Skip to main content
SpringerLink
Log in

An entropic optimization approach for a parameter identification problem in quasibrittle fracture

  • Industrial Applications
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

The cohesive crack model is a widely used idealization to represent simply and reliably the quasibrittle fracture behavior of concrete-like materials. However, knowledge of the parameters characterizing this model is of prime importance and cannot all be obtained directly from experiments. Typically, recourse is made to some inverse numerical approach. Our particular formulation can be elegantly cast as an instance of a challenging optimization problem known as a mathematical program with equilibrium (or, more precisely in our case, complementarity) constraints (MPEC). The present paper investigates application of an entropic optimization approach to solve the MPEC, and compares its performance with our previously proposed Fischer–Burmeister smoothing scheme. We use actual experimental data for the comparison.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barenblatt, G.I. 1962: The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech7, 55–129

    Google Scholar 

  2. Birbil, S.I.; Fang, S.-C.; Han, J. 2003: Entropic regularization approach for mathematical programs with equilibrium constraints. ERIM Research Report Series ERS-2002-71-LIS, Erasmus Research Institute for Management, Erasmus University, Rotterdam, The Netherlands

  3. Bolzon, G.; Ghilotti, D.; Maier, G. 1997: Parameter identification of the cohesive crack model. In: Sol, H.; Oomens, C.W.J. (eds.) Material identification using mixed numerical and experimental methods, pp. 213–222, Dordrecht: Kluwer Academic

  4. Bolzon, G.; Maier, G.; Novati, G. 1994: Some aspects of quasi-brittle fracture analysis as a linear complementarity problem. In: Bažant, Z.P.; Bittnar, Z.; Jirásek, M.; Mazars, J. (eds.) Fracture and damage in quasibrittle structures, pp. 159–174, London: E&FN Spon

  5. Brooke, A.; Kendrick, D.; Meeraus, A.; Raman, R. 1998: GAMS: a user’s guide. Gams Development Corporation, Washington DC 20007

  6. Carpinteri, A. 1989: Cusp catastrophe interpretation of fracture instability. J Mech Phys Solids37, 567–582

    Google Scholar 

  7. Denarié, E.; Saouma, V.E.; Iocco, A.; Varelas, D. 2001: Concrete fracture process zone characterization with fiber optics. J Eng Mech ASCE127, 494–502

    Google Scholar 

  8. Dirkse, S.P.; Ferris, M.C. 1995: The PATH solver: a non-monotone stabilization scheme for mixed complementarity problems. Optim Methods Softw5, 123–156

  9. Dolan, E.D.; Fourer, R.; Moré, J.J.; Munson, T.S. 2002: Optimization on the NEOS server. SIAM News35, 8–9

    Google Scholar 

  10. Drud, A. 1994: CONOPT – a large-scale GRG code. ORSA J Comput6, 207–216

    Google Scholar 

  11. Dugdale, D.S. 1960: Yielding of steel sheets containing slits. J Mech Phys Solids8, 100–104

    Google Scholar 

  12. Facchinei, F.; Jiang, H.; Qi, L. 1999. A smoothing method for mathematical programs with equilibrium constraints. Math Program85, 107–134

    Google Scholar 

  13. Fang, S.C.; Rajasekera, J.R.; Tsao, H.S. 1997: Entropy optimization and mathematical programming. Norwell:Kluwer Academic

  14. Hillerborg, A.; Modéer, M.; Petersson, P.E. 1976: Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res6, 773–782

    Google Scholar 

  15. Kanzow, C. 1996. Some noninterior continuation methods for linear complementarity problems. SIAM J Matrix Anal Appl17, 851–868

    Google Scholar 

  16. Luo, Z.Q.; Pang, J.S.; Ralph, D. 1996: Mathematical programs with equilibrium constraints. Cambridge: Cambridge University Press

  17. Maier, G. 1981: Inverse problem in engineering plasticity: a quadratic programming approach. Academia Nazionale dei LinceiLXX (Serie VIII), 203–209

  18. Olsen, D.H. 1998: Concrete fracture and crack growth: a fracture mechanics approach. Department of Structural Engineering and Materials. Report No. 42, Series R, Technical University of Denmark

  19. Tin-Loi, F.; Li, H. 2000: Numerical simulations of quasibrittle fracture processes using the discrete cohesive crack model. Int J Mech Sci42, 367–379

    Google Scholar 

  20. Tin-Loi, F.; Que, N.S. 2001: Parameter identification of quasibrittle materials as a mathematical program with equilibrium constraints. Comput Methods Appl Mech Eng190, 5819–5836

    Google Scholar 

  21. Tin-Loi, F.; Que, N.S. 2002a: Nonlinear programming approaches for an inverse problem in quasibrittle fracture. Int J Mech Sci44, 843–858

  22. Tin-Loi, F.; Que, N.S. 2002b: Identification of cohesive crack fracture parameters by evolutionary search. Comput Methods Appl Mech Eng191, 5741–5760

  23. Tin-Loi, F.; Xia, S.H. 2001: Holonomic softening: models and analysis. Mech Struct Mach29, 65–84

    Google Scholar 

  24. Wittmann, F.H. (ed.) 1996: Fracture mechanics of concrete structures, Vol. III. Freiburg, Germany: AEDIFICATIO Publishers

Download references

Author information

Authors and Affiliations

  1. School of Civil and Environmental Engineering, University of New South Wales, Sydney, 2052, Australia

    F. Tin-Loi

Authors
  1. F. Tin-Loi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Tin-Loi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tin-Loi, F. An entropic optimization approach for a parameter identification problem in quasibrittle fracture. Struct Multidisc Optim 28, 442–450 (2004). https://doi.org/10.1007/s00158-004-0453-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-004-0453-5

Keywords

Search

Navigation