Computers and Concrete

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Investigating spurious cracking in finite element models for concrete fracture

  • Received : 2022.10.01
  • Accepted : 2022.12.20
  • Published : 2023.02.25
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Abstract

This paper presents an investigation of variables that cause spurious cracking in numerical modeling of concrete fracture. Spurious cracks appear due to the approximate nature of numerical modeling. They overestimate the dissipated energy, leading to divergent results with mesh refinement. This paper is limited to quasi-static loading regime, homogeneous models, cracking as the only nonlinear mode of deformation and cracking only due to tensile loading. Under these conditions, some variables that can be related to spurious cracking are: mesh alignment, ductility, crack band width, structure size, mesh refinement and load increment size. Case studies illustrate the effect of each variable and convergence analyses demonstrate that, after all, load-increment size is the most important variable. Theoretically, a sufficiently small load increment is able to eliminate or at least alleviate the detrimental influence of the other variables. Such load-increment size might be prohibitively small, rendering the simulation unfeasible. Hence, this paper proposes two alternatives. First, it is proposed an algorithm that automatically find such small load increment size automatically, which not necessarily avoid large computations. Then, it is proposed a double simulation technique, in which the crack is forced to propagate through the localization zone.

Keywords

Acknowledgement

The authors would like to acknowledge National Agency of Petroleum, Natural Gas and Biofuels (ANP) and Funding Authority for Studies and Projects (FINEP) for the funding of a research scholarship through PRH-9.1, as well as Brazilian National Council for Scientific and Technological Development (CNPq) and Coordination for the Improvement of Higher Education Personnel (CAPES) for their support to this work.

