various kinds of analysis purposes since the artificial data presents an alternative to a high amount of experimental data.
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References
Bard, Y. (1974) Nonlinear Parameter Estimation. Academic Press, Inc., New York
Bodner, S R., Partom, Y. (1975) Constitutive Equations for Elastic-Viscoplastic Strain Hardening Materials. Journal of Applied Mechanics 42, 385–389
Bodner, S.R (2002) Unified Plasticity for Engineering Applications. Mathematical Concepts and Methods in Science and Engineering 47, Kluwer Academic / Plenum Publishers, New York
Brockwell, P.J., Davis, R.A. (1991) Time Series: Theory and Methods, Second Edition, Springer Verlag, New York
Bruhns, O., Anding, D.K. (1999) On the Simultaneous Estimation of Model Parameters Used in Constitutive Laws for Inelastic Material Behaviour. Int. J. Plasticity 15 (12), 1311–1340.
Chaboche, J.L. (1977) Viscoplastic Constitutive Equations for the Description of Cyclic and Anisotropic Behaviour of Metals. Bulletin de l’Academie Polonaise des Sciences, Série Sc. et Techn. 15 (1), 33–41
Chaboche, J.L. (1989) Constitutive Equations for Cyclic Plasticity and Cyclic Viscoplasticity. Int. J. Plasticity 5, 283–295
Chaboche, J.L., Rousselier, G. (1983) On the Plastic and Viscoplastic Constitutive Equations-Part I: Rules Developed with Internal Variable Concept. Journal of Pressure Vessel Technology 105, 153–158
Chan, K S., Bodner, S R., Lindholm, U.S. (1988) Phenomenological Modelling of Hardening and Thermal Recovery in Metals. Journal of Engineering Materials and Technology 110, 1–8
Doltsinis, I. (1999) Stochastic Analysis of Multivariate Systems in Computational Mechanics and Engineering. CIMNE, Barcelona
Eichenauer, J., Lehn, J. (1986) A Non-linear Congruential Pseudo Random Number Generator. Statistical Papers 27, 315–326
Hartmann, G., Kollmann F.G. (1987) A Computational Comparison of the Inelastic Constitutive Models of Hart and Miller. Acta Mechan. 69, 139–165
Haupt, P., Kamlah, M., Tsakmakis, Ch. (1992) Continuous Representation of Hardening Properties in Cyclic Plasticity. Int. J. Plasticity 8, 803–817
Huber, N. (2000) Anwendung Neuronaler Netze bei nichtlinearen Problemen der Mechanik. Habilitationsschrift, Wissenschaftliche Berichte FZKA 6504
Kennedy, W.J. Jr., Gentle, J.E. (1980) Statistical Computing. Statistics: Textbooks and Monographs 33, Marcel Dekker, Inc., New York
Krempl, E., McMahon, J.J., Yao, D. (1986) Viscoplasticity Based on Overstress with a Differential Growth Law for the Equilibrium Stress. Mechanics of Materials 5, 35–48
Kunkel, R., Kollmann F.G. (1997) Identification of Constants of a Viscoplastic Constitutive Model for a Single Crystal Alloy. Acta Mechan. 124, 27–45
Lehmann, E.L. (1975) Nonparametrics: Statistical Methods Based on Ranks. McGraw-Hill
Lemaitre, J., Chaboche, J.L. (1990) Mechanics of Solid Materials. Cambridge University Press
Mahnken, R., Stein, E. (1996) Parameter Identification for Viscoplastic Models Based on Analytical Derivatives of a Least-squares Functional and Stability Investigations. Int. J. Plasticity 12 4, 451–479
More, J.J. (1977) The Levenberg-Marquard Algorithm: Implementation and Theory. Lecture Notes Math. 630, Springer Verlag, Berlin — Heidelberg — New York, 105–116
Müüller, PH., Nollau, V., Polovinkin, A.I. (1986). Stochastische Suchverfahren. Verlag Harry Deutsch, Thun u. Frankfurt/Main
Price, W.L. (1978) A Controlled Random Search Procedure for Global Optimization. In: Dixon, L.C.W., Szegö, G.P., Towards Global Optimization 2, North-Holland Publishing Company, Amsterdam, pp. 71–84
Reuter, R., Hülsmann, J. (2000) Achieving Design Targets through Stochastic Simulation. Madymo User’s Conference, Paris
Schwan, S. (2000) Identifikation der Parameter inelastischer Werkstoffmodelle: Statistische Analyse und Versuchsplanung. Dissertation, Technische Universität Darmstadt
Schwan, S., Lehn, J., Harth, T., Kollmann, F.G. (2002) Identification of Material Parameters for Inelastic Constitutive Models, Part I: Stochastic Methods. Int. J. Plasticity, submitted
Schwan, S., Lehn, J., Harth, T., Kollmann, F.G. (2002) Identification of Material Parameters for Inelastic Constitutive Models, Part II: Statistical Analysis and Design of Experiments. Int. J. Plasticity, submitted
Seibert, T. (1996) Simulationstechniken zur Untersuchung der Streuungen bei der Identifikation der Parameter inelastischer Werkstoffmodelle. Dissertation, Fachbereich Mathematik der Technischen Hochschule Darmstadt
Seibert, T., Lehn, J., Schwan, S., Kollmann, F.G. (2000) Identification of Material Parameters for Inelastic Constitutive Models: Stochastic Simulations for the Analysis of Deviations. Continuum Mechanics and Thermodynamics 12, 95–120
Senchenkov, I.K., Tabieva, G.A. (1996) Determination of the Parameters of the Bodner-Partom Model for Thermoviscoplastic Deformation of Materials. International Applied Mechanics 32 (2), 132–139
Steck, E.A. (1985) A Stochastic Model for the High-Temperature Plasticity of Metals. Int. J. Plasticity 1, 243–258
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Harth, T., Lehn, J., Kollmann, F.G. (2003). Identification of Material Parameters for Inelastic Constitutive Models: Stochastic Simulation. In: Hutter, K., Baaser, H. (eds) Deformation and Failure in Metallic Materials. Lecture Notes in Applied and Computational Mechanics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36564-8_6
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DOI: https://doi.org/10.1007/978-3-540-36564-8_6
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