Composite structural parts have been successfully introduced in high performance industries. Nowadays, also lower performance, high volume production industries are looking for the application of composites in their products. Especially attractive are textile composites (woven, braided, etc.) because of their better drapability and higher resistance to out-of-plane and dynamic loads. Currently, however, extensive mechanical tests are needed to properly design a composite structure. This is a requirement the large volume industries typically do not have the resources nor the time for. Reducing the need for structural tests can only be done if reliable simulation techniques are available. Simulation techniques for fatigue loading are particularly interesting because products generally have to perform their function over a period of time. For the textile structural composites concerned in this paper, some notable modeling techniques have been developed over the past 15 years. These techniques are presented here and the state of the art is established together with insights for future development by comparing the state of the art with the modeling techniques for laminates from unidirectional (UD) laminae.

References

References
1.
Ayranci
,
C.
, and
Carey
,
J.
,
2008
, “
2D Braided Composites: A Review for Stiffness Critical Applications
,”
Compos. Struct.
,
85
(
1
), pp.
43
58
.10.1016/j.compstruct.2007.10.004
2.
Ladevèze
,
P.
,
2004
, “
Multiscale Modelling and Computational Strategies for Composites
,”
Int. J. Numer. Methods Eng.
,
60
(
1
), pp.
233
253
.10.1002/nme.960
3.
McCartney
,
L.
,
2008
, “
Energy Methods for Fatigue Damage Modelling of Laminates
,”
Compos. Sci. Technol.
,
68
(
13
), pp.
2601
2615
.10.1016/j.compscitech.2008.04.044
4.
Zhang
,
C.
, and
Xu
,
X.
,
2013
, “
Finite Element Analysis of 3D Braided Composites Based on Three Unit-Cells Models
,”
Compos. Struct.
,
98
, pp.
130
142
.10.1016/j.compstruct.2012.11.003
5.
Degrieck
,
J.
, and
Van Paepegem
,
W.
,
2001
, “
Fatigue Damage Modeling of Fibre-Reinforced Composite Materials: Review
,”
ASME Appl. Mech. Rev.
,
54
(
4
), pp.
279
300
.10.1115/1.1381395
6.
Pascoe
,
J.
,
Alderliesten
,
R.
, and
Benedictus
,
R.
,
2013
, “
Methods for the Prediction of Fatigue Delamination Growth in Composites and Adhesive Bonds: A Critical Review
,”
Eng. Fract. Mech.
,
112–113
, pp.
72
96
.10.1016/j.engfracmech.2013.10.003
7.
Icardi
,
U.
,
Locatto
,
S.
, and
Longo
,
A.
,
2007
, “
Assessment of Recent Theories for Predicting Failure of Composite Laminates
,”
ASME Appl. Mech. Rev.
,
60
(
2
), pp.
76
86
.10.1115/1.2515639
8.
Post
,
N. L.
,
Case
,
S. W.
, and
Lesko
,
J. J.
,
2008
, “
Modeling the Variable Amplitude Fatigue of Composite Materials: A Review and Evaluation of the State of the Art for Spectrum Loading
,”
Int. J. Fatigue
,
30
(
12
), pp.
2064
2086
.10.1016/j.ijfatigue.2008.07.002
9.
Soden
,
P.
,
Kaddour
,
A.
, and
Hinton
,
M.
,
2004
, “
Recommendations for Designers and Researchers Resulting From the World-Wide Failure Exercise
,”
Compos. Sci. Technol.
,
64
(
3–4
), pp.
589
604
.10.1016/S0266-3538(03)00228-8
10.
Quaresimin
,
M.
,
Susmel
,
L.
, and
Talreja
,
R.
,
2010
, “
Fatigue Behaviour and Life Assessment of Composite Laminates Under Multiaxial Loadings
,”
Int. J. Fatigue
,
32
(
1
), pp.
2
16
.10.1016/j.ijfatigue.2009.02.012
11.
Liu
,
P.
, and
Zheng
,
J.
,
2010
, “
Recent Developments on Damage Modeling and Finite Element Analysis for Composite Laminates: A Review
,”
Mater. Des.
,
31
(
8
), pp.
3825
3834
.10.1016/j.matdes.2010.03.031
12.
Daggumati
,
S.
,
De Baere
,
I.
,
Van Paepegem
,
W.
,
Degrieck
,
J.
,
Xu
,
J.
,
Lomov
,
S.
, and
Verpoest
,
I.
,
2013
, “
Fatigue and Post-Fatigue Stress-Strain Analysis of a 5-Harness Satin Weave Carbon Fibre Reinforced Composite
,”
Compos. Sci. Technol.
,
74
, pp.
20
27
.10.1016/j.compscitech.2012.09.012
13.
Cox
,
B.
,
Dadkhah
,
M.
, and
Inman
,
R.
,
1992
, “
Mechanisms of Compressive Failure in 3D Composites
,”
Acta Metall. Mater.
,
40
(
12
), pp.
3285
3298
.10.1016/0956-7151(92)90042-D
14.
Kawai
,
M.
, and
Matsuda
,
Y.
,
2012
, “
Anisomorphic Constant Fatigue Life Diagrams for a Woven Fabric Carbon/Epoxy Laminate at Different Temperatures
,”
Composites, Part A
,
43
(
4
), pp.