References

  1. Ahrens, J., Geveci, B. and Law, C. (2005), "Paraview: An end-user tool for large data visualization", The visualization handbook, Elsevier.
  2. Andrade, R.G.M.de (2020), Prefabricated High-Performance Steel-Fiber Reinforced Concrete Structure for Urban Short Span Highway Bridges, Federal University of Rio de Janeiro.
  3. Areias, P.M. and Belytschko, T. (2005), "Analysis of three-dimensional crack initiation and propagation using the extended finite element method", Int. J. Numer. Methods Eng., 63(5), 760-788. https://doi.org/10.1002/nme.1305.
  4. Ayachit, U. (2015), The Paraview Guide: A Parallel Visualization Application, Kitware, Inc., Clifton Park, NY, USA.
  5. Bazant, Z., Kazemi, M. and Gettu, R. (1989), "Recent studies of size effect in concrete structures", Transactions of the 10th International Conference on Structural Mechanics in Reactor Technology, Anaheim, August.
  6. Bazant, Z.P. and Asce, F. (1984), "Size effect in blunt fracture: Concrete, rock, metal", J. Eng. Mech., 110(4), 518-535. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:4(518).
  7. Bazant, Z.P. and Cedolin, L. (1980), "Fracture mechanics of reinforced concrete", J. Eng. Mech. Div., 106(6), 1287-1306. https://doi.org/10.1061/JMCEA3.0002665.
  8. Bazant, Z.P. and Chen, E.P. (1997), "Scaling of structural failure", Appl. Mech. Rev., 50(10), 593-627. https://doi.org/10.1115/1.3101672.
  9. Bazant, Z.P. and Oh, B.H. (1983), "Crack band theory for fracture of concrete", Mater. Constr., 16(3), 155-177. https://doi.org/10.1007/BF02486267.
  10. Bi, J., Huo, L., Zhao, Y. and Qiao, H. (2010), "Modified the smeared crack constitutive model of fiber reinforced concrete under uniaxial loading", Constr. Build. Mater., 250, 118916. https://doi.org/10.1016/j.conbuildmat.2020.118916.
  11. Bitencourt Jr, L.A.G. (2015), "Numerical modeling of failure processes in steel fiber reinforced cementitious materials", Ph.D. Dissertation, University of Sao Paulo, Butanta.
  12. Brant, C.A.C., Costa, G.L.X.da, Andrade, R.G.M.de and Fairbairn, E.R.M. (2021), "Finite element modelling of cracking in fiber-reinforced concrete beams", Proceedings of the Ibero-Latin-American Congress on Computational Methods in Engineering, Rio de Janeiro, November.
  13. Cervera, M. and Chiumenti, M. (2006a), "Mesh objective tensile cracking via a local continuum damage model and a crack tracking technique", Comput. Methods Appl. Mech. Eng., 196(1-3), 304-320. https://doi.org/10.1016/j.cma.2006.04.008.
  14. Cervera, M. and Chiumenti, M. (2006b), "Smeared crack approach: Back to the original track", Int. J. Numer. Anal. Methods Geomech., 30(12), 1173-1199. https://doi.org/10.1002/nag.518
  15. Costa, G.L.X.da, Brant, C.A.C., Andrade, R.G.M.de, and Fairbairn, E.R.M. (2021), "Finite Element analyses of mesh-objectivity for Smeared, Damage and Discrete models applied to concrete cracking", Proceedings of the Ibero-Latin-American Congress on Computational Methods in Engineering, Rio de Janeiro, November.
  16. Daniels, H.E. (1945), "The statistical theory of the strength of bundles of threads", Proc. Royal Soc. London., 183(995), 405-435. https://doi.org/10.1098/rspa.1945.0011.
  17. Dodds Jr, R.H., Darwin, D., Smith, J.L. and Leibengood, L.D. (1982), "Grid size effects with smeared cracking in finite element analysis of reinforced concrete", NSF/CEE-82034; University of Kansas Lawrence, Kansas.
  18. Gouveia, A.V., Barros, J.A., Azevedo, A.F. and Sena-Cruz, J. (2008), "Multi-fixed smeared 3d crack model to simulate the behavior of fiber reinforced concrete structures", CCC2008-Challenges for Civil Construction, Faculdade de Engenharia Porto, Portugal, April.
  19. Jager, P., Steinmann, P. and Kuhl, E. (2008), "On local tracking algorithms for the simulation of three-dimensional discontinuities", Comput. Mech., 42(3), 395-406. https://doi.org/10.1007/s00466-008-0249-3.
  20. Jirasek, M. (2004), "Non-local damage mechanics with application to concrete", Revue Francaise de Genie Civil, 8(5-6), 683-707. https://doi.org/10.1080/12795119.2004.9692625.
  21. Jirasek, M. (2011), Damage and Smeared Crack Models, Springer, Vienna, Austria.
  22. Jirasek, M. and Bauer, M. (2012), "Numerical aspects of the crack band approach", Comput. Struct., 110, 60-78. https://doi.org/10.1016/j.compstruc.2012.06.006.
  23. Kang, J., Kim, K., Lim, Y.M. and Bolander, J.E. (2014), "Modeling of fiber-reinforced cement composites: Discrete representation of fiber pullout", Int. J. Solid. Struct., 51(10), 1970-1979. https://doi.org/10.1016/j.ijsolstr.2014.02.006.
  24. Kormeling, H.A. and Reinhardt, H.W. (1983), "Determination of the fracture energy of normal concrete and epoxy modified concrete", Stevin Laboratory 5-83-18; Delft University of Technology.
  25. Kwan, A., Wang, Z. and Chan, H. (1999), "Mesoscopic study of concrete II: Nonlinear finite element analysis", Comput. Struct., 70(5), 545-556. https://doi.org/10.1016/j.ijsolstr.2014.02.006.
  26. Leibengood, L.D., Darwin, D. and Dodds, R.H. (1984), "Finite Element Analysis of Concrete Fracture Specimens", SM Report No. 11; University of Kansas Center for Research, Inc.
  27. Leibengood, L.D., Darwin, D. and Dodds, R.H. (1986), "Parameters affecting FE analysis of concrete structures", J. Struct. Eng., 112(2), 326-341. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:2(326).
  28. Mota, M.T., Fairbairn, E.M., Ribeiro, F.L., Rossi, P., Tailhan, J.L., Andrade, H.C. and Rita, M.R. (2021), "A 3D probabilistic model for explicit cracking of concrete", Comput. Concrete, 27(6), 549-562. https://doi.org/10.12989/cac.2021.27.6.549.
  29. Oliver, J. (1989), "A consistent characteristic length for smeared cracking models", Int. J. Numer. Methods Eng., 28(2), 461-474. https://doi.org/10.1002/nme.1620280214
  30. Oliver, J., Huespe, A.E., Samaniego, E. and Chaves, E.W.V. (2004), "Continuum approach to the numerical simulation of material failure in concrete", Int. J. Numer. Anal. Methods Geomech., 28(7-8), 609-632. https://doi.org/10.1002/nag.365.
  31. Oliver, J. and Huespe, A.E. (2004), "Continuum approach to material failure in strong discontinuity settings", Comput. Methods Appl. Mech. Eng., 193(30-32), 3195-3220. https://doi.org/10.1016/j.cma.2003.07.013.
  32. Pan, Y., Kang, J., Ichimaru, S. and Bolander, J.E. (2020), "Multi-field models of fiber reinforced concrete for structural applications", Appl. Sci., 11(1), 184. https://doi.org/10.3390/app11010184.
  33. Peirce, F.T. (1926), "Tensile tests for cotton yarns: 'The weakest link' theorems on the strength of long and of composite specimens", J. Text. Inst. Trans., 17, 355-368. https://doi.org/10.1080/19447027.1926.10599953.
  34. Radtke, F.K.F. (2012), "Computational modelling of fibre-reinforced cementitious composites: An analysis of discrete and mesh-independent techniques", Doctoral Thesis, Delft University of Technology, Delft.
  35. Rastiello, G., Tailhan, J.L., Rossi, P. and Dal Pont, S. (2015), "Macroscopic probabilistic cracking approach for the numerical modelling of fluid leakage in concrete", Ann. Solid Struct. Mech., 7(1), 1-16. https://doi.org/10.1007/s12356-015-0038-6.
  36. Rossi, P. and Wu, X. (1992), "Probabilistic model for material behaviour analysis and appraisement of concrete structures", Mag. Concrete Res., 44(161), 271-280. https://doi.org/10.1680/macr.1992.44.161.271.
  37. Saloustros, S., Cervera, M. and Pela, L. (2019), "Challenges, tools and applications of tracking algorithms in the numerical modelling of cracks in concrete and masonry structures", Arch. Comput. Methods Eng., 26(4), 961-1005. https://doi.org/10.1007/s11831-018-9274-3.
  38. Slobbe, A.T. (2015), "Propagation and band width of smeared cracks", Ph.D. thesis, Delft University of Technology, Delft.
  39. Tailhan, J.L., Rossi, P., Phan, T.S., Rastiello, G. and Foulliaron, J. (2013), "Multi scale probabilistic approaches and strategies for the modelling of concrete cracking", VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS-8), Ciudad Real, March.
  40. Tailhan, J.L., Dal Pont, S. and Rossi, P. (2010), "From local to global probabilistic modeling of concrete cracking", Ann. Solid Struct. Mech., 1(2), 103-115. https://doi.org/10.1007/s12356-010-0008-y.
  41. Wang, Z.M., Kwan, A.K.H. and Chan, H.C. (1999), "Mesoscopic study of concrete I: Generation of random aggregate structure and finite element mesh", Comput. Struct., 70(5), 533-544. https://doi.org/10.1016/S0045-7949(98)00177-1.