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Mathematical Problems in Engineering
Volume 2017, Article ID 3861526, 14 pages
https://doi.org/10.1155/2017/3861526
Research Article

Simplified Qualitative Discrete Numerical Model to Determine Cracking Pattern in Brittle Materials by Means of Finite Element Method

1Departamento de Ingeniería Mecánica, Fundación Universidad de América, Bogotá, Colombia
2Departamento de Ingeniería Mecánica y Mecatrónica, Universidad Nacional de Colombia, Bogotá, Colombia
3Departamento de Ingeniería Civil y Agrícola, Universidad Nacional de Colombia, Bogotá, Colombia
4Universidad Politécnica de Cataluña, Barcelona, Spain

Correspondence should be addressed to J. Ochoa-Avendaño; oc.ude.lanu@aaohcofj

Received 16 March 2017; Accepted 31 May 2017; Published 2 July 2017

Academic Editor: Fabrizio Greco

Copyright © 2017 J. Ochoa-Avendaño et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. R. Ingraffea, “Computational Fracture Mechanics,” in Encyclopedia of computational mechanics, pp. 1–35, 1986, chapter 11. View at Publisher · View at Google Scholar
  2. B. Cotterell, “The past, present, and future of fracture mechanics,” Engineering Fracture Mechanics, vol. 69, no. 5, pp. 533–553, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Jirásek, “Conditions of uniqueness for finite elements with embedded cracks,” in Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS '20), September 2000. View at Scopus
  4. M. Jirásek and B. Patzák, “Models for quasibrittle failure: Theoretical and computational aspects,” in Proceedings of the Second European Conference on Computational Mechanics, (ECCM '01), Cracow, Poland, 2001.
  5. P. A. Wawrzynek and A. R. Ingraffea, “An interactive approach to local remeshing around a propagating crack,” Finite Elements in Analysis and Design, vol. 5, no. 1, pp. 87–96, 1989. View at Publisher · View at Google Scholar · View at Scopus
  6. L. F. Martha, P. A. Wawrzynek, and A. R. Ingraffea, “Arbitrary crack representation using solid modeling,” Engineering with Computers, vol. 9, no. 2, pp. 63–82, 1993. View at Publisher · View at Google Scholar · View at Scopus
  7. J. Cervenka and V. E Saouma, “Discrete crack modeling in concrete structures,” 1995.
  8. B. J. Carter, C. S. Chen, and A. R. Ingraffea, A Topology Based System for Simulating 3D Crack Growth in Solid and Shell Structures, ICF 9, Sydney, Australia, 2012.
  9. E. N. Dvorkin, A. M. Cuitiño, and G. Gioia, “Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions,” International Journal for Numerical Methods in Engineering, vol. 30, no. 3, pp. 541–564, 1990. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Klisinski, K. Runesson, and S. Sture, “Finite element with inner softening band,” Journal of Engineering Mechanics, vol. 117, no. 3, pp. 575–587, 1991. View at Publisher · View at Google Scholar · View at Scopus
  11. J. Simo and J. Oliver, “A new approach to the analysis and simulation of strain softening in solids,” Fracture and Damage in Quasibrittle Structures, 1994. View at Google Scholar
  12. C. Daux, N. Moës, J. Dolbow, N. Sukumar, and T. Belytschko, “Arbitrary branched and intersecting cracks with the extended finite element method,” International Journal for Numerical Methods in Engineering, vol. 48, no. 12, pp. 1741–1760, 2000. View at Publisher · View at Google Scholar · View at Scopus
  13. N. Moës, J. Dolbow, and T. Belytschko, “A finite element method for crack growth without remeshing,” International Journal for Numerical Methods in Engineering, vol. 46, no. 1, pp. 131–150, 1999. View at Publisher · View at Google Scholar · View at Scopus
  14. T. Belytschko and T. Black, “Elastic crack growth in finite elements with minimal remeshing,” International Journal for Numerical Methods in Engineering, vol. 45, no. 5, pp. 601–620, 1999. View at Publisher · View at Google Scholar · View at Scopus
  15. Z. P. Bažant and B. H. Oh, “Crack band theory for fracture of concrete,” Materials and Structures, vol. 16, no. 3, pp. 155–177, 1983. View at Publisher · View at Google Scholar · View at Scopus