647
657
.10.1016/j.compositesa.2012.01.009
15.
Kawai
,
M.
,
Matsuda
,
Y.
, and
Yoshimura
,
R.
,
2012
, “
A General Method for Predicting Temperature-Dependent Anisomorphic Constant Fatigue Life Diagram for a Woven Fabric Carbon/Epoxy Laminate
,”
Composites, Part A
,
43
(
6
), pp.
915
925
.10.1016/j.compositesa.2012.01.025
16.
Kawai
,
M.
, and
Taniguchi
,
T.
,
2006
, “
Off-Axis Fatigue Behavior of Plain Weave Carbon/Epoxy Fabric Laminates at Room and High Temperatures and Its Mechanical Modeling
,”
Composites, Part A
,
37
(
2
), pp.
243
256
.10.1016/j.compositesa.2005.07.003
17.
Kawai
,
M.
, and
Murata
,
T.
,
2010
, “
A Three-Segment Anisomorphic Constant Life Diagram for the Fatigue of Symmetric Angle-Ply Carbon/Epoxy Laminates at Room Temperature
,”
Composites, Part A
,
41
(
10
), pp.
1498
1510
.10.1016/j.compositesa.2010.06.012
18.
Vania
,
A.
, and
Carvelli
,
V.
,
2010
,
Fitting Approach of the Fatigue Tensile Response of Textile Composite Materials
,
Destech Publications, Inc.
,
Lancaster, UK
.
19.
Carvelli
,
V.
,
Gramellini
,
G.
,
Lomov
,
S. V.
,
Bogdanovich
,
A. E.
,
Mungalov
,
D. D.
, and
Verpoest
,
I.
,
2010
, “
Fatigue Behavior of Non-Crimp 3D Orthogonal Weave and Multi-Layer Plain Weave E-Glass Reinforced Composites
,”
Compos. Sci. Technol.
,
70
(
14
), pp.
2068
2076
.10.1016/j.compscitech.2010.08.002
20.
Mouritz
,
A. P.
,
2005
, “
A Simple Fatigue Life Model for Three-Dimensional Fiber-Polymer Composites
,”
J. Compos. Mater.
,
40
(
5
), pp.
455
469
.10.1177/0021998305055199
21.
Toumi
,
R. B.
,
Renard
,
J.
,
Monin
,
M.
, and
Nimdum
,
P.
,
2013
, “
Fatigue Damage Modelling of Continuous E-Glass Fibre/Epoxy Composite
,”
Procedia Eng.
,
66
, pp.
723
736
.10.1016/j.proeng.2013.12.126
22.
Tamuzs
,
V.
,
Dzelzitis
,
K.
, and
Reifsnider
,
K.
,
2008
, “
Prediction of the Cyclic Durability of Woven Composite Laminates
,”
Compos. Sci. Technol.
,
68
(
13
), pp.
2717
2721
.10.1016/j.compscitech.2008.04.033
23.
Tamuzs
,
V.
,
Dzelzitis
,
K.
, and
Reifsnider
,
K.
,
2004
, “
Fatigue of Woven Composite Laminates in Off-Axis Loading I. The Mastercurves
,”
Appl. Compos. Mater.
,
11
(
5
), pp.
259
279
.10.1023/B:ACMA.0000037132.63191.3a
24.
Tamuzs
,
V.
,
Dzelzitis
,
K.
, and
Reifsnider
,
K.
,
2004
, “
Fatigue of Woven Composite Laminates in Off-Axis Loading II. Prediction of the Cyclic Durability
,”
Appl. Compos. Mater.
,
11
(
5
), pp.
281
293
.10.1023/B:ACMA.0000037131.70402.5e
25.
Naderi
,
M.
, and
Khonsari
,
M. M.
,
2012
, “
A Comprehensive Fatigue Failure Criterion Based on Thermodynamic Approach
,”
J. Compos. Mater.
,
46
(
4
), pp.
437
447
.10.1177/0021998311419540
26.
Naderi
,
M.
,
Kahirdeh
,
A.
, and
Khonsari
,
M. M.
,
2012
, “
Dissipated Thermal Energy and Damage Evolution of Glass/Epoxy Using Infrared Thermography and Acoustic Emission
,”
Composites, Part B
,
43
(
3
), pp.
1613
1620
.10.1016/j.compositesb.2011.08.002
27.
Naderi
,
M.
, and
Khonsari
,
M.
,
2012
, “
Thermodynamic Analysis of Fatigue Failure in a Composite Laminate
,”
Mech. Mater.
,
46
, pp.
113
122
.10.1016/j.mechmat.2011.12.003
28.
Naderi
,
M.
, and
Khonsari
,
M.
,
2013
, “
On the Role of Damage Energy in the Fatigue Degradation Characterization of a Composite Laminate
,”
Composites, Part B
,
45
(
1
), pp.
528
537
.10.1016/j.compositesb.2012.07.028
29.
Naderi
,
M.
,
Amiri
,
M.
, and
Khonsari
,
M. M.
,
2010
, “
On the Thermodynamic Entropy of Fatigue Fracture
,”
Proc. R. Soc. A
,
466
(
2114
), pp.
423
438
.10.1098/rspa.2009.0348
30.
