Advertisement

Crack propagation using the continuum strong discontinuity approach by the BEM: some numerical remarks

  • Tiago S. Mendonça
  • Rodrigo G. Peixoto
  • Gabriel O. Ribeiro
Technical Paper
  • 61 Downloads

Abstract

Some numerical remarks regarding the crack evolution in failure analysis by the BEM using cells with embedded strong discontinuities are addressed in this work. A comparative study between the generation of these cells at any iteration or only after a step convergence is firstly performed. Moreover, an analysis is carried out related to the cells size growth throughout the iterative-incremental process. As reference, some classical problems whose experimental results are available in the literature are used for the numerical analysis which is performed considering the implicit formulation of the boundary element method together with the continuum strong discontinuity approach. It was verified that the results are coincident for different numbers of steps considered in the simulations when cells are generated during any iteration, showing step size independence in this case, while the same is not true for the case of cells generated only after step convergence, in which a large number of steps are required for a good accuracy. Finally, it is shown that a small increase in cell size throughout the analysis contributes to the reduction in numerical processing time without significantly affecting the results accuracy.

Keywords

Implicit boundary element method Continuum strong discontinuity approach Failure mechanics Step size dependence 

Notes

Acknowledgements

The authors would like to acknowledge CNPq (National Council of Scientific and Technological Development), CAPES (Coordination of Improvement of Higher Education Personnel) and FAPEMIG (Minas Gerais State Research Foundation) for financial supports.

