This paper presents an analysis of interacting cracks using a generalized finite element method (GFEM) enriched with so-called global-local functions. In this approach, solutions of local boundary value problems computed in a global-local analysis are used to enrich the global approximation space through the partition of unity framework used in the GFEM. This approach is related to the global-local procedure in the FEM, which is broadly used in industry to analyze fracture mechanics problems in complex three-dimensional geometries. In this paper, we compare the effectiveness of the global-local FEM with the GFEM with global-local enrichment functions. Numerical experiments demonstrate that the latter is much more robust than the former. In particular, the GFEM is less sensitive to the quality of boundary conditions applied to local problems than the global-local FEM. Stress intensity factors computed with the conventional global-local approach showed errors of up to one order of magnitude larger than in the case of the GFEM. The numerical experiments also demonstrate that the GFEM can account for interactions among cracks with different scale sizes, even when not all cracks are modeled in the global domain.

1.
Kayama
,
M.
, and
Totsuka
,
N.
, 2002, “
Influence of Interaction Between Multiple Cracks on Stress Corrosion Crack Propagation
,”
Corros. Sci.
0010-938X,
44
, pp.
2333
2352
(2002).
2.
Kayama
,
M.
, and
Kitamura
,
T.
, 2004, “
A Simulation on Growth of Multiple Small Cracks Under Stress Corrosion
,”
Int. J. Fract.
0376-9429,
130
, pp.
787
801
.
3.
Kebir
,
H.
,
Roelandt
,
J. M.
, and
Chambon
,
L.
, 2006, “
Dual Boundary Element Method Modelling of Aircraft Structural Joints With Multiple Site Damage
,”
Eng. Fract. Mech.
0013-7944,
73
, pp.
418
434
.
4.
Seyedi
,
M.
,
Taheri
,
S.
, and
Hild
,
F.
, 2006, “
Numerical Modeling of Crack Propagation and Shielding Effects in a Striping Network
,”
Nucl. Eng. Des.
0029-5493,
236
, pp.
954
964
.
5.
Felippa
,
C. A.
, 2004, “
Introduction to Finite Element Methods
,” Course Notes, Department of Aerospace Engineeing Sciences, University of Colorado at Boulder, available at http://www.colorado.edu/engineering/Aerospace/CAS/courses.d/IFEM.d/http://www.colorado.edu/engineering/Aerospace/CAS/courses.d/IFEM.d/.
6.
Noor
,
A. K.
, 1986, “
Global-Local Methodologies and Their Applications to Nonlinear Analysis
,”
Finite Elem. Anal. Design
0168-874X,
2
, pp.
333
346
.
7.
Diamantoudis
,
A. Th.
, and
Labeas
,
G. N.
, 2005, “
Stress Intensity Factors of Semi-Elliptical Surface Cracks in Pressure Vessels by Global-Local Finite Element Methodology
,”
Eng. Fract. Mech.
0013-7944,
72
, pp.
1299
1312
.
8.
Duarte
,
C. A.
,
Kim
,
D.-J.
, and
Babuška
,
I.
, 2007,
Advances in Meshfree Techniques
(
Computational Methods in Applied Sciences
, Vol.
5
),
V. M. A.
Leitão
,
C. J. S.
Alves
, and
C. A.
Duarte
, eds.,
Springer
,
The Netherlands
, pp.
1
26
.
9.
Duarte
,
C. A.
, and
Kim
,
D.-J.
, 2008, “
Analysis and Applications of a Generalized Finite Element Method With Global-Local Enrichment Functions
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
197
(
6–8
), pp.
487
504
.
10.
Civelek
,
M. B.
, and
Erdogan
,
F.
, 1982, “
Crack Problems for a Rectangular Plate and an Infinite Strip
,”
Int. J. Fract.
0376-9429,
19
, pp.
139
159
.
11.
Sun
,
C. T.
, and
Mao
,
K. M.
, 1988, “
A Global-Local Finite Element Method Suitable for Parallel Computations
,”
Comput. Struct.
0045-7949,
29
, pp.
309
315
.
12.
Babuška
,
I.
, and
Strouboulis
,
T.
, 2001,
The Finite Element Method and its Reliability
(
Numerical Mathematics and Scientific Computation
)
Oxford Science
,
New York
.
13.
Babuška
,
I.
, and
Melenk
,
J. M.
, 1997, “
The Partition of Unity Finite Element Method
,”
Int. J. Numer. Methods Eng.
0029-5981,
40
, pp.
727
758
.
14.
Duarte
,
C. A.
,
Babuška
,
I.
, and
Oden
,
J. T.
, 2000, “
Generalized Finite Element Methods for Three Dimensional Structural Mechanics Problems
,”
Comput. Struct.
0045-7949,
77
, pp.
215
232
.
15.
Oden
,
J. T.
,
Duarte
,
C. A.
, and
Zienkiewicz
,
O. C.
, 1998, “
A New Cloud-Based hp Finite Element Method
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
153
, pp.
117
126
.
16.
Strouboulis
,
T.
,
Copps
,
K.
, and
Babuška
,
I.
, 2001, “
The Generalized Finite Element Method
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
, pp.
4081
4193
.
17.
Duarte
,
C. A.
,
Kim
,
D.-J.
, and
Quaresma
,
D. M.
, 2006, “
Arbitrarily Smooth Generalized Finite Element Approximations
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
196
, pp.
