In this paper, an inertia-based stabilizing method is proposed to overcome the loss of numerical convergence in quasi-static simulations of fracture problems with unstable (fast or dynamic) crack propagation. The method guarantees unconditional convergence as the time increment step progressively decreases and it does not need any numerical damping or other solution enhancement parameters. It has been demonstrated, through direct simulations of several numerical examples with severe local or global instabilities, that the proposed method can effectively and efficiently overcome severe instability points unconditionally and regain stability if there exist mechanisms for stable crack propagation after passing through such instability points. In all the numerical tests, the new method outperforms other solution enhancement techniques, such as numerical damping, arc-length method, and implicit dynamic simulation method, in the solution accuracy and numerical robustness.
Issue Section:
Research Papers
References
1.
Spearing
, S. M.
, and Beaumont
, P. W. R.
, 1992
, “Fatigue Amage Mechanics of Composite Materials. I: Experimental Measurement of Damage and Post-Fatigue Properties
,” Compos. Sci. Technol.
, 44
(2
), pp. 159
–168
.2.
Yang
, Q. D.
, and Cox
, B. N.
, 2005
, “Cohesive Models for Damage Evolution in Laminated Composites
,” Int. J. Fract.
, 133
(2
), pp. 107
–137
.3.
Hallett
, S. R.
, and Wisnom
, M. R.
, 2006
, “Experimental Investigation of Progressive Damage and the Effect of Layup in Notched Tensile Tests
,” J. Compos. Mater.
, 40
(2
), pp. 119
–141
.4.
Yang
, Q. D.
, Rugg
, K.
, Cox
, B. N.
, and Shaw
, M. C.
, 2003
, “Failure in the Junction Region of T-Stiffeners: 3D-Braided vs. 2D Tape Laminate Stiffeners
,” Int. J. Solids Struct.
, 40
(7
), pp. 1653
–1668
.5.
Xie
, J.
, and Waas
, A.
, 2015
, “Predictions of Delamination Growth for Quasi-Static Loading of Composite Laminates
,” ASME J. Appl. Mech.
, 82
(8
), p. 081004
.6.
Cox
, B. N.
, and Yang
, Q. D.
, 2006
, “In Quest of Virtual Tests for Structural Composites
,” Science
, 314
(5802
), pp. 1102
–1107
.7.
Llorca
, J.
, González
, C.
, Molina-Aldareguía
, J. M.
, Segurado
, J.
, Seltzer
, R.
, Sket
, F.
, Rodríguez
, M.
, Sádaba
, S.
, Muñoz
, R.
, and Canal
, L. P.
, 2011
, “Multiscale Modeling of Composite Materials: A Roadmap Towards Virtual Testing
,” Adv. Mater.
, 23
(44
), pp. 5130
–5147
.8.
Yang
, Q. D.
, Cox
, B. N.
, Fang
, X. J.
, and Zhou
, Z. Q.
, 2011
, “Virtual Testing for Advanced Aerospace Composites: Advances and Future Needs
,” ASME J. Eng. Mater. Technol.
, 133
(1
), p. 011002
.9.
Jia
, Y. J.
, and Liu
, B.
, 2015
, “Crack Branching Characteristics at Different Propagation Speeds: From Quasi-Static to Supersonic Regime
,” ASME J. Appl. Mech.
, 81
(12
), p. 124501
.10.
Needleman
, A.
, 2015
, “The Effect of Rate Dependence on Localization of Deformation and Failure in Softening Solids
,” ASME J. Appl. Mech.
, 82
(2
), p. 021002
.11.
Moës
, N.
, Dolbow
, J.
, and Belytschko
, T.
, 1999
, “A Finite Element Method for Crack Growth Without Remeshing
,” Int. J. Numer. Methods Eng.
, 46
(1
), pp. 131
–150
.12.
Moës
, N.
, and Belytschko
, T.
, 2002
, “Extended Finite Element Method for Cohesive Crack Growth
,” Eng. Fract. Mech.
, 69
(7
), pp. 813
–833
.13.
Belytschko
, T.
, Gracia
, R.
, and Ventura
, G.
, 2009
, “A Review of Extended/Generalized Finite Element Methods for Material Modeling
,” Modelling Simul. Mater. Sci. Eng.
, 17
, p. 043001
.14.
Huynh
, D. B. P.
, and Belytschko
, T.
, 2009
, “The Extended Finite Element Method for Fracture in Composite Materials
,” Int. J. Numer. Methods Eng.
, 77
(2
), pp. 214
–239
.15.
Hettich
, T.
, Hund
, A.
, and Ramm
, E.
