Stochastic calibration of local constitutive models through measurements at the macroscale in heterogeneous media

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 37-40, 2006, Pages 4971-4990

  Fedele, R ^a   Maier, G ^a   Whelan, M ^b  

^a POLITECNICO DI MILANO   (Italy)

^b JOINT RESEARCH CENTRE   (Italy)

Author keywords

Composites; Heterogeneous materials; Homogenization; Inverse problems; Monte Carlo simulation; Non linear filters; Parameter identification; Weighted least squares

Indexed keywords

COMPUTER SIMULATION; DUCTILITY; ELASTOPLASTICITY; HARDENING; IDENTIFICATION (CONTROL SYSTEMS); INVERSE PROBLEMS; MATHEMATICAL MODELS; MECHANICAL PROPERTIES; MONTE CARLO METHODS; PERFORATING; RANDOM PROCESSES;

HETEROGENEOUS MATERIALS; HOMOGENIZATION; NON-LINEAR FILTERS; WEIGHTED LEAST-SQUARES;

STEEL SHEET;

COMPUTER SIMULATION; DUCTILITY; ELASTOPLASTICITY; HARDENING; IDENTIFICATION (CONTROL SYSTEMS); INVERSE PROBLEMS; MATHEMATICAL MODELS; MECHANICAL PROPERTIES; MONTE CARLO METHODS; PERFORATING; RANDOM PROCESSES; STEEL SHEET;

EID: 33744923984     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.07.026     Document Type: Article

References (47)

