Nowadays, conventional materials have been progressively replaced by composite materials in a wide variety of applications. Particularly, fiber reinforced composite laminates are widely used. The appropriate design of elements made of this type of material requires the use of constitutive models capable of estimating their stiffness and strength. A general constitutive model for fiber reinforced laminated composites is presented in this paper. The model is obtained as a generalization of classical mixture theory taking into account the relations among the strains and stresses in the components and the composite in principal symmetry directions of the material. The constitutive equations for the laminated composite result from the combination of lamina constitutive equations that also result from the combination of fibers and matrix. It is assumed that each one of the components are orthotropic and elastoplastic. Basic assumptions of the proposed model and the resulting equations are first presented in the paper. The numerical algorithm developed for the implementation in a three-dimensional (3D) finite element nonlinear program is also described. The paper is completed with application examples and comparison with experimental results. The comparison shows the capacity of the proposed model for the simulation of stiffness and strength of different composite laminates.

1.
Chaboche
,
J. L.
,
Lesne
,
O.
, and
Pottier
,
T.
, 1998, “
Continuum Damage Mechanics of Composites: Towards a Unified Approach
,”
Damage Mechanics in Engineering Materials, Studies in Applied Mechanics 46
,
Elsevier Voyiadjis, Ju and Chaboche
,
Elsevier
, Vol.
46
, pp.
3
26
.
2.
Oller
,
S.
,
Miquel
,
J.
, and
Zalamea
,
F.
, 2005, “
Composite Material Behavior Using a Homogenization Double Scale Method
,”
J. Engrg. Mech. Div.
0044-7951,
131
, pp.
65
79
.
3.
Huang
,
Z.
, 2001, “
Micromechanical Prediction of Ultimate Strength of Transversely Isotropic Fibrous Composites
,”
Int. J. Solids Struct.
0020-7683,
38
, pp.
4147
4172
.
4.
Hinton
,
M. J.
, and
Soden
,
P. D.
, 1998, “
Predicting Failure in Composite Laminates: The Background to the Exercise
,”
Compos. Sci. Technol.
0266-3538,
58
, pp.
1001
1010
.
5.
Soden
,
P. D.
,
Hinton
,
M. J.
, and
Kaddour
,
A. S.
, 1998, “
Lamina Properties, Lay-Up Configurations and Loading Conditions for a Range of Fibre-Reinforced Composite Laminates
,”
Compos. Sci. Technol.
0266-3538,
58
, pp.
1011
1022
.
6.
Hinton
,
M. J.
,
Kaddour
,
A. S.
, and
Soden
,
P. D.
, 2002, “
Evaluation of Failure Prediction in Composite Laminates: Background to ‘Part B’ of the Exercise
,”
Compos. Sci. Technol.
0266-3538,
62
, pp.
1481
1488
.
7.
Soden
,
P. D.
,
Hinton
,
M. J.
, and
Kaddour
,
A. S.
, 2002, “
Biaxial Test Results for Strength and Deformation of a Range of E-Glass and Carbon Fiber Reinforced Composite Laminates: Failure Exercise Benchmark Data
,”
Compos. Sci. Technol.
0266-3538,
62
, pp.
1489
1514
.
8.
Hinton
,
M. J.
,
Kaddour
,
A. S.
, and
Soden
,
P. D.
, 2004, “
Evaluation of Failure Prediction in Composite Laminates: Background to ‘Part C’ of the Exercise
,”
Compos. Sci. Technol.
0266-3538,
64
, pp.
321
327
.
9.
Soden
,
P. D.
,
Hinton
,
M. J.
, and
Kaddour
,
A. S.
, 1998, “
A Comparison of the Predictive Capabilities of Current Failure Theories for Composite Laminates
,”
Compos. Sci. Technol.
0266-3538,
58
, pp.
1225
1254
.
10.
Kaddour
,
A. S.
,
Hinton
,
M. J.
, and
Soden
,
P. D.
, 2004, “
A Comparison of the Predictive Capabilities of Current Failure Theories for Composite Laminates: Additional Contributions
,”
Compos. Sci. Technol.
0266-3538,
64
, pp.
449
476
.
11.
Hinton
,
M. J.
,
Kaddour
,
A. S.
, and
Soden
,
P. D.
, 2004, “
A Further Assessment of the Predictive Capabilities of Current Failure Theories for Composite Laminates: Comparison with Experimental Evidence
,”
Compos. Sci. Technol.
0266-3538,
64
, pp.
549
588
.
12.
Soden
,
P. D.
,
Kaddour
,
A. S.
, and
Hinton
,
M. J.
, 2004, “
Recommendations for Designers and Researchers Resulting From the World-Wide Failure Exercise
,”
Compos. Sci. Technol.
0266-3538,
64
, pp.
589
604
.
13.
Zinoviev
,
P.
,
Grigoriev
,
S. V.
,
Labedeva
,
O. V.
, and
Tairova
,
L. R.
, 1998, “
Strength of Multilayered Composites Under Plane Stress State
,”
Compos. Sci. Technol.
0266-3538,
58
, pp.
1209
1224
.
14.
Zinoviev
,
P.