, 2008
, “Modeling of Failure in Composites by X-FEM and Level Sets Within a Multiscale Framework
,” Comput. Methods Appl. Mech. Eng.
, 197
(5
), pp. 414
–424
.16.
van de Meer
, F. P.
, and Sluys
, L. J.
, 2009
, “A Phantom Node Formulation With Mixed Mode Cohesive Law for Splitting in Laminates
,” Int. J. Fract.
, 158
(2
), pp. 107
–124
.17.
van de Meer
, F. P.
, Oliver
, C.
, and Sluys
, L. J.
, 2010
, “Computational Analysis of Progressive Failure in a Notched Laminate Including Shear Nonlinearity and Fiber Failure
,” Compos. Sci. Technol.
, 70
(4
), pp. 692
–700
.18.
De Carvalho
, N. V.
, Chen
, B. Y.
, Pinho
, S. T.
, Ratcliffe
, J. G.
, Baiz
, P. M.
, and Tay
, T. E.
, 2015
, “Modeling Delamination Migration in Cross-Ply Tape Laminates
,” Composites, Part A
, 71
, pp. 192
–203
.19.
Chen
, B. Y.
, Pinho
, S. T.
, De Carvalho
, N. V.
, Baiz
, P. M.
, and Tay
, T. E.
, 2014
, “A Floating Node Method for the Modelling of Discontinuities in Composites
,” Eng. Fract. Mech.
, 127
, pp. 104
–134
.20.
Iarve
, E. V.
, Mollenhauer
, D.
, and Kim
, R.
, 2005
, “Theoretical and Experimental Investigation of Stress Redistribution in Open-Hole Composite Laminates Due to Damage Accumulation
,” Composites, Part A
, 36
(2
), pp. 163
–171
.21.
Iarve
, E. V.
, Gurvich
, M. R.
, Mollenhauer
, D.
, Rose
, C. A.
, and Davila
, C. G.
, 2011
, “Mesh Independent Matrix Cracking and Delamination Modelling in Laminated Composites
,” Int. J. Numer. Methods Eng.
, 88
(8
), pp. 749
–773
.22.
Iarve
, E. V.
, Hoos
, K. H.
, and Mollenhauer
, D.
, 2014
, “Damage Initiation and Propagation Modeling in Laminated Composites Under Fatigue Loading
,” American Society for Composites 29th Technical Conference
, La Jolla, CA, Sept. 8–10, pp. 3440
–3456
.23.
Ling
, D. S.
, Yang
, Q. D.
, and Cox
, B. N.
, 2009
, “An Augmented Finite Element Method for Modeling Arbitrary Discontinuities in Composite Materials
,” Int. J. Fract.
, 156
(1
), pp. 53
–73
.24.
Fang
, X. J.
, Yang
, Q. D.
, Cox
, B. N.
, and Zhou
, Z. Q.
, 2011
, “An Augmented Cohesive Zone Element for Arbitrary Crack Coalescence and Bifurcation in Heterogeneous Materials
,” Int. J. Numer. Methods Eng.
, 88
(9
), pp. 841
–861
.25.
Fang
, X. J.
, Zhou
, Z. Q.
, Cox
, B. N.
, and Yang
, Q. D.
, 2011
, “High-Fidelity Simulations of Multiple Fracture Processes in a Laminated Composites in Tension
,” J. Mech. Phys. Solids
, 59
(7
), pp. 1355
–1373
.26.
Qiao
, H.
, Chen
, W. Q.
, Yang
, Q. D.
, and Lua
, J.
, 2011
, “Augmented Cohesive Elements for Efficient Delamination Analysis of Composite Laminates
,” ASME J. Eng. Mater. Technol.
, 133
(4
), p. 041010
.27.
Liu
, W.
, Yang
, Q. D.
, Mohammadizadeh
, S.
, Su
, X. Y.
, and Ling
, D. S.
, 2013
, “An Accurate and Efficient Augmented Finite Element Method for Arbitrary Crack Interactions
,” ASME J. Appl. Mech.
, 80
(4
), p. 041033
.28.
Liu
, W.
, Yang
, Q. D.
, Mohammadizadeh
, S.
, and Su
, X. Y.
, 2014
, “An Efficient Augmented Finite Element Method (A-FEM) for Arbitrary Cracking and Crack Interaction in Solids
,” Int. J. Numer. Methods Eng.
, 99
(6
), pp. 438
–468
.29.
Davila
, C. G.
, Camanho
, P. P.
, and Turon
, A.
, 2008
, “Effective Simulation of Delamination in Aeronautical Structures Using Shells and Cohesive Elements
,” J. Aircr.
, 45
(2
), pp. 663
–672
.30.