Movaghghar
,
A.
, and
Lvov
,
G. I.
,
2011
, “
An Energy Model for Fatigue Life Prediction of Composite Materials Using Continuum Damage Mechanics
,”
Appl. Mech. Mater.
,
110–116
, pp.
1353
1360
.10.4028/www.scientific.net/AMM.110-116.1353
31.
Movaghghar
,
A.
, and
Lvov
,
G. I.
,
2012
, “
A Method of Estimating Wind Turbine Blade Fatigue Life and Damage Using Continuum Damage Mechanics
,”
Int. J. Damage Mech.
,
21
(
6
), pp.
810
821
.10.1177/1056789511419693
32.
Movaghghar
,
A.
, and
Lvov
,
G. I.
,
2012
, “
Theoretical and Experimental Study of Fatigue Strength of Plain Woven Glass/Epoxy Composite
,”
J. Mech. Eng.
,
58
(
3
), pp.
175
182
.10.5545/sv-jme.2011.135
33.
Mao
,
H.
, and
Mahadevan
,
S.
,
2002
, “
Fatigue Damage Modelling of Composite Materials
,”
Compos. Struct.
,
58
(
4
), pp.
405
410
.10.1016/S0263-8223(02)00126-5
34.
Kumar
,
R.
, and
Talreja
,
R.
,
2000
, “
Fatigue Damage Evolution in Woven Fabric Composites
,” Collection of the 41st
AIAA/ASME/ASCE/AHS/ASC
Structures, Structural Dynamics, and Materials Conference and Exhibit
, Vol.
1
, Pts. 1–3, pp.
1841
1849
.10.2514/6.2000-1685
35.
Toubal
,
L.
,
Karama
,
M.
, and
Lorrain
,
B.
,
2006
, “
Damage Evolution and Infrared Thermography in Woven Composite Laminates Under Fatigue Loading
,”
Int. J. Fatigue
,
28
(
12
), pp.
1867
1872
.10.1016/j.ijfatigue.2006.01.013
36.
Montesano
,
J.
,
Selezneva
,
M.
,
Fawaz
,
Z.
,
Poon
,
C.
, and
Behdinan
,
K.
,
2012
, “
Elevated Temperature Off-Axis Fatigue Behavior of an Eight-Harness Satin Woven Carbon-Fiber/Bismaleimide Laminate
,”
Composites, Part A
,
43
(
9
), pp.
1454
1466
.10.1016/j.compositesa.2012.04.016
37.
Slaughter
,
W.
, and
Fleck
,
N.
,
1993
, “
Compressive Fatigue of Fibre Composites
,”
J. Mech. Phys. Solids
,
41
(
8
), pp.
1265
1284
.10.1016/0022-5096(93)90079-U
38.
Dadkhah
,
M.
,
Cox
,
B.
, and
Morris
,
W.
,
1995
, “
Compression-Compression Fatigue of 3D Woven Composites
,”
Acta Metall.
,
43
(
12
), pp.
4235
4245
.10.1016/0956-7151(95)00137-K
39.
Chen
,
H.
,
Shivakumar
,
K.
, and
Abali
,
F.
,
2006
, “
A Comparison of Total Fatigue Life Models for Composite Laminates
,”
Fatigue Fract. Eng. Mater. Struct.
,
29
(
1
), pp.
31
39
.10.1111/j.1460-2695.2006.00958.x
40.
Shivakumar
,
K.
,
Chen
,
H.
,
Abali
,
F.
,
Le
,
D.
, and
Davis
,
C.
,
2006
, “
A Total Fatigue Life Model for Mode I Delaminated Composite Laminates
,”
Int. J. Fatigue
,
28
(
1
), pp.
33
42
.10.1016/j.ijfatigue.2005.04.006
41.
Bak
,
B. L. V.
,
Sarrado
,
C.
,
Turon
,
A.
, and
Costa
,
J.
,
2014
, “
Delamination Under Fatigue Loads in Composite Laminates: A Review on the Observed Phenomenology and Computational Methods
,”
ASME Appl. Mech. Rev.
,
66
(
6
), p.
060803
.10.1115/1.4027647
42.
Post
,
N.
,
Bausano
,
J.
,
Case
,
S.
, and
Lesko
,
J.
,
2006
, “
Modeling the Remaining Strength of Structural Composite Materials Subjected to Fatigue
,”
Int. J. Fatigue
,
28
(
10
), pp.
1100
1108
.10.1016/j.ijfatigue.2006.02.016
43.
Post
,
N. L.
,
Cain
,
J.
,
McDonald
,
K. J.
,
Case
,
S. W.
, and
Lesko
,
J. J.
,
2008
, “
Residual Strength Prediction of Composite Materials: Random Spectrum Loading
,”
Eng. Fract. Mech.
,
75
(
9
), pp.
2707
2724
.10.1016/j.engfracmech.2007.03.002
44.
Reifsnider
,
K. L.
, and
Case
,
S. W.
,
2002
,
Damage Tolerance and Durability of Material Systems
,
Wiley Interscience
, Hoboken, NJ.
45.
Khan
,
Z.
,
Al-Sulaiman
,
F. A.
,
Farooqi
,
J. K.
, and
Younas
,
M.