References

  1. 1.
    Arrea M, Ingraffea AR (1982) Mixed-mode crack propagation in mortar and concrete. In: Technical report 81-13, Department of Structural Engineering, Cornell University, Ithaca, USA (1982)Google Scholar
  2. 2.
    Botta AS, Venturini WS, Benallal A (2005) BEM applied to damage models emphasizing localization and associated regularization techniques. Eng Anal Bound Elem 29:814–827CrossRefGoogle Scholar
  3. 3.
    García-Álvarez V, Gettu R, Carol I (2012) Analysis of mixed-mode fracture in concrete using interface elements and a cohesive crack model. Sadhana 37:187–205MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hatzigeorgiou GD, Beskos DE (2002) Static analysis of 3D damaged solids and structures by BEM. Eng Anal Bound Elem 26:521–526CrossRefGoogle Scholar
  5. 5.
    Lin FB, Yan G, Bažant ZP, Ding F (2002) Nonlocal strain-softening model of quasi-brittle materials using boundary element method. Eng Anal Bound Elem 26:417–424CrossRefGoogle Scholar
  6. 6.
    Mallardo V (2009) Integral equations and nonlocal damage theory: a numerical implementation using the bdem. Int J Fract 157:13–32CrossRefGoogle Scholar
  7. 7.
    Mallardo V, Alessandri C (2004) Arc-length procedures with bem in physically nonlinear problems. Eng Anal Bound Elem 28:547–559CrossRefGoogle Scholar
  8. 8.
    Manzoli O, Oliver J, Cervera M (1998) Localización de deformación: Análisis y simulación numérica de discontinuidades en mecánica de sólidos. Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE). Monografía n. 44. BarcelonaGoogle Scholar
  9. 9.
    Manzoli OL, Pedrini RA, Venturini WS (2009) Strong discontinuity analysis in solid mechanics using boundary element method. In: Spountzakis EJ, Aliabadi MH (eds) Advances in boundary element techniques X. Atenas, Grécia, pp 323–329Google Scholar
  10. 10.
    Manzoli OL, Venturini WS (2004) Uma formulação do MEC para simulação numérica de descontinuidades fortes. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 20(3):215–234MathSciNetGoogle Scholar
  11. 11.
    Manzoli OL, Venturini WS (2007) An implicit BEM formulation to model strong discontinuities. Comput Mech 40:901–909CrossRefGoogle Scholar
  12. 12.
    Oliver J (1996) Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 1: fundamentals. Int J Numer Methods Eng 39:3575–3600CrossRefGoogle Scholar
  13. 13.
    Oliver J (1996) Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 2: numerical simulation. Int J Numer Methods Eng 39:3601–3623CrossRefGoogle Scholar
  14. 14.
    Oliver J (2000) On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations. Int J Solids Struct 37:7207–7229MathSciNetCrossRefGoogle Scholar
  15. 15.
    Oliver J, Cervera M, Manzoli O (1998) On the use of strain-softening models for the simulation of strong discontinuities in solids. In: de Borst R, van der Giessen E (eds) Material instabilities in solids, vol 8. Wiley, Chichester, pp 107–123Google Scholar
  16. 16.
    Oliver J, Cervera M, Manzoli O (1999) Strong discontinuities and continuum plasticity models: the strong discontinuity approach. Int J Plast 15:319–351CrossRefGoogle Scholar
  17. 17.
    Oliver J, Huespe AE, Blanco S, Linero DL (2006) Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach. Comput Methods Appl Mech Eng 195:7093–7114CrossRefGoogle Scholar
  18. 18.
    Oliver J, Huespe AE, Pulido MDG, Chaves E (2002) From continuum mechanics to fracture mechanics: the strong discontinuity approach. Eng Fract Mech 69:113–136CrossRefGoogle Scholar
  19. 19.
    Oliver J, Huespe AE, Samaniego E (2003) A study on finite elements for capturing strong discontinuities. Int J Numer Methods Eng 56:2135–2161MathSciNetCrossRefGoogle Scholar
  20. 20.
    Peixoto RG, Anacleto FES, Ribeiro GO, Pitangueira RLS, Penna SS (2016) A solution strategy for non-linear implicit BEM formulation using a unified constitutive modelling framework. Eng Anal Bound Elem 64:295–310MathSciNetCrossRefGoogle Scholar
  21. 21.
    Peixoto RG, Ribeiro GO, Pitangueira RLS (2016) Concrete fracture analysis using the continuum strong discontinuity approach and the boundary element method. In: Ávila SM (ed.) Proceedings of the XXXVII Iberian Latin-American congress on computational methods in engineering—CILAMCE. Brasília, DF, BrasilGoogle Scholar
  22. 22.
    Peixoto RG, Ribeiro GO, Pitangueira RLS (2018) A progressive cells activation algorithm for physically non-linear BEM analysis. J Braz Soc Mech Sci Eng 40:112CrossRefGoogle Scholar
  23. 23.
    Peixoto RG, Ribeiro GO, Pitangueira RLS, Penna SS (2017) The strong discontinuity approach as a limit case of strain localization in the implicit BEM formulation. Eng Anal Bound Elem 80:127–141MathSciNetCrossRefGoogle Scholar
  24. 24.
    Portela A, Aliabadi MH, Rooke DP (1992) The dual boundary element method: effective implementation for cracked problems. Int J Numer Methods Eng 33:1269–1287CrossRefGoogle Scholar
  25. 25.
    Portela A, Aliabadi MH, Rooke DP (1993) Dual boundary element analysis of fatigue crack growth. In: Aliabadi MH, Brebbia CA (eds) Advances in boundary element methods for fracture mechanics, vol 1. Elsevier, Londres, pp 1–46zbMATHGoogle Scholar
  26. 26.
    Simo JC, Oliver J, Armero F (1993) An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. Comput Mech 12:277–296MathSciNetCrossRefGoogle Scholar
  27. 27.
    Sládek J, Sládek V, Bažant ZP (2003) Non-local boundary integral formulation for softening damage. Int J Numer Methods Eng 57:103–116CrossRefGoogle Scholar
  28. 28.
    Telles JCF, Carrer JAM (1991) Implicit procedures for the solution of elastoplastic problems by the boundary element method. Math Comput Modell 15:303–311CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Departamento de Engenharia de EstruturasUniversidade Federal de Minas GeraisBelo HorizonteBrazil

Personalised recommendations