Dynamic crack propagation in plates weakened by inclined cracks: an investigation based on peridynamics
A. SHAFIEI
Dynamic crack propagation in plates weakened by inclined cracks: an investigation based on peridynamics
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.
peridynamics / inclined crack / dynamic fracture / crack branching
[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: 1–38
|
[2] |
Zehnder A. Fracture Mechanics. Springer Netherlands, 2012
|
[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): 1391–1411
CrossRef
Google scholar
|
[4] |
Areias P, Rabczuk T, Camanho P P. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics, 2013, 52(4): 931–947
CrossRef
Google scholar
|
[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): 45–57
CrossRef
Google scholar
|
[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): 48–71
|
[7] |
Ravi-Chandar. Dyanamic Fracture. Elsevier, 2004
|
[8] |
Areias P M A, Rabczuk T, Camanho P P. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63
CrossRef
Google scholar
|
[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): 2437–2455
CrossRef
Google scholar
|
[10] |
Song J, Wang H, Belytschko T. A comparative study on finite element method for dynamic fracture. Computational Mechanics, 2008, 42(2): 239–250
CrossRef
Google scholar
|
[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): 2316–2343
CrossRef
Google scholar
|
[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): 273–495
CrossRef
Google scholar
|
[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): 1099–1122
CrossRef
Google scholar
|
[14] |
Silling S. Reformulation of elasticity theory for discontinuities and long-rang forces. Journal of the Mechanics and Physics of Solids, 2000, 48(1): 175–209
CrossRef
Google scholar
|
[15] |
Silling S, Lehoucq R. Peridynamic theory of solid mechanics. Advances in Applied Mechanics, 2010, 44(10): 73–168
|
[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): 527–541
CrossRef
Google scholar
|
[17] |
Budarapu P, Gracie R, Bordas S, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148
CrossRef
Google scholar
|
[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): 223–248
CrossRef
Google scholar
|
[19] |
Parks M, Lehoucq R, Plimpton S, Silling S. Implementing peridynamics within a molecular dynamics code. Computer Physics Communications, 2008, 179: 777–783
|
[20] |
Parks M, Seleson P, Plimpton S, Lehoucq R, Silling S. Peridynamics with LAMMPS: A User Guide v0.2 Beta, Sandia Report, 2010
|
[21] |
Silling S, Weckner O, Askari E, Bobaru F. Crack nucleation in a peridynamic solid. International Journal of Fracture, 2010, 162(1–2): 219–227
CrossRef
Google scholar
|
[22] |
Madenci E, Oterkus E. Peridynamics theory and its applications. New York: Springer-Verlag, 2014
|
[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): 165–177
CrossRef
Google scholar
|
[24] |
Ha Y D, Bobaru F. Studies of dynamic crack propagation and crack branching with Peridynamics. International Journal of Fracture, 2010, 162(1–2): 229–244
CrossRef
Google scholar
|
[25] |
Ha Y D, Bobaru F. Characteristics of dynamic brittle fracture captured with Peridynamics. Engng Fract Mech, 2011 (78): 1156–1168
|
[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: 762–782
CrossRef
Google scholar
|
[27] |
Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-Horizon Peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476
CrossRef
Google scholar
|
[28] |
Silling S, Askari E. A mesh free method based on the peridynamic model of solid Mechanics. Comput Struct, 2005, 83(17): 1526–1535
|
[29] |
Sticker B, Schachinger E. Basic Concepts in Computational Physics. Springer, 2014
|
/
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