33
56
.
18.
Oden
,
J. T.
, and
Duarte
,
C. A.
, 1997,
Recent Developments in Computational and Applied Mechanics
,
B. D.
Reddy
, ed.,
International Center for Numerical Methods in Engineering (CIMNE)
,
Barcelona, Spain
, pp.
302
321
.
19.
Oden
,
J. T.
, and
Duarte
,
C. A. M.
, 1996,
The Mathematics of Finite Elements and Applications—Highlights 1996
,
J. R.
Whiteman
, ed.,
Wiley
,
New York
, Chap. 2, pp.
35
54
.
20.
Duarte
,
C. A.
,
Hamzeh
,
O. N.
,
Liszka
,
T. J.
, and
Tworzydlo
,
W. W.
, 2001, “
A Generalized Finite Element Method for the Simulation of Three-Dimensional Dynamic Crack Propagation
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
, pp.
2227
2262
.
21.
Moes
,
N.
,
Dolbow
,
J.
, and
Belytschko
,
T.
, 1999, “
A Finite Element Method for Crack Growth Without Remeshing
,”
Int. J. Numer. Methods Eng.
0029-5981,
46
, pp.
131
150
.
22.
Sukumar
,
N.
,
Moes
,
N.
,
Moran
,
B.
, and
Belytschko
,
T.
, 2000, “
Extended Finite Element Method for Three-Dimensional Crack Modelling
,”
Int. J. Numer. Methods Eng.
0029-5981,
48
(
11
), pp.
1549
1570
.
23.
Wells
,
G. N.
, and
Sluys
,
L. J.
, 2001, “
A New Method for Modeling Cohesive Cracks Using Finite Elements
,”
Int. J. Numer. Methods Eng.
0029-5981,
50
, pp.
2667
2682
.
24.
Simone
,
A.
, 2004, “
Partition of Unity-Based Discontinuous Elements for Interface Phenomena
,”
Int. J. Math. Model.
0270-0225,
20
, pp.
465
478
.
25.
Duarte
,
C. A.
,
Reno
,
L. G.
, and
Simone
,
A.
, 2007, “
A High-Order Generalized FEM for Through-The-Thickness Branched Cracks
,”
Int. J. Numer. Methods Eng.
0029-5981,
72
(
3
), pp.
325
351
.
26.
Strouboulis
,
T.
,
Zhang
,
L.
, and
Babuška
,
I.
, 2003, “
Generalized Finite Element Method Using Mesh-Based Handbooks: Application to Problems in Domains With Many Voids
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
192
, pp.
3109
3161
.
27.
Szabo
,
B. A.
, and
Babuška
,
I.
, 1988, “
Computation of the Amplitude of Stress Singular Terms for Cracks and Reentrant Corners
,”
Fracture Mechanics: Nineteenth Symposium
,
T. A.
Cruse
, ed.,
American Society for Testing and Materials
,
Philadelphia
, pp.
101
124
, ASTM STP, 969.
28.
Pereira
,
J. P.
, and
Duarte
,
C. A.
, 2005, “
Extraction of Stress Intensity Factors From Generalized Finite Element Solutions
,”
Eng. Anal. Boundary Elem.
0955-7997,
29
, pp.
397
413
.
29.
Pereira
,
J. P.
, and
Duarte
,
C. A.
, 2004, “
Computation of Stress Intensity Factors for Pressurized Cracks Using the Generalized Finite Element Method and Superconvergent Extraction Techniques
,”
XXV Iberian Latin-American Congress on Computational Methods in Engineering
, Recife, PE, Brazil, Nov.,
P. R. M.
Lyra
,
S. M. B. A.
da Silva
,
F. S.
Magnani
,
L. J.
do
,
N.
Guimaraes
,
L. M.
da Costa
, and
E.
Parente
, Jr.
, eds.
30.
Babuška
,
I.
, and
Andersson
,
B.
, 2005, “
The Splitting Method as a Tool for Multiple Damage Analysis
,”
SIAM J. Sci. Comput. (USA)
1064-8275,
26
, pp.
1114
1145
.
31.
Yohannes
,
A.
,
Cartwright
,
D. J.
, and
Collins
,
R. A.
, 1996, “
Application of a Discontinuous Strip Yield Model to Multiple Site Damage in Stiffened Sheets
,”
The 1996 Forth International Conference on Computer-Aided Assesment and Control
,
Fukuoka, Japan
, pp.
565
572
.
32.
Wang
,
L.
,
Brust
,
F. W.
, and
Atluri
,
S. N.
, 1997, “
The Elastic-Plastic Finite Element Alternating Method (EPFEAM) and the Prediction of Fracture Under WFD Conditions in Aircraft Structures
,”
Comput. Mech.
0178-7675,
19
, pp.
356
369
.
33.
Stern
,
M.
,
Becker
,
E. B.
, and
Dunham
,
R. S.
, 1976, “
A Contour Integral Computation of Mixed-Mode Stress Intensity Factors
,”
Int. J. Fract.
0376-9429,
12
, pp.
359
368
.
34.
Pereira
,
J. P.
, and
Duarte
,
C. A.
, 2006, “
The Contour Integral Method for Loaded Cracks
,”
Int. J. Math. Model.
0270-0225,
22
(
5
), pp.
421
432
.
You do not currently have access to this content.