,
2001
, “
Fatigue Life Predictions in Woven Carbon Fabric/Polyester Composites Based on Modulus Degradation
,”
J. Reinf. Plast. Compos.
,
20
(
5
), pp.
377
398
.10.1177/073168401772678706
46.
Van Paepegem
,
W.
, and
Degrieck
,
J.
,
2005
, “
Simulating Damage and Permanent Strain in Composites Under In-Plane Fatigue Loading
,”
Comput. Struct.
,
83
(
23–24
), pp.
1930
1942
.10.1016/j.compstruc.2005.03.005
47.
Hochard
,
C.
,
Payan
,
J.
, and
Bordreuil
,
C.
,
2006
, “
A Progressive First Ply Failure Model for Woven Ply CFRP Laminates Under Static and Fatigue Loads
,”
Int. J. Fatigue
,
28
(
10
), pp.
1270
1276
.10.1016/j.ijfatigue.2006.02.024
48.
Wen
,
C.
, and
Yazdani
,
S.
,
2008
, “
Anisotropic Damage Model for Woven Fabric Composites During Tension-Tension Fatigue
,”
Compos. Struct.
,
82
(
1
), pp.
127
131
.10.1016/j.compstruct.2007.01.003
49.
Hansen
,
U.
,
1999
, “
Damage Development in Woven Fabric Composites During Tension-Tension Fatigue
,”
J. Compos. Mater.
,
33
(
7
), pp.
614
639
.10.1177/002199839903300702
50.
Tate
,
J. S.
, and
Kelkar
,
A. D.
,
2008
, “
Stiffness Degradation Model for Biaxial Braided Composites Under Fatigue Loading
,”
Composites, Part B
,
39
(
3
), pp.
548
555
.10.1016/j.compositesb.2007.03.001
51.
Van Paepegem
,
W.
, and
Degrieck
,
J.
,
2002
, “
A New Coupled Approach of Residual Stiffness and Strength for Fatigue of Fibre-Reinforced Composites
,”
Int. J. Fatigue
,
24
(
7
), pp.
747
762
.10.1016/S0142-1123(01)00194-3
52.
Van Paepegem
,
W.
, and
Degrieck
,
J.
,
2003
, “
Modelling Damage and Permanent Strain in Fibre-Reinforced Composites Under In-Plane Fatigue Loading
,”
Compos. Sci. Technol.
,
63
(
5
), pp.
677
694
.10.1016/S0266-3538(02)00257-9
53.
Van Paepegem
,
W.
, and
Degrieck
,
J.
,
2004
, “
Simulating In-Plane Fatigue Damage in Woven Glass Fibre-Reinforced Composites Subject to Fully Reversed Cyclic Loading
,”
Fatigue Fract. Eng. Mater. Struct.
,
27
(
12
), pp.
1197
1208
.10.1111/j.1460-2695.2004.00851.x
54.
Hochard
,
C.
, and
Thollon
,
Y.
,
2010
, “
A Generalized Damage Model for Woven Ply Laminates Under Static and Fatigue Loading Conditions
,”
Int. J. Fatigue
,
32
(
1
), pp.
158
165
.10.1016/j.ijfatigue.2009.02.016
55.
Hochard
,
C.
,
Miot
,
S.
, and
Thollon
,
Y.
,
2014
, “
Fatigue of Laminated Composite Structures With Stress Concentrations
,”
Composites, Part B
,
65
, pp.
11
16
.10.1016/j.compositesb.2013.10.020
56.
Bordreuil
,
C.
, and
Hochard
,
C.
,
2004
, “
Finite Element Computation of Woven Ply Laminated Composite Structures up to Rupture
,”
Appl. Compos. Mater.
,
11
(
3
), pp.
127
143
.10.1023/B:ACMA.0000026474.67067.b6
57.
Thollon
,
Y.
, and
Hochard
,
C.
,
2009
, “
A General Damage Model for Woven Fabric Composite Laminates up to First Failure
,”
Mech. Mater.
,
41
(
7
), pp.
820
827
.10.1016/j.mechmat.2009.02.009
58.
Benamira
,
M.
,
Hochard
,
C.
, and
Haiahem
,
A.
,
2011
, “
Behaviour to Failure of Fibre Mat Reinforced Composite Under Combined Loading Conditions
,”
Composites, Part B
,
42
(
6
), pp.
1412
1419
.10.1016/j.compositesb.2011.05.017
59.
Payan
,
J.
, and
Hochard
,
C.
,
2002
, “
Damage Modelling of Laminated Carbon/Epoxy Composites Under Static and Fatigue Loadings
,”
Int. J. Fatigue
,
24
(
2
), pp.
299
306
.10.1016/S0142-1123(01)00085-8
60.
Ladeveze
,
P.
, and
LeDantec
,
E.
,
1992
, “
Damage Modelling of the Elementary Ply for Laminated Composites
,”
Compos. Sci. Technol.
,
43
(
3
), pp.
257
267
.10.1016/0266-3538(92)90097-M
61.
Whitney
,
J.
, and
Nuismer
,
R.
,
1974
, “
Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations
,”
J. Compos. Mater.
,
8
(
3
), pp.
253
265
.10.1177/002199837400800303
62.
Huang
,
Z.-M.
