A finite element method for the simulation of dynamic cracks in thin shells and its applications to quasibrittle fracture problem are presented. Discontinuities in the translational and angular velocity fields are introduced to model cracks by the extended finite element method. The proposed method is implemented for the Belytschko–Lin–Tsay shell element, which has high computational efficiency because of its use of a one-point integration scheme. Comparisons with elastoplastic crack propagation experiments involving quasibrittle fracture show that the method is able to reproduce experimental fracture patterns quite well.
Issue Section:
Advances in Impact Engineering
1.
Belytschko
, T.
, and Black
, T.
, 1999, “Elastic Crack Growth in Finite Elements With Minimal Remeshing
,” Int. J. Numer. Methods Eng.
0029-5981, 45
(5
), pp. 601
–620
.2.
Moës
, N.
, Dolbow
, J.
, and Belytschko
, T.
, 1999, “A Finite Element Method for Crack Growth Without Remeshing
,” Int. J. Numer. Methods Eng.
0029-5981, 46
(1
), pp. 131
–150
.3.
Hansbo
, A.
, and Hansbo
, P.
, 2004, “A Finite Element Method for the Simulation of Strong and Weak Discontinuities in Solid Mechanics
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 193
, pp. 3523
–3540
.4.
Mergheim
, J.
, Kuhl
, E.
, and Steinmann
, P.
, 2005, “A Finite Element Method for the Computational Modelling of Cohesive Cracks
,” Int. J. Numer. Methods Eng.
0029-5981, 63
, pp. 276
–289
.5.
Song
, J. H.
, Areias
, P. M. A.
, and Belytschko
, T.
, 2006, “A Method for Dynamic Crack and Shear Band Propagation With Phantom Nodes
,” Int. J. Numer. Methods Eng.
0029-5981, 67
, pp. 868
–893
.6.
Areias
, P. M. A.
, Song
, J. H.
, and Belytschko
, T.
, 2005, “A Finite-Strain Quadrilateral Shell Element Based on Discrete Kirchhoff-Love Constraints
,” Int. J. Numer. Methods Eng.
0029-5981, 64
, pp. 1166
–1206
.7.
Areias
, P. M. A.
, Song
, J. H.
, and Belytschko
, T.
, 2006, “Analysis of Fracture in Thin Shells by Overlapping Paired Elements
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 195
, pp. 5343
–5360
.8.
Areias
, P. M. A.
, and Belytschko
, T.
, 2006, “A Comment on the Article: A Finite Element Method for Simulation of Strong and Weak Discontinuities in Solid Mechanics
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 195
, pp. 275
–1276
.9.
Belytschko
, T.
, Chen
, H.
, Xu
, J.
, and Zi
, G.
, 2003, “Dynamic Crack Propagation Based on Loss of Hyperbolicity With a New Discontinuous Enrichment
,” Int. J. Numer. Methods Eng.
0029-5981, 58
, pp. 1873
–1905
.10.
Réthoré
, J.
, Gravouil
, A.
, and Combescure
, A.
, 2005, “An Energy-Conserving Scheme for Dynamic Crack Growth Using the Extended Finite Element Method
,” Int. J. Numer. Methods Eng.
0029-5981, 63
, pp. 631
–659
.11.
Elguedj
, T.
, Gravouil
, A.
, and Combescure
, A.
, 2006, “Appropriate Extended Functions for X-Fem Simulation of Plastic Fracture Mechanics
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 195
, pp. 501
–515
.12.
Cirak
, F.
, Ortiz
, M.
, and Pandolfi
, A.
, 2005, “A Cohesive Approach to Thin-Shell Fracture and Fragmentation
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 194
, pp. 2604
–2618
.13.
Areias
, P. M. A.
, and Belytschko
, T.
, 2005, “Nonlinear Analysis of Shells With Arbitrary Evolving Cracks Using XFEM
,” Int. J. Numer. Methods Eng.
