• J.G.M. van Mier
Conference paper


Different fracture models for brittle disordered materials require varying empirical c ntent in the form of model parameters that, somehow, must be measured in an experiment. The success of a model to ‘predict ’ situations hitherto unexplored by experiment depends on the correctness of the empirical content of the model, i.e. on the success in capturing material behaviour in the said model parameters. For fracture this seems only possible when the model is capable of simulating fracture mechanisms to a high degree of accuracy in the first place. Different models may be applicable at different scale levels, use may be limited by constraints from the roughness of the material structure itself (RVE), but in the end when fracture becomes fatal, specimens/structures are separated into two or more distinct parts separated by localised macrocracks of size similar to the characteristic size of the considered specimen/structure. In particular deriving correct empirical content for the localisation stage is extremely difficult due to intertwining of material and structural effects. In classical fracture mechanics these effects are elegantly taken care of in the structure of the theory, but in models based on continuum principles, the link between material and structure is lost, resulting in tremendous difficulties in determining the empirical content. The solution must be found in physics-based approaches, which are based on correctly simulating fracture mechanisms in the first place


Fracture Model Interfacial Transition Zone Empirical Content Initial Notch Cohesive Crack Model 
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  1. 1.
    M.F. Kaplan, Crack propagation and the fracture of concrete, ACI Journal, 58(5), 591–610 (1961).Google Scholar
  2. 2.
    J.G.M. van Mier, in: Scaling Laws in Ice Mechanics and Ice Dynamics, edited by J. Dempsey and H.H. Shen (Kluwer Academic Publishers, Dordrecht, 2001), pp. 171–182.Google Scholar
  3. 3.
    R.H. Evans and H.S. Marathe, Microcracking and stress-strain curves for concrete in tension, Mater. Struct. (RILEM), 1, 61–64 (1968)Google Scholar
  4. 4.
    A. Hillerborg, M. Modéer and P.-E.Peterson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cem.Conc.Res., 6(6), 773–782 (1976).CrossRefGoogle Scholar
  5. 5.
    J.G.M. van Mier, and Ch. Shi, Stability issues in uniaxial tensile tests on brittle disordered materials, Int.J.Solids Struct., 39(13/14), 3359–3372 (2002).Google Scholar
  6. 6.
    J.G.M. van Mier, (2004) In: Proc. 5th Int. Conf. on ‘Fracture of Concrete and Concrete Structures’ (FraMCoS-V), edited by V.C Li, C.K.Y.Leung, K.J. Willam, and S.L. Billington, (IA-FraMCoS, Evanston, IL, 2004), pp. 11–30.Google Scholar
  7. 7.
    M.R.A. van Vliet and J.G.M. van Mier, Experimental investigation of size effect in concrete and sandstone under uniaxial tension, Engng. Fract. Mech., 65 (2/3), 165–188 (2000).CrossRefGoogle Scholar
  8. 8.
    Z.P. Bažant and B-H.Oh, Crack band theory for fracture of concrete, Mater. Struct. (RILEM), 16(93), 155–177 (1983).Google Scholar
  9. 9.
    B. Trunk, Einfluss der Bauteilgrösse auf die Bruchenergie von Beton, Building Materials Reports, ETH Zurich, Volume 11, Aedificatio Publishers (2000), p. 155.Google Scholar
  10. 10.
    C. Iacono, L.J. Sluys and J.G.M. van Mier, Estimation of model parameters in non-local damage theories by inverse analysis techniques, Comput.Methods Appl.Mech.Engrg., 2006 (in print).Google Scholar
  11. 11.
    Z.P. Bažant, Size effect in blunt fracture: Concrete, rock, metal, J.Eng.Mech. (ASCE), 518–535 (1984).Google Scholar
  12. 12.
    A. Carpinteri and B. Chiaia, Multifractal nature of concrete fracture surfaces and size-effects on nominal fracture energy, Mater. Struct.(RILEM), 28, 435–443 (1995).CrossRefGoogle Scholar
  13. 13.