,
2002
, “
Fatigue Life Prediction of a Woven Fabric Composite Subjected to Biaxial Cyclic Loads
,”
Composites, Part A
,
33
(
2
), pp.
253
266
.10.1016/S1359-835X(01)00091-4
63.
Huang
,
Z.-M.
,
2000
, “
A Unified Micromechanical Model for the Mechanical Properties of Two Constituent Composite Materials Part I: Elastic Behavior
,”
J. Thermoplast. Compos. Mater.
,
13
(
4
), pp.
252
271
.10.1177/089270570001300401
64.
Huang
,
Z.-M.
,
2001
, “
Micromechanical Prediction of Ultimate Strength of Transversely Isotropic Fibrous Composites
,”
Int. J. Solids Struct.
,
38
(
22
), pp.
4147
4172
.10.1016/S0020-7683(00)00268-7
65.
Huang
,
Z.-M.
,
2005
, “
Efficient Approach to the Structure-Property Relationship of Woven and Braided Fabric-Reinforced Composites up to Failure
,”
J. Reinf. Plast. Compos.
,
24
(
12
), pp.
1289
1309
.10.1177/0731684405049860
66.
Huang
,
Z.-M.
,
2004
, “
A Bridging Model Prediction of the Ultimate Strength of Composite Laminates Subjected to Biaxial Loads
,”
Compos. Sci. Technol.
,
64
(
3–4
), pp.
395
448
.10.1016/S0266-3538(03)00220-3
67.
Huang
,
Z.-M.
, and
Liu
,
L.
,
2014
, “
Predicting Strength of Fibrous Laminates Under Triaxial Loads Only Upon Independently Measured Constituent Properties
,”
Int. J. Mech. Sci.
,
79
, pp.
105
129
.10.1016/j.ijmecsci.2013.08.010
68.
Gude
,
M.
,
Hufenbach
,
W.
, and
Koch
,
I.
,
2010
, “
Damage Evolution of Novel 3D Textile-Reinforced Composites Under Fatigue Loading Conditions
,”
Compos. Sci. Technol.
,
70
(
1
), pp.
186
192
.10.1016/j.compscitech.2009.10.010
69.
Cuntze
,
R.
,
1997
,
Neue Bruchkriterien und Festigkeitsnachweise für Unidirektionalen Faserkunststoffverbund Unter Mehrachsiger Beanspruchung: Modellbildung und Experimente; BMBF-Förderkennzeichen 03N8002; Abschlußbericht 1997 (Issue 506 of 5]: [Fortschritt-Berichte VDI), VDI-Verlag
, Dusseldorf, Germany.
70.
Montesano
,
J.
,
Fawaz
,
Z.
,
Behdinan
,
K.
, and
Poon
,
C.
,
2013
, “
Fatigue Damage Characterization and Modeling of a Triaxially Braided Polymer Matrix Composite at Elevated Temperatures
,”
Compos. Struct.
,
101
, pp.
129
137
.10.1016/j.compstruct.2013.01.030
71.
Montesano
,
J.
,
Bougherara
,
H.
, and
Fawaz
,
Z.
,
2014
, “
Application of Infrared Thermography for the Characterization of Damage in Braided Carbon Fiber Reinforced Polymer Matrix Composites
,”
Composites, Part B
,
60
, pp.
137
143
.10.1016/j.compositesb.2013.12.053
72.
Gagel
,
A.
,
Fiedler
,
B.
, and
Schulte
,
K.
,
2006
, “
On Modelling the Mechanical Degradation of Fatigue Loaded Glass-Fibre Non-Crimp Fabric Reinforced Epoxy Laminates
,”
Compos. Sci. Technol.
,
66
(
5
), pp.
657
664
.10.1016/j.compscitech.2005.07.037
73.
Xu
,
J.
,
2011
, “
Meso-Scale Finite Element Fatigue Modelling of Textile Composite Materials
,” Ph.D. thesis, KU Leuven, Belgium.
74.
Xu
,
J.
,
Lomov
,
S. V.
,
Verpoest
,
I.
,
Daggumati
,
S.
,
Paepegem
,
W. V.
,
Degrieck
,
J.
, and
Olave
,
M.
,
2014
, “
A Progressive Damage Model of Textile Composites on Meso-Scale Using Finite Element Method: Static Damage Analysis
,”
J. Compos. Mater.
,
48
(
25
), pp.
3091
3109
.10.1177/0021998313507008
75.
Zako
,
M.
,
Uetsuji
,
Y.
, and
Kurashiki
,
T.
,
2003
, “
Finite Element Analysis of Damaged Woven Fabric Composite Materials
,”
Compos. Sci. Technol.
,
63
(
3–4
), pp.
507
516
.10.1016/S0266-3538(02)00211-7
76.
Liu
,
Y.
, and
Mahadevan
,
S.
,
2007
, “
A Unified Multiaxial Fatigue Damage Model for Isotropic and Anisotropic Materials
,”
Int. J. Fatigue
,
29
(
2
), pp.
347
359
.10.1016/j.ijfatigue.2006.03.011
77.
Min
,
J.
,
Xue
,
D.
, and
Shi
,
Y.
,
2014
, “
Micromechanics Modeling for Fatigue Damage Analysis Designed for Fabric Reinforced Ceramic Matrix Composites
,”
Compos. Struct.