1. van Rens B., Brekelmans W., and Baaijens F. Homogenization of the elastoplastic behavior of perforated plates. Comput. Struct. 69 (1998) 537-545
2. van der Sluis O., Schreurs P., and Brekelman W. Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructural modelling. Mech. Mater. 32 (2000) 449-462
3. Carvelli V., Maier G., and Taliercio A. Kinematic limit analysis of periodic heterogeneous media. Comput. Model. Engrg. Sci. 1 1 (2000) 15-26
4. Maier G., and Carvelli V. A kinematic method for shakedown and limit analysis of periodic composites. In: Weichart D., and Maier G. (Eds). Inelastic Behaviour of Structures Under Variable Repeated Loads. CISM Lecture Notes vol. 432 (2001) 115-132
5. Lee Y., and Chen F. Yield criterion for a perforated sheet with a uniform triangular pattern of round holes and low ligament ratio. J. Mater. Proc. Tech. 103 (2000) 353-361
6. Yoshida F., Urabe M., Hino R., and Toropov V. Inverse approach to identification of material parameters of cyclic elasto-plasticity for component layers of a bimetallic sheet. Int. J. Plasticity 19 (2003) 2149-2170
7. In: Mróz Z., and Stavroulakis G. (Eds). Parameter Identification of Materials and Structures. CISM Lecture Notes vol. 469 (2004), Springer-Verlag, Wien
8. Chaboche J., and Rousselier G. On the plastic and viscoplastic constitutive equations-Part ii: Application of the internal variable concept to the 316 stainless steel. J. Press. Vess. Tech. ASME 105 (1983) 159-164
9. Kaliszky S. Plasticity: Theory and Engineering Applications (1990), Elsevier, Amsterdam
10. Fedele R., Filippini M., and Maier G. Constitutive model calibration for railway wheel steel through tension-torsion tests. Comput. Struct. 83 (2005) 1005-1020
11. Suquet P. Elements of homogenization for inelastic solid mechanics. In: Sanchez-Palencia E., and Zaoui A. (Eds). Homogenization Techniques for Composite Media. CISM Lecture Notes (1987), Springer-Verlag, Wien 194-280
12. Anthoine A. Derivation of the in-plane elastic characteristics of masonry through homogenization theory. Int. J. Solids Struct. 32 2 (1995) 137-163
13. Taliercio A., and Coruzzi R. Mechanical behaviour of brittle matrix composites: a homogenization approach. Int. J. Solids Struct. 36 (1999) 3591-3615
14. Michel J., Moulinec H., and Suquet P. Effective properties of composite materials with periodic microstructure: a computational approach. Comput. Methods Appl. Mech. Engrg. 172 (1999) 109-143
15. Bolzon G., Ghilotti D., and Maier G. Strength of periodic elastic-brittle composites evaluated through homogenization and parameter identification. Eur. J. Mech.-A/Solids 21 (2002) 355-378
16. Abaqus, Release 6.3. Theory and User's manuals, Hibbit, Karlsson and Sorensen Inc., Pawtucket, RI, USA, 2003.
17. Anthoine A. Homogenization of periodic masonry: plane stress, generalized plane strain or 3d modelling?. Commun. Numer. Meth. Engrg. 13 (1997) 319-326
18. Maier G. Inverse problem in engineering plasticity: a quadratic programming approach. Rend. Acc. Naz. Lincei 4 (1981) 201-209
19. Maier G., Giannessi F., and Nappi A. Indirect identification of yield limits by mathematical programming. J. Engrg. Struct. 4 (1982) 86-98
20. Bruhns O., and Anding D. On the simultaneous estimation of model parameters used in constitutive laws for inelastic material behaviour. Int. J. Plasticity 15 (1999) 1311-1340
21. Harth T., Schwan S., Lehn J., and Kollmann F. Identification of material parameters for inelastic constitutive models: statistical analysis and design of experiments. Int. J. Plasticity 20 (2004) 1403-1440
22. Tarantola A. Inverse Problems Theory. Methods for Data Fitting and Model Parameter Elsevier Applied Science (1987), Elsevier Applied Science, Southampton
23. Bui H. Inverse Problems in the Mechanics of Materials: An Introduction (1994), CRC Press, London
24. Papadrakakis M., Papadopoulos V., and Lagaros N. Structural reliability analysis of elastic-plastic structures using neural networks and Monte Carlo simulation. Comput. Methods Appl. Mech. Engrg. 136 1-2 (1996) 145-163
25. Ditlevsen O., and Madsen H. Structural Reliability Methods (1996), John Wiley & Sons, New York
26. Olsson A., Sandberg G., and Dahlblom O. On latin hypercube sampling for structural reliability analysis. Struct. Safety 25 (2003) 47-68
27. Anderson T. An Introduction to Multivariate Statistical Analysis. third ed. (2003), John Wiley & Sons, New York
28. Catlin D. Estimation, Control and the Discrete Kalman Filter (1989), Springer-Verlag, Applied Mathematical Sciences, Berlin
29. Kailath T., Sayed A., and Hassibi B. Linear Estimation (2000), Prentice Hall, London
30. Bittanti S., Maier G., and Nappi A. Inverse problems in structural elasto-plasticity: a Kalman filter approach. In: Sawczuk A., and Bianchi G. (Eds). Plasticity Today, CISM Book (1984), Elsevier Applied Science Publishers, London 311-329
31. Gelb A. Applied Optimal Estimation (1992), The MIT Press, Cambridge
32. Bolzon G., Fedele R., and Maier G. Parameter identification of a cohesive crack model by Kalman filter. Comput. Methods Appl. Mech. Engrg. 191 (2002) 2847-2871
33. Lemenager E., and Bouet T. Kalman filtering: a new approach for building global approximations. Application to the inverse optimization of an explosively formed penetrator. Struct. Opt. 14 (1997) 158-164
34. Corigliano A., and Mariani S. Parameter identification in explicit structural dynamics: performance of the extended Kalman filter. Comput. Methods Appl. Mech. Engrg. 193 36 (2004) 3807-3835
35. S. Julier, J. Uhlman, A general method for approximating nonlinear transformations of probability distributions, Robotics Research Group, Department of Engineering Science, University of Oxford, Available from: .
36. Bohn C., and Unbehauen H. The application of matrix differential calculus for the derivation of simplified expressions in approximate nonlinear filtering algorithms. Automatica 36 (2000) 1553-1560
37. Norgaard M., Pulsen N., and Ravn O. New developments in state estimation for nonlinear systems. Automatica 36 (2000) 1627-1638
38. Kazafumi I., and Kaiqi X. Gaussian filters for nonlinear filtering problems. IEEE Trans. Automat. Control 45 5 (2000) 910-927
39. Bazaraa M., Sherali H., and Shetty C. Nonlinear Programming. Theory and Algorithms (1993), John Wiley & Sons, New York
40. Coleman T., and Li Y. An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Opt. 6 2 (1996) 418-445
41. Matlab6.5, Optimization Toolbox Manual, The MathWorks Inc., 2003.
42. Bates D., and Watts D. Nonlinear Regression Analysis and its Applications (1988), John Wiley & Sons, New York
43. Ishikawa H., and Sasaki K. Deformation induced anisotropy and memorized back stress in constitutive model. Int. J. Plasticity 14 7 (1998) 627-646
44. Li S., Hoferlin E., Baela A., Houtte P., and Teodosiu C. Finite element modeling of plastic anisotropy induced by texture and strain-path change. Int. J. Plasticity 19 5 (2003) 647-674
45. Zahl D., and McMeeking M. The influence of residual stress on the yielding of metal matrix composites. Acta Metall. Mater. 39 6 (1991) 1117-1122
46. Bolzon G., Maier G., and Panico M. Material model calibration by indentation, imprint mapping and inverse analysis. Int. J. Solids Struct. 41 (2004) 2957-2975
47. Bocciarelli M., Bolzon G., and Maier G. Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping. Mech. Mater. 37 8 (2005) 855-868