    E. Prado and J.G.M. van Mier, Effect of particle structure on mode I fracture process inconcrete, Engng. Fract. Mech., 70(14), 1793–1807 (2003).CrossRefGoogle Scholar
  14. 14.
    G. Lilliu and J.G.M. van Mier, On the relative use of micro-mechanical lattice analysis of 3-phase particle composites, Engng. Fract. Mech., 2006, accepted.Google Scholar
  15. 15.
    I. Markovic, High Performance Hybrid Fibre Concrete—Development and Utilisation, PhDthesis, Delft University of Technology, January 16, 2006, p.211.Google Scholar
  16. 16.
    M.R.A. van Vliet, Size Effect of Fracture in Concrete and Rock under Uniaxial Tension, PhD-thesis, Delft University of Technology, January 31, 2000, p. 192.Google Scholar
  17. 17.
    A.S. Elkadi, Fracture Scaling of Concrete under Multiaxial Compression, PhD-thesis, Delft University of Technology, December 20, 2005, p. 179.Google Scholar
  18. 18.
    A.S. Elkadi and J.G.M. van Mier, Experimental investigation of size effect in concrete fracture under multiaxial compression, Int. J. Fract., Special Issue Symposium 34, ICF-11, (2006), accepted.Google Scholar
  19. 19.
    J.G.M. van Mier, Mode I fracture of concrete: Discontinuous crack growth and crack interface grain bridging, Cem. Conc. Res., 21(1), 1–15 (1991).CrossRefGoogle Scholar
  20. 20.
    P. Stähli and J.G.M. van Mier, Manufacturing, fibre anisotropy and fracture of hybrid fibre concrete, Engng.Fract.Mech., 2006 (in print).Google Scholar
  21. 21.
    H.K. Man and J.G.M. van Mier, Analysis of 2D—and 3D—fracture scaling by means of 3Dlattice simulations, In Proc. ECF-16 ‘Failure Analysis of Nano and Engineering Materials and Structures’, Aleaxandroupolis, Greece, July 3–7, 2006 (in press).Google Scholar
  22. 22.
    P.E. Roelfstra, H. Sadouki and F.H. Wittmann, Le Béton Numérique, Mater Struct. (RILEM), 18(107), 327–335 (1986).Google Scholar
  23. 23.
    E. Schlangen and J.G.M. van Mier, Experimental and numerical analysis of the micromechanisms of fracture of cement-based composites, Cem. Conc. Comp., 14(2), 105–118 (1992).CrossRefGoogle Scholar
  24. 24.
    P. Trtik, E.N. Landis, M. Stampanoni, P. Stähli and J.G.M. van Mier, Micro-tensile testing and 3D imaging of hydrated Portland cement, Mater.Struct (RILEM) 2006, submitted.Google Scholar
  25. 25.
    J.G.M. van Mier, Fracture Processes of Concrete (CRC Press, Boca Raton, FL, USA, 1997).Google Scholar
  26. 26.
    J.G.M. van Mier, Strain-Softening of Concrete under Multiaxial Loading Conditions, PhDthesis, Eindhoven University of Technology, November 1984, p. 349.Google Scholar
  27. 27.
    J.G.M. van Mier, Multiaxial strain-softening of concrete, Mater. Struct. (RILEM), 19(111), 179–200 (1986).CrossRefGoogle Scholar
  28. 28.
    J.A. Hudson, S.L. Crouch and C. Fairhurst, Soft, stiff and servo-controlled testing machines: A review with reference to rock failure, Eng.Geol., 6, 155–189 (1972).CrossRefGoogle Scholar
  29. 29.
    M.D. Kotsovos, Effect of testing techniques on the post-ultimate behaviour of concrete in compression, Mater Struct. (RILEM), 16(91), 3–12 (1983).Google Scholar
  30. 30.
    J.G.M. van Mier, S.P. Shah, M. Arnaud, J.P. Balayssac, A. Bascoul, S. Choi, D. Dasenbrock, G. Ferrara, C. French, M.E. Gobbi, B.L. Karihaloo, G. König, M.D. Kotsovos, J. Labuz, D. Lange-Kornbak, G. Markeset, M.N. Pavlovic, G. Simsch, K-C. Thienel, A. Turatsinze, M. Ulmer, H.J.G.M. van Geel, M.R.A. van Vliet, D. Zissopoulos, Strain-softening of concrete in uniaxial compression—Report of the Round-Robin test carried out by RILEM TC 148SSC, Mater. Struct. (RILEM), 30(198), 195–209(1997).CrossRefGoogle Scholar

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© Springer 2006

Authors and Affiliations

  • J.G.M. van Mier
    • 1
  1. 1.Materials Research CentreInstitute for Building MaterialsZurichSwitzerland

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