Advertisement

Dynamic crack propagation in plates weakened by inclined cracks: an investigation based on peridynamics

  • A. Shafiei
Research Article
  • 31 Downloads

Abstract

Peridynamics is a theory in solid mechanics that uses integral equations instead of partial differential equations as governing equations. It can be applied to fracture problems in contrast to the approach of fracture mechanics. In this paper by using peridynamics, the crack path for inclined crack under dynamic loading were investigated. The peridynamics solution for this problem represents the main features of dynamic crack propagation such as crack bifurcation. The problem is solved for various angles and different stress values. In addition, the influence of geometry on inclined crack growth is studied. The results are compared with molecular dynamic solutions that seem to show reasonable agreement in branching position and time.

Keywords

peridynamics inclined crack dynamic fracture crack branching 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Rabczuk T. Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives. ISRN Applied Mathematics, 2013: 1–38MATHGoogle Scholar
  2. 2.
    Zehnder A. Fracture Mechanics. Springer Netherlands, 2012CrossRefGoogle Scholar
  3. 3.
    Rabczuk T, Bordas S, Zi G. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411CrossRefGoogle Scholar
  4. 4.
    Areias P, Rabczuk T, Camanho P P. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics, 2013, 52(4): 931–947CrossRefMATHGoogle Scholar
  5. 5.
    Amiri F, Anitescu C, Arroyo M, Bordas S, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Rabczuk T, Gracie R, Song J H, Belytschko T. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, (81): 48–71MathSciNetMATHGoogle Scholar
  7. 7.
    Ravi-Chandar. Dyanamic Fracture. Elsevier, 2004Google Scholar
  8. 8.
    Areias PMA, Rabczuk T, Camanho P P. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63CrossRefGoogle Scholar
  9. 9.
    Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455CrossRefMATHGoogle Scholar
  10. 10.
    Song J, Wang H, Belytschko T. A comparative study on finite element method for dynamic fracture. Computational Mechanics, 2008, 42(2): 239–250CrossRefMATHGoogle Scholar
  11. 11.
    Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343CrossRefMATHGoogle Scholar
  12. 12.
    Rabczuk T, Bordas S, Zi G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 273–495CrossRefMATHGoogle Scholar
  13. 13.
    Areias P, Rabczuk T. Finite strain fracture of plates and shells with configurational forces and edge rotation. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Silling S. Reformulation of elasticity theory for discontinuities and long-rang forces. Journal of the Mechanics and Physics of Solids, 2000, 48(1): 175–209MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Silling S, Lehoucq R. Peridynamic theory of solid mechanics. Advances in Applied Mechanics, 2010, 44(10): 73–168CrossRefGoogle Scholar
  16. 16.
    Talebi H, Silani M, Bordas S P A, Kerfriden P, Rabczuk T. Molecular dynamics/XFEM coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture. International Journal for Multiscale Computational Engineering, 2013, 11(6): 527–541CrossRefGoogle Scholar
  17. 17.
    Budarapu P, Gracie R, Bordas S, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148CrossRefMATHGoogle Scholar
  18. 18.
    Rahman R, Foster J T, Haque A. A multiscale modeling scheme based on peridynamic theory. International Journal of Multiscale Computational Engineering, 2014, 12(3): 223–248CrossRefGoogle Scholar
  19. 19.
    Parks M, Lehoucq R, Plimpton S, Silling S. Implementing peridynamics within a molecular dynamics code. Computer Physics Communications, 2008, 179: 777–783CrossRefMATHGoogle Scholar
  20. 20.
    Parks M, Seleson P, Plimpton S, Lehoucq R, Silling S. Peridynamics with LAMMPS: A User Guide v0.2 Beta, Sandia Report, 2010Google Scholar
  21. 21.
    Silling S, Weckner O, Askari E, Bobaru F. Crack nucleation in a peridynamic solid. International Journal of Fracture, 2010, 162(1–2): 219–227CrossRefMATHGoogle Scholar
  22. 22.
    Madenci E, Oterkus E. Peridynamics theory and its applications. New York: Springer-Verlag, 2014CrossRefMATHGoogle Scholar
  23. 23.
    Kilic B, Madenci E. Peridiction of crack paths in a quenched glass plate by using peridynamic theory. International Journal of Fracture, 2009, 156(2): 165–177CrossRefMATHGoogle Scholar
  24. 24.
    Ha Y D, Bobaru F. Studies of dynamic crack propagation and crack branching with Peridynamics. International Journal of Fracture, 2010, 162(1–2): 229–244CrossRefMATHGoogle Scholar
  25. 25.
    Ha Y D, Bobaru F. Characteristics of dynamic brittle fracture captured with Peridynamics. Engng Fract Mech, 2011 (78): 1156–1168CrossRefGoogle Scholar
  26. 26.
    Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: a stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782MathSciNetCrossRefGoogle Scholar
  27. 27.
    Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-Horizon Peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476MathSciNetCrossRefGoogle Scholar
  28. 28.
    Silling S, Askari E. A mesh free method based on the peridynamic model of solid Mechanics. Comput Struct, 2005, 83(17): 1526–1535CrossRefGoogle Scholar
  29. 29.
    Sticker B, Schachinger E. Basic Concepts in Computational Physics. Springer, 2014CrossRefMATHGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringYazd UniversityYazdIran
  2. 2.Institute of Structural MechanicsBauhaus UniversityWeimarGermany

Personalised recommendations