Citation: Bozo Vazic, Hanlin Wang, Cagan Diyaroglu, Selda Oterkus, Erkan Oterkus. Dynamic propagation of a macrocrack interacting with parallel small cracks[J]. AIMS Materials Science, 2017, 4(1): 118-136. doi: 10.3934/matersci.2017.1.118
[1] | Hillerborg A, Modeer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res 6: 773–781. doi: 10.1016/0008-8846(76)90007-7 |
[2] | Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42: 1397–1434. doi: 10.1016/0022-5096(94)90003-5 |
[3] | Skumar N, Moes N, Moran B, et al. (2000) Extended finite element method for three-dimensional crack modelling. Int J Numer Meth Eng 48: 1549–1570. |
[4] | Moes N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69: 813–833. doi: 10.1016/S0013-7944(01)00128-X |
[5] | Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract 162: 229–244. doi: 10.1007/s10704-010-9442-4 |
[6] | Benz W, Asphaug E (1995) Simulations of brittle solids using smooth particle hydrodynamics. Comput Phys Commun 87: 253–265. doi: 10.1016/0010-4655(94)00176-3 |
[7] | Rabczuk T, Belytschko T (2007) A three dimensional large deformation meshfree method for arbitrary evolving cracks. Comput Method Appl M 196: 2777–2799. doi: 10.1016/j.cma.2006.06.020 |
[8] | Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Meth Eng 61: 2316–2343. doi: 10.1002/nme.1151 |
[9] | Griffths DV, Mustoe GGW (2001) Modelling of elastic continua using a grillage of structural elements based on discrete element concepts. Int J Numer Meth Eng 50: 1759–1775. doi: 10.1002/nme.99 |
[10] | Bolander JE, Sukumar N (2005) Irregular lattice model for quasistatic crack propagation. Phys Rev B 71: 094106. doi: 10.1103/PhysRevB.71.094106 |
[11] | O’Brien GS, Bean CJ (2011) An irregular lattice method for elastic wave propagation. Geophys J Int 187: 1699–1707. doi: 10.1111/j.1365-246X.2011.05229.x |
[12] | Pazdniakou A, Adler PM (2012) Lattice spring models. Transport Porous Med 93: 243–262. doi: 10.1007/s11242-012-9955-6 |
[13] | Morrison CN, Zhang M, Liu D, et al. (2015) Site-bond lattice modelling of damage process in nuclear graphite under bending Transactions, SMiRT-23 Manchester, United Kingdom. |
[14] | Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48: 175–209. doi: 10.1016/S0022-5096(99)00029-0 |
[15] | Silling SA, Askari A (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83: 1526–1535. doi: 10.1016/j.compstruc.2004.11.026 |
[16] | Silling SA, Epton M, Weckner O, et al. (2007) Peridynamics states and constitutive modeling. J Elasticity 88: 151–184. doi: 10.1007/s10659-007-9125-1 |
[17] | Diyaroglu C, Oterkus E, Oterkus S, et al. (2015) Peridynamics for bending of beams and plates with transverse shear deformation. Int J Solids Struct 69: 152–168. |
[18] | Oterkus S, Madenci E (2015) Peridynamics for antiplane shear and torsional deformations. J Mech Mater Struct 10: 167–193. doi: 10.2140/jomms.2015.10.167 |
[19] | Perre P, Almeida G, Ayouz M, et al. (2016) New modelling approaches to predict wood properties from its cellular structure: image-based representation and meshless methods. Ann Forest Sci 73: 147–162. doi: 10.1007/s13595-015-0519-0 |
[20] | Oterkus E, Madenci E (2012) Peridynamics for failure prediction in composites. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii. |
[21] | Oterkus E, Barut A, Madenci E (2010) Damage Growth Prediction from Loaded Composite Fastener Holes by Using Peridynamic Theory. 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Orlando, Florida. |
[22] | Madenci E, Oterkus E (2014) Peridynamic Theory and Its Applications, Springer, New York. |
[23] | Kilic B, Madenci E (2010) An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory. Theor Appl Fract Mec 53: 194–204. doi: 10.1016/j.tafmec.2010.08.001 |
[24] | Ayatollahi MR, Aliha MRM (2009) Analysis of a new specimen for mixed mode fracture tests on brittle materials. Eng Fract Mech 76: 1563–1573. doi: 10.1016/j.engfracmech.2009.02.016 |
[25] | Wang H, Liu Z, Xu D, et al. (2016) Extended finite element method analysis for shielding and amplification effect of a main crack interacted with a group of nearby parallel microcracks. Int J Damage Mech 25: 4–25. doi: 10.1177/1056789514565933 |
[26] | Rubinstein AA (1985) Macrocrack interaction with semi-infinite microcrack array. Int J Fract 27: 113–119. |