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.
. [J]. Frontiers of Structural and Civil Engineering, 2018, 12(4): 527-535.
A. SHAFIEI. Dynamic crack propagation in plates weakened by inclined cracks: an investigation based on peridynamics. Front. Struct. Civ. Eng., 2018, 12(4): 527-535.
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 https://doi.org/10.1016/j.compstruc.2008.08.010
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 https://doi.org/10.1007/s00466-013-0855-6
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 https://doi.org/10.1007/s00466-013-0891-2
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 https://doi.org/10.1016/j.tafmec.2014.06.006
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 https://doi.org/10.1016/j.cma.2010.03.031
10
Song J, Wang H, Belytschko T. A comparative study on finite element method for dynamic fracture. Computational Mechanics, 2008, 42(2): 239–250 https://doi.org/10.1007/s00466-007-0210-x
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 https://doi.org/10.1002/nme.1151
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 https://doi.org/10.1007/s00466-006-0122-1
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 https://doi.org/10.1002/nme.4477
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 https://doi.org/10.1016/S0022-5096(99)00029-0
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 https://doi.org/10.1615/IntJMultCompEng.2013005838
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 https://doi.org/10.1007/s00466-013-0952-6
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 https://doi.org/10.1615/IntJMultCompEng.2014007954
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 https://doi.org/10.1007/s10704-010-9447-z
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 https://doi.org/10.1007/s10704-009-9355-2
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 https://doi.org/10.1007/s10704-010-9442-4
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 https://doi.org/10.1016/j.cma.2016.12.031
27
Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-Horizon Peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476 https://doi.org/10.1002/nme.5257
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