  16. T. Belytschko, J. Fish, and B. E. Engelmann, “A finite element with embedded localization zones,” Computer Methods in Applied Mechanics and Engineering, vol. 70, no. 1, pp. 59–89, 1988. View at Publisher · View at Google Scholar · View at Scopus
  17. A. Huerta, P. Díez, A. Rodríguez-Ferran, and G. Pijaudier-Cabot, “Error estimation and adaptive finite element analysis of softening solids,” Studies in Applied Mechanics, vol. 47, no. C, pp. 333–347, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  18. Z. Shi, “Crack analysis in structural concrete: theory and applications,” 2009.
  19. Y. R. Rashid, “Ultimate strength analysis of prestressed concrete pressure vessels,” Nuclear Engineering and Design, vol. 7, no. 4, pp. 334–344, 1968. View at Publisher · View at Google Scholar · View at Scopus
  20. D. S. Dugdale, “Yielding of steel sheets containing slits,” Journal of the Mechanics and Physics of Solids, vol. 8, no. 2, pp. 100–104, 1960. View at Publisher · View at Google Scholar · View at Scopus
  21. G. I. Barenblatt, “The mathematical theory of equilibrium cracks in brittle fracture,” Advances in Applied Mechanics, vol. 7, no. C, pp. 55–129, 1962. View at Publisher · View at Google Scholar · View at Scopus
  22. D. Ngo and A. C. Scordelis, “Finite element analysis of reinforced concrete beams,” ACI Journal Proceedings, vol. 64, no. 3, pp. 152–163, 1967. View at Publisher · View at Google Scholar
  23. A. Hillerborg, M. Modéer, and P.-E. Petersson, “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements,” Cement and Concrete Research, vol. 6, no. 6, pp. 773–781, 1976. View at Publisher · View at Google Scholar · View at Scopus
  24. I. Carol, P. C. Prat, and C. M. López, “Normal/shear cracking model: application to discrete crack analysis,” Journal of Engineering Mechanics, vol. 123, no. 8, pp. 765–773, 1997. View at Publisher · View at Google Scholar · View at Scopus
  25. I. Carol, C. M. López, and O. Roa, “Micromechanical analysis of quasi-brittle materials using fracture based interface elements,” International Journal for Numerical, vol. 52, no. 1-2, pp. 193–215, 2001. View at Publisher · View at Google Scholar
  26. A. Caballero, K. J. Willam, and I. Carol, “Consistent tangent formulation for 3D interface modeling of cracking/fracture in quasi-brittle materials,” Computer Methods in Applied Mechanics and Engineering, vol. 197, no. 33–40, pp. 2804–2822, 2008. View at Publisher · View at Google Scholar · View at Scopus
  27. A. Caggiano, G. Etse, and E. Martinelli, “Zero-thickness interface model formulation for failure behavior of fiber-reinforced cementitious composites,” Computers and Structures, vol. 98-99, pp. 23–32, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. V. P. Nguyen, “An open source program to generate zero-thickness cohesive interface elements,” Advances in Engineering Software, vol. 74, pp. 27–39, 2014. View at Publisher · View at Google Scholar · View at Scopus
  29. O. L. Manzoli, A. L. Gamino, E. A. Rodrigues, and G. K. S. Claro, “Modeling of interfaces in two-dimensional problems using solid finite elements with high aspect ratio,” Computers and Structures, vol. 94-95, pp. 70–82, 2012. View at Publisher · View at Google Scholar · View at Scopus
  30. O. L. Manzoli, M. A. Maedo, L. A. G. Bitencourt, and E. A. Rodrigues, “On the use of finite elements with a high aspect ratio for modeling cracks in quasi-brittle materials,” Engineering Fracture Mechanics, vol. 153, pp. 151–170, 2016. View at Publisher · View at Google Scholar · View at Scopus
  31. T. Belytschko, N. Moës, S. Usui, and C. Parimi, “Arbitrary discontinuities in finite elements,” International Journal for Numerical Methods in Engineering, vol. 50, no. 4, pp. 993–1013, 2001. View at Publisher · View at Google Scholar · View at Scopus
  32. J. M. Sancho, J. Planas, D. A. Cendón, E. Reyes, and J. C. Gálvez, “An embedded crack model for finite element analysis of concrete fracture,” Engineering Fracture Mechanics, vol. 74, no. 1-2, pp. 75–86, 2007. View at Publisher · View at Google Scholar · View at Scopus