,
Labedeva
,
O. V.
, and
Tairova
,
L. R.
, 2002, “
Coupled Analysis of Experimental and Theoretical Results on the Deformation and Failure of Laminated Composites Under a Plane State of Stress
,”
Compos. Sci. Technol.
0266-3538,
62
, pp.
11711
11724
.
15.
Bogetti
,
T. A.
,
Hoppel
,
C. P. R.
,
Harik
,
V. M.
,
Newill
,
J. F.
, and
Burns
,
B. P.
, 2004, “
Predicting the Nonlinear Response and Progressive Failure of Composite Laminates
,”
Compos. Sci. Technol.
0266-3538,
64
, pp.
477
485
.
16.
Liu
,
K. S.
, and
Tsai
,
S. W.
, 1998, “
A Progressive Quadratic Failure Criterion of Alaminate
,”
Compos. Sci. Technol.
0266-3538,
58
, pp.
1023
3102
.
17.
Kuraishi
,
A.
,
Tsai
,
S. W.
, and
Liu
,
K. A.
, 2002, “
A Progressive Quadratic Failure Criterion Part B
,”
Compos. Sci. Technol.
0266-3538,
62
, pp.
1682
1696
.
18.
Puck
,
A.
, and
Schurmann
,
H.
, 1998, “
Failure Analysis of FRP Laminates by Means of Physically Based Phenomenological Models
,”
Compos. Sci. Technol.
0266-3538,
58
, pp.
1045
1068
.
19.
Puck
,
A.
, and
Schurmann
,
H.
, 2002, “
A Failure Analysis of FRP Laminates by Means of Physically Based Phenomenological Models—Part B
,”
Compos. Sci. Technol.
0266-3538,
62
, pp.
11633
11672
.
20.
Cuntze
,
R. G.
, and
Freund
,
A. A.
, 2004, “
The Predictive Capability of Failure Mode Concept-Based Strength Criteria for Multidirectional Laminates
,”
Compos. Sci. Technol.
0266-3538,
64
, pp.
343
377
.
21.
Oller
,
S.
,
Oñate
,
E.
,
Miquel
,
J.
, and
Botello
,
S.
, 1996, “
A Plastic Damage Constitutive Model for Composite Materials
,”
Int. J. Solids Struct.
0020-7683,
33
(
17
), pp.
2501
2518
.
22.
Luccioni
,
B.
, and
López
,
D.
, 2002, “
Modelo Para Materiales Compuestos Con Deslizamiento de Fibras
,” Análisis y
Cálculo de Estructuras de Materiales Compuestos
,
CIME, Barcelona, España
, Chap. 13 pp.
411
431
.
23.
Luccioni
,
B.
,
López
,
D.
, and
Danesi
,
R.
, 2005, “
Bond Slip in Reinforced Concrete Elements
,”
J. Struct. Eng.
0733-9445,
131
(
11
), pp.
1690
1696
.
24.
Betten
,
J.
, 1988, “
Application of Tensor Functions to the Formulation of Yield Criteria for Anisotropic Materials
,”
Int. J. Plast.
0749-6419,
4
, pp.
29
46
.
25.
Oller
,
S.
,
Botello
,
S.
,
Miquel
,
J.
, and
Oñate
,
E.
, 1995, “
An Anisotropic Elasto-Plastic Model Based on an Isotropic Formulation
,”
Eng. Comput.
0264-4401,
12
, pp.
245
262
.
26.
Luccioni
,
B.
,
Oller
,
S.
, and
Danesi
,
R.
, 1995, “
Plastic Damaged Model for Anisotropic Materials
,”
Appl. Mech. Eng.
1425-1655,
1
, pp.
124
129
.
27.
Luccioni
,
B.
,
Oller
,
S.
, and
Danesi
,
R.
, 1996, “
Coupled Plastic-Damaged Model
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
129
,
81
89
.
28.
Car
,
E.
,
Oller
,
S.
, and
Oñate
,
E.
, 1999, “
A Large Strain Plasticity Model for Anisotropic Material—Composite Material Application
,”
Int. J. Plast.
0749-6419,
17
(
11
), pp.
1437
1463
.
29.
Oller
,
S.
,
Car
,
E.
, and
Lubliner
,
J.
, 2003, “
Definition of a General Implicit Orthotropic Yield Criterion
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
192
, pp.
895
912
.
30.
Luccioni
,
B.
, and
Martín
,
P. E.
, 1997, “
Modelo Elastoplástico Para Materiales Ortótropos
,”
Mét. Num. Cálc. Dis. Ing. RIMNI
,
13
(
4
), pp.
603
614
.
31.
Kriz
,
R. D.
, and
Stinchomb
,
W. W.
, 1979,
Exp. Mech.
0014-4851,
19
,
41
.
32.
Gundel
,
D. B.
, and
Wawner
,
F. E.
, 1997, “
Experimental and Theoretical Assessment of the Longitudinal Tensile Strength of Unidirectional SiC-Fiber/Titanium-Matrix Composites
,”
Compos. Sci. Technol.
0266-3538,
57
, pp.
471
481
.
This content is only available via PDF.
You do not currently have access to this content.