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Application of a variable order singular element to dynamic fracture mechanics

Abstract

The dynamic response characteristics of a variable order singular element proposed by Akin (1976) have been examined in application to several stationary crack/dynamic boundary condition problems in the work by Thesken and Gudmundson (1985). Presented here are the numerical solutions for the benchmark problem of that study, an infinite strip/semi-infinite crack problem having a closed analytical solution form given by Nilsson (1973). Time integration of the problem was conducted explicitly using the central difference scheme. The dynamic stress intensity factor KI(t) was computed using two different approaches: a local approach using the COD relation to K I and a global approach employing the dynamic J-integral. The effects of mesh refinement and time step duration were examined with a series of refined grids and proportionally decreasing time steps. Results are presented in the form of non-dimensional K J(t) histories and are compared to the existing analytical solution.

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References

  1. Akin, J.E. (1976): The generation of elements with singularities. Int. J. Num. Meth. Eng. 10, 1249–1259

  2. Atluri, S.N. ; Nishioka, T.; Nakagaki, M. (1979): Numerical modeling of dynamic and nonlinear crack propagation in finite bodies by moving singular elements. In: Pertrone, N.; Atluri, S.N. (eds.): Nonlinear and dynamic fracture mechanics, ASME 35, 37–67

  3. Atluri, S.N.; Nakagaki, M. (1986): Computational methods for plane problems of fracture, chapter 6. In: Atluri, S. N. (ed): Computational methods in the mechanics of fracture. Amsterdam: Elsevier

  4. Barsoum, R.S. (1976): On the use of isoparametric finite elements in linear fracture mechanics. Int. J. Num. Meth. Eng. 10, 25–37

  5. Bathe, K.J.; Wilson, E.L. (1976): Numerical methods in finite element analysis. p. 101. Englewood Cliffs: Prenctice-Hall

  6. Blackburn, W.S. (1973): Calculation of stress intensity factors at crack tips using special finite elements. In: Whiteman, J.R. (ed): The mathematics of finite elements and applications. London: Academic Press

  7. Brickstad, B. (1983): A FEM analysis of crack arrest experiments. Int. J. Fracture 21, 177–194

  8. Brickstad, B.; Nilsson, F. (1980): Explicit time integration in FEM analysis of dynamic crack propagation. pp. 473–487. Numerical Methods in Fracture Mechanics, Swansea

  9. Henshell, R.D.; Shaw, K.G. (1975): Crack tip finite elements are unnecessary. Int. J. Num. Meth. Eng. 9, 495–507

  10. Kishimoto, S.; Aoki, S.; Sakata, M. (1980): Dynamic stress intensity factors using J-integral and finite element method. Eng. Fract. Mech. 13, 387–394

  11. Nakamura, T.; Shih, F.; Freund, L.B. (1984): Computational methods based on an energy integral in dynamic fracture. Providence: Brown University, Div. of Engineering

  12. Nilsson, F. (1973): A path-independent integral for transient crack problems. Int. J. Solids Struct. 9, 1107–1115

  13. Nishioka, T.; Atluri, S.N. (1980b): Numerical modeling of dynamic crack propagation in finite bodies, by moving singular elements: 1: Formulation. ASME J. Appl. Mech. 47, 570–576

  14. Nishioka, T.; Atluri, S.N. (1980a): Numerical modeling of dynamic crack propagation in finite bodies, by moving singular elements. 2: results. ASME J. Appl. Mech. 47, 577–583

  15. Nishioka, T.; Atluri, S.N. (1983): A numerical study of the use of path independent integrals in elastodynamic crack propagation. Eng. Fract. Mech. 18, 23–33

  16. Nishioka, T.; Stonesifer, R.B.; Atluri, S.N. (1981): An evaluation of several moving singularity finite element models for fast fracture analysis. Eng. Fract. Mech. 15, 205–218

  17. Sindelar, P. (1978): Brottmekanisk dimensionering mot utmattning. Rapport HU-2013, Flygtekniska Försöksanstalten, Stockholm, Sweden

  18. Thesken, J.C.; Gudmundson, P. (1985): Application of the Akin singular element to dynamic fracture mechanics. Rpt. 65, TRITA-HFL-0065 ISSN 0281-1502, Dept, of Strength of Materials and Solid Mechanics, The Royal Institute of Technology, Stockholm, Sweden

  19. Tracey, J.E.; Cook, T.S. (1977): Analysis of power type singularities using finite elements. Int. Num. Meth. Eng. 11, 1225–1233

  20. Yamada, Y.; Ezawa, Y.; Nishiguchi, I. (1979): Reconsiderations on singularity or crack-tip elements. IJNME, 14, 1525–1544

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Communicated by S.N. Atluri, October 7, 1986

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Thesken, J.C., Gudmundson, P. Application of a variable order singular element to dynamic fracture mechanics. Computational Mechanics 2, 307–316 (1987). https://doi.org/10.1007/BF00296424

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Keywords

  • Stress Intensity Factor
  • Dynamic Stress
  • Dynamic Fracture
  • Crack Problem
  • Mesh Refinement