,
111
, pp.
213
223
.10.1016/j.compstruct.2013.12.025
78.
Naik
,
A.
,
1994
, “
Analysis of Woven and Braided Fabric Reinforced Composites
,” Analytical Services & Materials, Inc., VA, Technical Report No. 194930.
79.
Yang
,
G.
,
Sun
,
B.
, and
Gu
,
B.
,
2014
, “
Large-Scale Finite Element Analysis of a 3D Angle-Interlock Woven Composite Undergoing Low-Cyclic Three-Point Bending Fatigue
,”
J. Text. Inst.
,
105
(
3
), pp.
275
293
.10.1080/00405000.2013.836785
80.
Wu
,
L.
,
Zhang
,
F.
,
Sun
,
B.
, and
Gu
,
B.
,
2014
, “
Finite Element Analyses on Three-Point Low-Cyclic Bending Fatigue of 3-D Braided Composite Materials at Microstructure Level
,”
Int. J. Mech. Sci.
,
84
, pp.
41
53
.10.1016/j.ijmecsci.2014.03.036
81.
Wu
,
L.
,
Sun
,
B.
, and
Gu
,
B.
,
2015
, “
Numerical Analyses of Bending Fatigue of Four-Step Three-Dimensional Rectangular-Braided Composite Materials From Unit Cell Approach
,”
J. Text. Inst.
,
106
(
1
), pp.
67
79
.10.1080/00405000.2014.904077
82.
Wu
,
L.
, and
Gu
,
B.
,
2014
, “
Fatigue Behaviors of Four-Step Three-Dimensional Braided Composite Material: A Meso-Scale Approach Computation
,”
Text. Res. J.
,
84
(
18
), pp.
1915
1930
.10.1177/0040517514540767
83.
Kawai
,
M.
, and
Itoh
,
N.
,
2014
, “
A Failure-Mode Based Anisomorphic Constant Life Diagram for a Unidirectional Carbon/Epoxy Laminate Under Off-Axis Fatigue Loading at Room Temperature
,”
J. Compos. Mater.
,
48
(
5
), pp.
571
592
.10.1177/0021998313476324
84.
Wu
,
F.
, and
Yao
,
W.
,
2010
, “
A Fatigue Damage Model of Composite Materials
,”
Int. J. Fatigue
,
32
(
1
), pp.
134
138
.10.1016/j.ijfatigue.2009.02.027
85.
Hashin
,
Z.
,
1981
, “
Fatigue Failure Criteria for Unidirectional Fiber Composites
,”
ASME J. Appl. Mech.
,
48
(
4
), pp.
846
852
.10.1115/1.3157744
86.
Shokrieh
,
M.
, and
Lessard
,
L.
,
1997
, “
Multiaxial Fatigue Behaviour of Unidirectional Plies Based on Uniaxial Fatigue Experiments-I. Modelling
,”
Int. J. Fatigue
,
19
(
3
), pp.
201
207
.10.1016/S0142-1123(96)00074-6
87.
Yao
,
W.
, and
Himmel
,
N.
,
2000
, “
A New Cumulative Fatigue Damage Model for Fibre-Reinforced Plastics
,”
Compos. Sci. Technol.
,
60
(
1
), pp.
1
6
.
88.
Philippidis
,
T.
, and
Passipoularidis
,
V.
,
2007
, “
Residual Strength After Fatigue in Composites: Theory vs. Experiment
,”
Int. J. Fatigue
,
29
(
12
), pp.
2104
2116
.10.1016/j.ijfatigue.2007.01.019
89.
Reifsnider
,
K.
,
Case
,
S.
, and
Duthoit
,
J.
,
2000
, “
The Mechanics of Composite Strength Evolution
,”
Compos. Sci. Technol.
,
60
(
12
), pp.
2539
2546
.10.1016/S0266-3538(00)00047-6
90.
Papanikos
,
P.
,
Tserpes
,
K. I.
, and
Pantelakis
,
S.
,
2003
, “
Modelling of Fatigue Damage Progression and Life of CFRP Laminates
,”
Fatigue Fract. Eng. Mater. Struct.
,
26
(
1
), pp.
37
47
.10.1046/j.1460-2695.2003.00585.x
91.
Eliopoulos
,
E. N.
, and
Philippidis
,
T. P.
,
2011
, “
A Progressive Damage Simulation Algorithm for GFRP Composites Under Cyclic Loading. Part I: Material Constitutive Model
,”
Compos. Sci. Technol.
,
71
(
5
), pp.
742
749
.10.1016/j.compscitech.2011.01.023
92.
Eliopoulos
,
E. N.
, and
Philippidis
,
T. P.
,
2011
, “
A Progressive Damage Simulation Algorithm for GFRP Composites Under Cyclic Loading. Part II: FE Implementation and Model Validation
,”
Compos. Sci. Technol.
,
71
(
5
), pp.
750
757
.10.1016/j.compscitech.2011.01.025
93.
Lian
,
W.
, and
Yao
,
W.
,
2010
, “
Fatigue Life Prediction of Composite Laminates by FEA Simulation Method
,”
Int. J. Fatigue
,
32
(
1
), pp.