Ladevèze
, P.
, Allix
, O.
, Duo
, J. F.
, and Leveque
, D.
, 2000
, “A Mesomodel for Localisation and Damage Computation in Laminates
,” Comput. Methods Appl. Mech. Eng.
, 183
(1–2
), pp. 105
–122
.31.
Hilber
, H. M.
, Hughes
, T. J. R.
, and Taylor
, R. L.
, 1978
, “Collocation, Dissipation and ‘Overshoot’ for Time Integration Schemes in Structural Dynamics
,” Earthquake Eng. Struct. Dyn.
, 6
(1
), pp. 99
–117
.32.
Hilber
, H. M.
, Hughes
, T. J. R.
, and Taylor
, R. L.
, 1977
, “Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics
,” Earthquake Eng. Struct. Dyn.
, 5
(3
), pp. 283
–292
.33.
Riks
, E.
, 1979
, “An Incremental Approach to the Solution of Snapping and Buckling Problems
,” Int. J. Solids Struct.
, 15
(7
), pp. 529
–551
.34.
Crisfield
, M. A.
, 1981
, “A Fast Incremental/Iterative Solution Procedure That Handles ‘Snap-Through’
,” Comput. Struct.
, 13
(1–3
), pp. 55
–62
.35.
de Borst
, R.
, 1999
, “Computation of Post-Bifurcation and Post-Failure Behaviour of Strain-Softening Solids
,” Comput. Struct.
, 25
(2
), pp. 211
–224
.36.
Geers
, M. G. D.
, 1999
, “Enhanced Solution Control for Physically and Geometrically Nonlinear Problems. Part I—The Subplane Control Approach
,” Int. J. Numer. Methods Eng.
, 46
(2
), pp. 177
–204
.37.
May
, I. M.
, and Duan
, Y.
, 1997
, “A Local Arc-Length Procedure for Strain Softening
,” Comput. Struct.
, 64
(1–4
), pp. 297
–303
.38.
Liu
, W.
, Schesser
, D.
, Yang
, Q. D.
, and Ling
, D. S.
, 2015
, “A Consistency-Check Based Algorithm for Element Condensation in Augmented Finite Element Methods for Fracture Analysis
,” Eng. Fract. Mech.
, 139
, pp. 78
–97
.39.
ABAQUS
, 2011
, “ABAQUS Version 6.11 Theory Manual
,” ABAQUS Inc., Pawtucket, RI.40.
Hutchinson
, J. W.
, and Suo
, Z.
, 1992
, “Mixed Mode Cracking in Layered Materials
,” Adv. Appl. Mech.
, 29
, pp. 63
–191
.41.
Turon
, A.
, Davila
, C. G.
, Camanho
, P. P.
, and Costa
, J.
, 2007
, “An Engineering Solution for Mesh Size Effects in the Simulation of Delamination Using Cohesive Zone Models
,” Eng. Fract. Mech.
, 74
(10
), pp. 1665
–1682
.42.
Hallett
, S. R.
, and Wisnom
, M. R.
, 2006
, “Numerical Investigation of Progressive Damage and the Effect of Layup in Notched Tensile Tests
,” J. Compos. Mater.
, 40
(14
), pp. 1229
–1245
.43.
Yang
, Q. D.
, Fang
, X. J.
, Shi
, J.
, and Lua
, J.
, 2010
, “An Improved Cohesive Element for Shell Delamination Analyses
,” Int. J. Numer. Methods Eng.
, 83
(5
), pp. 611
–641
.44.
Zhou
, Z. Q.
, Fang
, X. J.
, Cox
, B. N.
, and Yang
, Q. D.
, 2010
, “The Evolution of a Transverse Intra-Ply Crack Coupled to Delamination Cracks
,” Int. J. Fract.
, 165
(1
), pp. 77
–92
.45.
Verhoosel
, C. V.
, Remmers
, J. J. C.
, and Gutierrez
, M. A.
, 2008
, “A Dissipation-Based Arc-Length Method for Robust Simulation of Brittle and Ductile Failure
,” Int. J. Numer. Methods Eng.
, 77
(9
), pp. 1290
–1321
.46.
Hughes
, T. J. R.
, and Liu
, W. K.
, 1978
, “Implicit–Explicit Finite Elements in Transient Analysis: Stability Theory
,” ASME J. Appl. Mech.
, 45
(2
), pp. 371
–374
.47.
Jung
, J.
, and Yang
, Q. D.
, “An Augmented Finite Element for Dynamic Crack Growth in Elastic Solids
,” Int. J. Fract.
(submitted).Copyright © 2015 by ASME
You do not currently have access to this content.
