Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper, we show that sensitivity analysis in connection with material parameter identification problems – using implicit finite elements of quasi-static problems on the basis of evolutionary-type constitutive equations – is related to simultaneous sensitivity equations and internal numerical differentiation. Thus, this study mainly focuses on investigating how these approaches are connected to the solution procedures based on finite elements. In addition, we discuss how to consider reaction forces in the sensitivity analysis, as this aspect is often neglected despite the fact that experimental results often involve force data.
Rocznik
Tom
Strony
113--126
Opis fizyczny
Bibliogr. 38 poz., tab.
Twórcy
autor
- Institute of Applied Mechanics Clausthal University of Technology Adolph-Roemer-Str. 2a, 38678 Clausthal-Zellerfeld, Germany
Bibliografia
- [1] W.P. Adamczyk, T. Kruczek, G. Moskal, R.A. Bialecki. Nondestructive technique of measuring heat conductivity of thermal barrier coatings. International Journal of Heat and Mass Transfer, 111: 442–450, 2017.
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- [3] K. Andresen, S. Dannemeyer, H. Friebe, R. Mahnken, R. Ritter, E. Stein. Parameter identifikation für ein plastisches Stoffgesetz mit FE-Methoden und Rasterverfahren [in German]. Bauingenieur, 71: 21–31, 1996.
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- [5] H.G. Bock. Recent advances in parameter identification techniques for ODEs. In C.W. Gear, T. Vu, P. Deuflhard, E. Hairer [Eds.], Numerical Treatment of Inverse Problems in Differential and Integral Equations, number 2 in Progress in Scientific Computing, pp. 95–121, Birkhäuser, Basel, 1983.
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- [8] A.M. Dunker. The decoupled direct method for calculating sensitivity coefficients in chemical kinetics. The Journal of Chemical Physics, 81, 1984.
- [9] P. Ellsiepen, S. Hartmann. Remarks on the interpretation of current non-linear finite-element-analyses as differential-algebraic equations. International Journal for Numerical Methods in Engineering, 51: 679–707, 2001.
- [10] P. Fritzen.Numerische Behandlung nichtlinearer Probleme der Elastizitäts- und Plastizitätstheorie. Doctoral thesis, Department of Mathematics, University of Darmstadt, 1997.
- [11] E. Hairer, G. Wanner. Solving Ordinary Differential Equations II. Springer, Berlin, 2nd revised edition, 1996.
- [12] S. Hartmann. A remark on the application of the Newton-Raphson method in non-linear finite element analysis. Computational Mechanics, 36(2): 100–116, 2005.
- [13] S. Hartmann, R.R. Gilbert. Identifiability of material parameters in solid mechanics. Published online Archive of Applied Mechanics, 2017.
- [14] S. Hartmann, K.J. Quint, A.-W. Hamkar. Displacement control in time-adaptive non-linear finite-element analysis. ZAMM Journal of Applied Mathematics and Mechanics,88(5): 342–364, 2008.
- [15] S. Hartmann, T. Tschöpe, L. Schreiber, P. Haupt. Large deformations of a carbon black-filled rubber. Experiment, optical measurement and parameter identification using finite elements. European Journal of Mechanics, Series A/Solids, 22: 309–324, 2003.
- [16] W. Hoyer, J.W. Schmidt. Newton-type decomposition methods for equations arising in network analysis. ZAMM Zeitschrift für Angewandte Mathematik und Mechanik, 64: 397–405, 1984.
- [17] N. Huber, C. Tsakmakis. Determination of constitutive properties from spherical indentation data using neural networks, Part I: plasticity with nonlinear and kinematic hardening. Journal of the Mechanics and Physics ofSolids, 47: 1589–1607, 1999.
- [18] N. Huber, C. Tsakmakis. Determination of constitutive properties from spherical indentation data using neural networks, Part II: the case of pure kinematic hardening in plasticity laws. Journal of the Mechanics and Physicsof Solids, 47: 1569–1588, 1999.