123
133
.10.1016/j.ijfatigue.2009.01.015
94.
Varvani-Farahani
,
A.
, and
Shirazi
,
A.
,
2007
, “
A Fatigue Damage Model for (0/90) FRP Composites Based on Stiffness Degradation of 0 and 90 Composite Plies
,”
J. Reinf. Plast. Compos.
,
26
(
13
), pp.
1319
1336
.10.1177/0731684407079771
95.
Shirazi
,
A.
, and
Varvani-Farahani
,
A.
,
2009
, “
A Stiffness Degradation Based Fatigue Damage Model for FRP Composites of (0/θ) Laminate Systems
,”
Appl. Compos. Mater.
,
17
(
2
), pp.
137
150
.
96.
Daniel
,
I.
, and
Ishai
,
O.
,
2006
,
Engineering Mechanics of Composite Materials
,
2nd ed.
,
Oxford University
,
New York
.
97.
Kassapoglou
,
C.
,
2010
,
Design and Analysis of Composite Structures
,
Wiley
,
Chichester, UK
.10.1002/9780470972700
98.
Quaresimin
,
M.
, and
Carraro
,
P.
,
2013
, “
On the Investigation of the Biaxial Fatigue Behaviour of Unidirectional Composites
,”
Composites, Part B
,
54
, pp.
200
208
.10.1016/j.compositesb.2013.05.014
99.
Quaresimin
,
M.
, and
Carraro
,
P.
,
2014
, “
Damage Initiation and Evolution in Glass/Epoxy Tubes Subjected to Combined Tension-Torsion Fatigue Loading
,”
Int. J. Fatigue
,
63
, pp.
25
35
.10.1016/j.ijfatigue.2014.01.002
100.
Quaresimin
,
M.
,
Carraro
,
P.
,
Mikkelsen
,
L.
,
Lucato
,
N.
,
Vivian
,
L.
,
Brondsted
,
P.
,
Sorensen
,
B.
,
Varna
,
J.
, and
Talreja
,
R.
,
2014
, “
Damage Evolution Under Cyclic Multiaxial Stress State: A Comparative Analysis Between Glass/Epoxy Laminates and Tubes
,”
Composites, Part B
,
61
, pp.
282
290
.10.1016/j.compositesb.2014.01.056
101.
Carraro
,
P.
, and
Quaresimin
,
M.
,
2014
, “
Modelling Fibre-Matrix Debonding Under Biaxial Loading
,”
Composites, Part A
,
61
, pp.
33
42
.10.1016/j.compositesa.2014.01.016
102.
Ernst
,
G.
,
Vogler
,
M.
,
Hühne
,
C.
, and
Rolfes
,
R.
,
2010
, “
Multiscale Progressive Failure Analysis of Textile Composites
,”
Compos. Sci. Technol.
,
70
(
1
), pp.
61
72
.10.1016/j.compscitech.2009.09.006
103.
Zhou
,
Y.
,
Lu
,
Z.
, and
Yang
,
Z.
,
2013
, “
Progressive Damage Analysis and Strength Prediction of 2D Plain Weave Composites
,”
Composites, Part B
,
47
, pp.
220
229
.10.1016/j.compositesb.2012.10.026
104.
Lu
,
Z.
,
Zhou
,
Y.
,
Yang
,
Z.
, and
Liu
,
Q.
,
2013
, “
Multi-Scale Finite Element Analysis of 2.5D Woven Fabric Composites Under On-Axis and Off-Axis Tension
,”
Comput. Mater. Sci.
,
79
, pp.
485
494
.10.1016/j.commatsci.2013.07.003
105.
Šmilauer
,
V.
,
Hoover
,
C. G.
,
Bažant
,
Z. P.
,
Caner
,
F. C.
,
Waas
,
A. M.
, and
Shahwan
,
K. W.
,
2011
, “
Multiscale Simulation of Fracture of Braided Composites Via Repetitive Unit Cells
,”
Eng. Fract. Mech.
,
78
(
6
), pp.
901
918
.10.1016/j.engfracmech.2010.10.013
106.
Rolfes
,
R.
,
Vogler
,
M.
,
Czichon
,
S.
, and
Ernst
,
G.
,
2011
, “
Exploiting the Structural Reserve of Textile Composite Structures by Progressive Failure Analysis Using a New Orthotropic Failure Criterion
,”
Comput. Struct.
,
89
(
11–12
), pp.
1214
1223
.10.1016/j.compstruc.2010.09.003
107.
Shokrieh
,
M. M.
, and
Lessard
,
L. B.
,
2000
, “
Progressive Fatigue Damage Modeling of Composite Materials, Part I: Modeling
,”
J. Compos. Mater.
,
34
(
13
), pp.
1056
1080
.10.1177/002199830003401301
108.
Shokrieh
,
M. M.
, and
Lessard
,
L. B.
,
2000
, “
Progressive Fatigue Damage Modeling of Composite Materials, Part II: Material Characterization and Model Verification
,”
J. Compos. Mater.
,
34
(
13
), pp.
1081
1116
.10.1177/002199830003401302
109.
Kennedy
,
C. R.
,
Brádaigh
,
C. M. O.
, and
Leen
,
S. B.
,
2013
, “
A Multiaxial Fatigue Damage Model for Fibre Reinforced Polymer Composites
,”
Compos. Struct.