  33. F. Greco, L. Leonetti, and P. Lonetti, “A two-scale failure analysis of composite materials in presence of fiber/matrix crack initiation and propagation,” Composite Structures, vol. 95, pp. 582–597, 2013. View at Publisher · View at Google Scholar · View at Scopus
  34. F. Feyel and J.-L. Chaboche, “FE 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials,” Computer Methods in Applied Mechanics and Engineering, vol. 183, no. 3-4, pp. 309–330, 2000. View at Publisher · View at Google Scholar · View at Scopus
  35. S. Rudraraju, A. Salvi, K. Garikipati, and A. M. Waas, “Predictions of crack propagation using a variational multiscale approach and its application to fracture in laminated fiber reinforced composites,” Composite Structures, vol. 94, no. 11, pp. 3336–3346, 2012. View at Publisher · View at Google Scholar · View at Scopus
  36. D. Bruno and F. Greco, “Mixed mode delamination in plates: a refined approach,” International Journal of Solids and Structures, vol. 38, no. 50-51, pp. 9149–9177, 2001. View at Publisher · View at Google Scholar · View at Scopus
  37. S. Ghosh, J. Bai, and P. Raghavan, “Concurrent multi-level model for damage evolution in microstructurally debonding composites,” Mechanics of Materials, vol. 39, no. 3, pp. 241–266, 2007. View at Publisher · View at Google Scholar · View at Scopus
  38. T. Belytschko, W. K. Liu, and B. Moran, Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, Chichester, UK, 2000. View at MathSciNet
  39. E. Onate, Structural Analysis with the Finite Element Method Linear Statics, vol. 2 of Lecture Notes on Numerical Methods in Engineering and Sciences, Springer, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  40. A. R. Ingraffea and M. Grigoriu, “Probabilistic fracture mechanics: a validation of predictive capability,” 1990.
  41. M. Arrea and A. Ingraffea, “Mixed-mode crack propagation in mortar and concrete,” 1982.
  42. T. N. Bittencourt, P. A. Wawrzynek, A. R. Ingraffea, and J. L. Sousa, “Quasi-automatic simulation of crack propagation for 2D lefm problems,” Engineering Fracture Mechanics, vol. 55, no. 2, pp. 321–334, 1996. View at Publisher · View at Google Scholar · View at Scopus
  43. H. Nguyen-Xuan, G. R. Liu, S. Bordas, S. Natarajan, and T. Rabczuk, “An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order,” Computer Methods in Applied Mechanics and Engineering, vol. 253, pp. 252–273, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  44. S. Geniaut and E. Galenne, “A simple method for crack growth in mixed mode with X-FEM,” International Journal of Solids and Structures, vol. 49, no. 15-16, pp. 2094–2106, 2012. View at Publisher · View at Google Scholar · View at Scopus
  45. S. M. Häusler, K. Lindhorst, and P. Horst, “Combination of the material force concept and the extended finite element method for mixed mode crack growth simulations,” International Journal for Numerical Methods in Engineering, vol. 85, no. 12, pp. 1522–1542, 2011. View at Publisher · View at Google Scholar · View at Scopus
  46. J.-C. Passieux, J. Réthoré, A. Gravouil, and M.-C. Baietto, “Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver,” Computational Mechanics, vol. 52, no. 6, pp. 1381–1393, 2013. View at Publisher · View at Google Scholar · View at Scopus
  47. G. Ventura, J. X. Xu, and T. Belytschko, “A vector level set method and new discontinuity approximations for crack growth by EFG,” International Journal for Numerical Methods in Engineering, vol. 54, no. 6, pp. 923–944, 2002. View at Publisher · View at Google Scholar · View at Scopus
  48. M. V. K. V. Prasad and C. S. Krishnamoorthy, “Computational model for discrete crack growth in plain and reinforced concrete,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 25-26, pp. 2699–2725, 2002. View at Publisher · View at Google Scholar · View at Scopus
  49. J. G. Rots, Computational Modeling of Concrete Fracture [Ph.D. Thesis], Delft University of Technology, 1988.