0029-5981, 62
, pp. 384
–415
.14.
Ortiz
, M.
, and Pandolfi
, A.
, 1999, “Finite-Deformation Irreversible Cohesive Elements for Three–Dimensional Crack-Propagation Analysis
,” Int. J. Numer. Methods Eng.
0029-5981, 44
, pp. 1267
–1282
.15.
Armero
, F.
, and Ehrlich
, D.
, 2006, “Finite Element Methods for the Multi-Scale Modeling of Softening Hinge Lines in Plates at Failure
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 195
, pp. 1283
–1324
.16.
Chao
, T. W.
, and Shepherd
, J. E.
, 2002, “Fracture Response of Externally-Flawed Cylindrical Shells to Internal Gaseous Detonation Loading
,” Emerging Technologies in Fluids, Structures, and Fluid/Structure Interactions
, ASME Pressure Vessels and Piping Conference
, Vancouver, BC, pp. 85
–98
.17.
Ahmad
, S.
, Irons
, B. B.
, and Zienkiewicz
, O. C.
, 1970, “Analysis of Thick and Thin Shell Structures by Curved Finite Elements
,” Int. J. Numer. Methods Eng.
0029-5981, 2
, pp. 419
–451
.18.
Hughes
, T. J. R.
, and Liu
, W. K.
, 1981, “Nonlinear Finite Element Analysis of Shells: Part 2, Two dimensional Shells
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 27
, pp. 167
–181
.19.
Hughes
, T. J. R.
, and Liu
, W. K.
, 1981, “Nonlinear Finite Element Analysis of Shells: Part 1, Three Dimensional Shells
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 26
, pp. 331
–362
.20.
Belytschko
, T.
, Lin
, J. I.
, and Tsay
, C. S.
, 1984, “Explicit Algorithms for the Nonlinear Dynamics of Shells
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 42
, pp. 225
–251
.21.
Belytschko
, T.
, Wong
, B. L.
, and Chiang
, H. Y.
, 1992, “Advances in One-Point Quadrature Shell Elements
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 96
, pp. 93
–107
.22.
Belytschko
, T.
, and Bachrach
, W. E.
, 1986, “Efficient Implementation of Quadrilaterals With High Coarse-Mesh Accuracy
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 54
, pp. 279
–301
.23.
Belytschko
, T.
, and Leviathan
, I.
, 1994, “Physical Stabilization of the 4-Node Shell Element With One Point Quadrature
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 113
, pp. 321
–350
.24.
Papoulia
, K. D.
, Sam
, C. H.
, and Vavasis
, S. A.
, 2003, “Time Continuity in Cohesive Finite Element Modeling
,” Int. J. Numer. Methods Eng.
0029-5981, 58
, pp. 679
–701
.25.
Chao
, T. W.
, 2004, “Gaseous Detonation-Driven Fracture of Tubes
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.26.
Johnson
, F. A.
, and Radon
, J. C.
, 1975, “Evaluation of Fracture Energy of Aluminum Alloys
,” J. Test. Eval.
0090-3973, 3
, pp. 364
–367
.27.
Johnson
, F. A.
, and Radon
, J. C.
, 1976, “Fracture Energy and Crack Tunnelling
,” J. Test. Eval.
0090-3973, 4
, pp. 209
–217
.28.
Roychowdhury
, S.
, Roy
, Y. D. A.
, and Dodds
, R. H.
, Jr., 2002, “Ductile Tearing in Thin Aluminum Panels: Experiments and Analyses Using Large-Displacement, 3-D Surface Cohesive Elements
,” Eng. Fract. Mech.
0013-7944, 69
, pp. 983
–1002
.29.
Beltman
, W. M.
, and Shepherd
, J. E.
, 2002, “Linear Elastic Response of Tubes to Internal Detonation Loading
,” J. Sound Vib.
0022-460X, 252
, pp. 617
–655
.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.