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Saw-tooth softening/stiffening - a stable computational procedure for RC structures

  • Rots, Jan G. (Faculty of Architecture and Faculty of Civil Engineering & Geosciences, Delft University of Technology) ;
  • Invernizzi, Stefano (Department of Structural Engineering and Geotechnics, Politecnico di Torino) ;
  • Belletti, Beatrice (Department of Civil and Environmental Engineering and Architecture, University of Parma)
  • Received : 2005.12.12
  • Accepted : 2006.05.03
  • Published : 2006.05.25

Abstract

Over the past years techniques for non-linear analysis have been enhanced significantly via improved solution procedures, extended finite element techniques and increased robustness of constitutive models. Nevertheless, problems remain, especially for real world structures of softening materials like concrete. The softening gives negative stiffness and risk of bifurcations due to multiple cracks that compete to survive. Incremental-iterative techniques have difficulties in selecting and handling the local peaks and snap-backs. In this contribution, an alternative method is proposed. The softening diagram of negative slope is replaced by a saw-tooth diagram of positive slopes. The incremental-iterative Newton method is replaced by a series of linear analyses using a special scaling technique with subsequent stiffness/strength reduction per critical element. It is shown that this event-by-event strategy is robust and reliable. First, the model is shown to be objective with respect to mesh refinement. Next, the example of a large-scale dog-bone specimen in direct tension is analyzed using an isotropic version of the saw-tooth model. The model is capable of automatically providing the snap-back response. Subsequently, the saw-tooth model is extended to include anisotropy for fixed crack directions to accommodate both tensile cracking and compression strut action for reinforced concrete. Three different reinforced concrete structures are analyzed, a tension-pull specimen, a slender beam and a slab. In all cases, the model naturally provides the local peaks and snap-backs associated with the subsequent development of primary cracks starting from the rebar. The secant saw-tooth stiffness is always positive and the analysis always 'converges'. Bifurcations are prevented due to the scaling technique.

Keywords

References

  1. Bazant, Z.P., and Cedolin, L. (1979), 'Blunt crack band propagation in finite element analysis', J. Eng. Mech. Div., ASCE. 105(2), 297-315
  2. Bazant, Z.P., and Oh, B.H. (1983), 'Crack band theory for fracture of concrete', Mater. Struct., 16(93), 155-177
  3. Beranek, W.J., and Hobbelman, G.J. (1995), '2D and 3D-Modelling of concrete as an assemblage of spheres: revaluation of the failure criterion', Fracture Mechanics of Concrete Structures. Proc. FRAMCOS-2, Wittmann F.H. (ed.), Freiburg: Aedificatio, 965-978
  4. Carpinteri, A., (1986), Mechanical Damage and Crack Growth in Concrete: Plastic Collapse to Brittle Fracture. Martinus Nijhoff Publishers, Dordrecht
  5. Carpinteri, A., Monetto, I. (1999), 'Snap-back analysis of fracture evolution in multi-cracked solids using boundary element method', Int. J. Fracture, 98, 225-241 https://doi.org/10.1023/A:1018660600546
  6. Crisfield, M.A. (1982), 'Accelerated solution techniques and concrete cracking', Comput. Methods Appl. Mech. Eng., 33, 585-607 https://doi.org/10.1016/0045-7825(82)90124-4
  7. Crisfield, M.A. (1984), 'Difficulties with current numerical models for reinforced-concrete and some tentative solutions', Proc. Int. Conf. Computer Aided Analysis and Design of Concrete Structures. I, 331-358 F. Damjanic, N. Bicanic et at. (eds)
  8. De Borst, R. (1987), 'Computation of post-bifurcation and post-failure behaviour of strain-softening solids', Comp. Struct., 25(2), 211-224 https://doi.org/10.1016/0045-7949(87)90144-1
  9. Feenstra, P.H., Rots, J.G., Arnesen, A., Teigen, J.G., Hoiseth, K.V. (1998) 'A 3D constitutive model for concrete based on a co-rotational crack concep', Computational Modelling of Concrete Structures, Proc. EURO-C 1998. De Borst et at. (eds), Balkema: Rotterdam, 13-22
  10. Gijsbers, F.B.J., and Hehemann, A.A. (1977), 'Some tensile tests on reinforced concrete', Report BI-77-61, TNO Inst. For Building Mat. And Struct., Delft
  11. Gilbert, R.I., and Warner, R. F. (1978), 'Tension stiffening in reinforced concrete slabs', J. Struct. Div., ASCE., 104(12), 1885-1900
  12. Jain, S.C., and Kennedy, J.B. (1974), 'Yield criterion for reinforced concrete slabs', J. Struct. Div., ASCE, 100(3), 631-644
  13. Rashid, Y.R. (1968), 'Analysis of prestressed concrete pressure vessels', Nuclear Eng. Design, 7(4), 334-344 https://doi.org/10.1016/0029-5493(68)90066-6
  14. Rots, J.G. (1988), 'Computational modeling of concrete fracture', Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands
  15. Rots, J.G. (2001), 'Sequentially linear continuum model for concrete fracture', Fracture Mechanics of Concrete Structures, Proc. FRAMCOS-4, de Borst R, Mazars J, Pijaudier-Cabot G, van Mier JGM, Balkema AA (eds). Lisse: The Netherlands, 831-839
  16. Rots, J.G., Belletti, B., Invemizzi, S. (2006) 'Simplified saw-tooth softening model for reinforced concrete structures', Proceedings of the 2nd International FIB Congress, 5-8 June, Napoli, Italy
  17. Rots, J.G., and Invernizzi, S. (2003), 'Regularized saw-tooth softening', Computational Modelling of Concrete Structures, Lisse: Balkema, 599-617 Bicanic N., de Borst R., Mang H., Meschke G. (eds)
  18. Rots, J.G. and Invernizzi, S. (2004a), 'Saw-tooth softening/stiffening model', Fracture Mechanics of Concrete Structures, Li VC, Leung C, Willam K, Billington S (eds). Proc. FraMCos-5, Ia FraMCos-5: USA, 375-382
  19. Rots, J.G., and Invemizzi, S. (2004b), 'Regularized sequentially linear saw-tooth softening model', Int. J. Numer. Analy. Methods Geomech, 28, 821-856 https://doi.org/10.1002/nag.371
  20. Rots, J.G., Nauta, P., Kusters, G.M.A., Blaauwendraad, J. (1985), 'Smeared crack approach and fracture localization in concrete', HERON, 30(1), 1-48
  21. Schlangen, E., and van Mier, J.G.M. (1992), 'Experimental and numerical analysis of micro-mechanisms of fracture of cement-based composites', Cem. Conc. Compo., 14, 105-118 https://doi.org/10.1016/0958-9465(92)90004-F
  22. Van Vliet M.R.A. (2000), 'Size effect in tensile fracture of concrete and rock', PhD thesis TV Delft, Faculty of Civil Engineering, Delft University Press, Delft, The Netherlands
  23. Walraven, J.C. (1978), 'The influence of depth on the shear strength of lightweight concrete beams without shear reinforcement', Report 5-78-4 Stevin Laboratory, Delft University of Technology, Delft

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