Stochastic approach to size effect in quasi-brittle materials

Comptes Rendus - Mecanique

Volumn 335, Issue 8, 2007, Pages 430-435

  Colliat, Jean Baptiste ^a   Hautefeuille, Martin ^a,b   Ibrahimbegovic, Adnan ^a   Matthies, Hermann G ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

Computational solid mechanics; Karhunen Lo ve expansion; Quasi brittle materials; Size effect

Indexed keywords

BRITTLENESS; MATERIALS SCIENCE; PROBLEM SOLVING; RANDOM PROCESSES;

BRITTLE MEDIUM; MONTE CARLO ANALYSIS; NUMERICAL MODEL; SIZE EFFECT; STOCHASTICITY; WEIBULL THEORY;

EID: 34548279854     PISSN: 16310721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crme.2007.06.005     Document Type: Article

References (22)

1. Ibrahimbegović A., and Brancherie D. Combined hardening and softening constitutive model of plasticity: precursor to shear line failure. Comp. Mech. 31 (2003) 88-100
2. Ibrahimbegović A. Mécanique non linéaire des solides déformables : formulation théorique et résolution numérique par éléments finis (2006), Lavoisier - Hermes Science
3. Weibull W. A statistical distribution function of wide applicability. J. Appl. Mech. 18 3 (1951) 293-297
4. Bažant Z.P. Probability distribution of energetic-statistical size effect in quasibrittle fracture. Prob. Eng. Mech. 19 (2004) 307-319
5. Sab K., and Lalaai I. Une approche unifiée des effets d'echelle dans les matériaux quasi fragiles. C. R. Acad. Sci. Paris II 316 9 (1993) 1187-1192
6. Carpenteri A. On the mechanics of quasi-brittle materials with a fractal microstructure. Eng. Frac. Mech. 70 (2003) 2321-2349
7. Hillerborg A., Modéer M., and Petersson P.E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res. 6 (1978) 773-782
8. Pijaudier-Cabot G., and Bažant Z.P. Nonlocal damage theory. J. Eng. Mech. 113 (1987) 1512-1533
9. Ibrahimbegovic A., and Melnyk S. Embedded discontinuity finite element method for modeling of localized failure in heterogeneous materials with structured mesh: an alternative to extended finite element method. Comput. Mech. 40 (2007) 149-155
10. Jirašek M. Comparative study on elements with embedded discontinuities. Comput. Meth. Appl. Mech. Eng. 188 (2000) 307-330
11. Ortiz M., Leroy Y., and Needleman A. A finite element method for localized failure analysis. Comput. Meth. Appl. Mech. Eng. 61 (1997) 189-214
12. Simo J.C., Olivier J., and Armero F. An analysis of strong discontinuity induced by strain softening solutions in rate-independent solids. J. Comput. Mech. 12 (1993) 277-296
13. Loève M. Probability Theory (1977), Springer-Verlag Berlin
14. Van Marcke E. Random Fields: Analysis and Synthesis (1983), MIT Press
15. Shannon C.E. A mathematical theory of communication. Bell System Tech. J. 27 (1948) 379-423 and 623-659
16. Soize C. Maximum Entropy Approach for modeling random uncertainties in transient elastodynamics. J. Acoust. Soc. Am. 109 5 (2001) 1979-1996
17. M. Hautefeuille, Lognormal random fields-mean and covariance, Internal report, 2006
18. Matthies H.G. Quantifying uncertainty: modern computational representation of probability and applications. In: Ibrahimbegovic A., and Kozar I. (Eds). Extreme Man-Made and Natural Hazards in Dynamics of Structures (2007), Springer, Berlin. 1-4020-5654-0
19. Hautefeuille M., Colliat J.B., and Ibrahimbegovic A. Stochastic approach for quasi-brittle failure of concrete structure. In: Ibrahimbegovic A., and Kozar I. (Eds). Extreme Man-Made and Natural Hazards in Dynamics of Structures (2007), Springer, Berlin. 1-4020-5654-0
20. Taylor R.L., and Zienkiewicz O.C. The Finite Element Method, vols. 1 and 2. sixth ed. (2005), Elsevier, Oxford
21. M. Krosche, R. Niekamp, H.G. Matthies, PLATON: A problem solving environment for computational steering of evolutionary optimisation on the grid, EUROGEN 2003, Barcelona
22. R. Niekamp, H.G. Matthies, CTL: a C++ Communication Template Library, GAMM Jahreshauptversammlung in Dresden, 21. 27 March 2004