,
106
, pp.
201
210
.10.1016/j.compstruct.2013.05.024
110.
Passipoularidis
,
V.
,
Philippidis
,
T.
, and
Brondsted
,
P.
,
2011
, “
Fatigue Life Prediction in Composites Using Progressive Damage Modelling Under Block and Spectrum Loading
,”
Int. J. Fatigue
,
33
(
2
), pp.
132
144
.10.1016/j.ijfatigue.2010.07.011
111.
Qian
,
C.
,
Westphal
,
T.
,
Kassapoglou
,
C.
, and
Nijssen
,
R.
,
2013
, “
Development of a Multi-Fibre Unit Cell for Use in Modelling of Fatigue of Unidirectional Composites
,”
Compos. Struct.
,
99
, pp.
288
295
.10.1016/j.compstruct.2012.11.010
112.
Qian
,
C.
,
Westphal
,
T.
, and
Nijssen
,
R.
,
2013
, “
Micro-Mechanical Fatigue Modelling of Unidirectional Glass Fibre Reinforced Polymer Composites
,”
Comput. Mater. Sci.
,
69
, pp.
62
72
.10.1016/j.commatsci.2012.10.015
113.
Violeau
,
D.
,
Ladevèze
,
P.
, and
Lubineau
,
G.
,
2009
, “
Micromodel-Based Simulations for Laminated Composites
,”
Compos. Sci. Technol.
,
69
(
9
), pp.
1364
1371
.10.1016/j.compscitech.2008.09.041
114.
Singh
,
C. V.
, and
Talreja
,
R.
,
2009
, “
A Synergistic Damage Mechanics Approach for Composite Laminates With Matrix Cracks in Multiple Orientations
,”
Mech. Mater.
,
41
(
8
), pp.
954
968
.10.1016/j.mechmat.2009.02.008
115.
Varna
,
J.
, and
Talreja
,
R.
,
2012
, “
Integration of Macro-and Microdamage Mechanics for the Performance Evaluation of Composite Materials
,”
Mech. Compos. Mater.
,
48
(
2
), pp.
145
160
.10.1007/s11029-012-9261-y
116.
Singh
,
C. V.
, and
Talreja
,
R.
,
2013
, “
A Synergistic Damage Mechanics Approach to Mechanical Response of Composite Laminates With Ply Cracks
,”
J. Compos. Mater.
,
47
(
20–21
), pp.
2475
2501
.10.1177/0021998312466121
117.
Singh
,
C. V.
, and
Talreja
,
R.
,
2010
, “
Evolution of Ply Cracks in Multidirectional Composite Laminates
,”
Int. J. Solids Struct.
,
47
(
10
), pp.
1338
1349
.10.1016/j.ijsolstr.2010.01.016
118.
Puck
,
A.
, and
Schürmann
,
H.
,
1998
, “
Failure Analysis of FRP Laminates by Means of Physically Based Phenomenological Models
,”
Compos. Sci. Technol.
,
58
(
7
), pp.
1045
1067
.10.1016/S0266-3538(96)00140-6
119.
Hallal
,
A.
,
Younes
,
R.
, and
Fardoun
,
F.
,
2013
, “
Review and Comparative Study of Analytical Modeling for the Elastic Properties of Textile Composites
,”
Composites, Part B
,
50
, pp.
22
31
.10.1016/j.compositesb.2013.01.024
120.
Kregers
,
A. F.
, and
Melbardis
,
Y.
,
1978
, “
Determination of the Deformability of Three-Dimensionally Reinforced Composites by the Stiffness Averaging Method
,”
Polym. Mech.
,
14
(
1
), pp.
1
5
.10.1007/BF00859550
121.
Whitney
,
T. J.
, and
Chou
,
T.-W.
,
1989
, “
Modeling of 3-D Angle-Interlock Textile Structural Composites
,”
J. Compos. Mater.
,
23
(
9
), pp.
890
911
.10.1177/002199838902300902
122.
Ladevèze
,
P.
, and
Dureisseix
,
D.
,
1999
, “
Une Nouvelle Stratégie de Calcul Micro/Macro en Mécanique des Structures
,”
C. R. Acad. Sci.
,
327
(
12
), pp.
1237
1244
.10.1016/S1287-4620(00)88647-0
123.
Xia
,
Z.
,
Chen
,
Y.
, and
Ellyin
,
F.
,
2000
, “
A Meso/Micro-Mechanical Model for Damage Progression in Glass-Fiber/Epoxy Cross-Ply Laminates by Finite-Element Analysis
,”
Compos. Sci. Technol.
,
60
(
8
), pp.
1171
1179
.10.1016/S0266-3538(00)00022-1
124.
Ladeveze
,
P.
,
2005
, “
A Bridge Between the Micro-and Mesomechanics of Laminates: Fantasy or Reality?
,”
Mechanics of the 21st Century
, pp.
187
201
.
10.1007/1-4020-3559-4
125.
Talreja
,
R.
,
2008
, “
Damage and Fatigue in Composites—A Personal Account
,”
Compos. Sci. Technol.
,
68
(
13
), pp.
2585
2591
.10.1016/j.compscitech.2008.04.042
You do not currently have access to this content.