- [19] S. Krämer.Einfluss von Unsicherheiten in Materialparametern auf Finite-Elemente Simulationen [in German]. PhD Thesis, report no. 5/2016, Institute of Applied Mechanics, Clausthal University of Technology, Clausthal-Zellerfeld, 2016.
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- [21] R. Kreissig, U. Benedix, U.-J. Goerke. Statistical aspects of the identification of material parameters for elasto-plastic models. Archive of Applied Mechanics, 71: 123–134, 2001.
- [22] C.L. Lawson, R.J. Hanson.Solving least squares problems. SIAM Society for Industrial and Applied Mathematics, Philadelphia, 1995.
- [23] H. Lee, J.H. Lee, G.M. Pharr. A numerical approach to spherical indentation techniques for material propertyevaluation. Journal of the Mechanics and Physics of Solids, 53: 2037–2069, 2005.
- [24] J.R. Leis, M.A. Kramer. The simultaneous solution and sensitivity analysis of systems described by ordinary differential equations. ACM Transactions on Mathematical Software, 14: 45–60, 1988.
- [25] R. Mahnken, E. Stein. A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Computer Methods in Applied Mechanics and Engineering, 136: 225–258, 1996.
- [26] R. Mahnken, E. Stein. Parameter identification for finite deformation elasto-plasticity in principal directions. Computer Methods in Applied Mechanics and Engineering, 147: 17–39, 1997.
- [27] T. Netz, A.-W. Hamkar, S. Hartmann. High-order quasi-static finite element computations in space and time with application to finite strain viscoelasticity. Computers and Mathematics with Applications,66: 441–459, 2013.
- [28] J. Nocedal, S.J. Wright. Numerical Optimization. Springer, New York, 1999.
- [29] K.J. Quint. Thermomechanically coupled processes for functionally graded materials: experiments, modelling, and finite element analysis using high-order DIRK-methods. PhD Thesis, report no. 2/2012, Institute of Applied Mechanics, Clausthal University of Technology, Clausthal-Zellerfeld, 2012.
- [30] N.B.G. Rabbat, A.L. Sangiovanni-Vincentelli, H.Y. Hsieh. A multilevel Newton algorithm with macromodeling and latency for the analysis of large-scale nonlinear circuits in the time domain. IEEE Transactions on Circuits and Systems, 26: 733–740, 1979.
- [31] G. Rauchs, J. Bardon, D. Georges. Identification of the material parameters of a viscous hyperelastic constitutive law from spherical indentation tests of rubber and validation by tensile tests. Mechanics of Materials, 42: 961–973, 2010.
- [32] S. Rothe, P. Erbts, A. Düster, S. Hartmann. Monolithic and partitioned coupling schemes for thermo-viscoplasticity. Computer Methods in Applied Mechanics and Engineering, 293: 375–410, 2015.
- [33] G. Scheday.Theorie und Numerik der Parameteridentifikation von Materialmodellen der finiten Elastizität und Inelastizität auf der Grundlage optischer Feldmessmethoden [in German]. PhD Thesis, Report No. I-11 (2003),University of Stuttgart (Germany), Institute of Mechanics, 2003.
- [34] K. Schittkowski. Numerical Data Fitting in Dynamical Systems. Kluwer Academic Publ., Dordrecht, 2002.
- [35] S. Schmaltz, K. Willner. Material parameter identification utilizing optical full-field strain measurement and digital image correlation. Journal of the Japanese Society for Experimental Mechanics, 13: s120–s125, 2013.
- [36] D.S. Schnur, N. Zabaras. An inverse method for determining elastic material properties and a material interface. International Journal for Numerical Methods in Engineering, 33: 2039–2057, 1992.
- [37] P. Shi, I. Babuška. Analysis and computation of a cyclic plasticity model by aid of Ddassl. Computational Mechanics, 19: 380–385, 1997.
- [38] J. Wittekindt. Die numerische Lösung von Anfangs-Randwertproblemen zur Beschreibung inelastischen Werkstoffverhaltens [in German]. Doctoral Thesis, Department of Mathematics, University of Darmstadt, 1991.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8d3f0044-fd2e-4809-914d-f63758748230