An efficient and novel micromechanical computational platform for progressive failure analysis of fiber-reinforced composites is presented. The numerical framework is based on a recently developed micromechanical platform built using a class of refined beam models called Carrera unified formulation (CUF), a generalized hierarchical formulation which yields a refined structural theory via variable kinematic description. The crack band theory is implemented in the framework to capture the damage propagation within the constituents of composite materials. The initiation and orientation of the crack band in the matrix are determined using the maximum principal stress state and the traction-separation law governing the crack band growth is related to the fracture toughness of the matrix. A representative volume element (RVE) containing randomly distributed fibers is modeled using the component-wise (CW) approach, an extension of CUF beam model based on Lagrange type polynomials. The efficiency of the proposed numerical framework is achieved through the ability of the CUF models to provide accurate three-dimensional (3D) displacement and stress fields at a reduced computational cost. The numerical results are compared against experimental data available in the literature and an analogous 3D finite element model with the same constitutive crack band model. The applicability of CUF beam models as a novel micromechanical platform for progressive failure analysis as well as the multifold efficiency of CUF models in terms of CPU time are highlighted.

References

References
1.
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
.
2.
Naghipour
,
P.
,
Arnold
,
S. M.
,
Pineda
,
E. J.
,
Stier
,
B.
,
Hansen
,
L.
,
Bednarcyk
,
B. A.
, and
Waas
,
A. M.
,
2016
, “
Multiscale Static Analysis of Notched and Unnotched Laminates Using the Generalized Method of Cells
,”
J. Compos. Mater.
,
51
(10), pp. 1433–1454.
3.
Kanouté
,
P.
,
Boso
,
D. P.
,
Chaboche
,
J. L.
, and
Schrefler
,
B. A.
,
2009
, “
Multiscale Methods for Composites: A Review
,”
Arch. Comput. Methods Eng.
,
16
(
1
), pp.
31
75
.
4.
Pineda
,
E. J.
,
Waas
,
A. M.
,
Bednarcyk
,
B. A.
,
Arnold
,
S. M.
, and
Collier
,
C. S.
,
2009
, “
Multiscale Failure Analysis of Laminated Composite Panels Subjected to Blast Loading Using FEAMAC/Explicit
,” NASA Glenn Research Center, Cleveland, OH, Report No.
NASA/TM-2009-215813
.https://ntrs.nasa.gov/search.jsp?R=20090041557
5.
Zhang
,
D.
,
Waas
,
A. M.
, and
Yen
,
C. F.
,
2015
, “
Progressive Damage and Failure Response of Hybrid 3D Textile Composites Subjected to Flexural Loading—Part II: Mechanics Based Multiscale Computational Modeling of Progressive Damage and Failure
,”
Int. J. Solids Struct.
,
75–76
, pp.
321
335
.
6.
Allix
,
O.
,
Dommanget
,
M.
,
Gratton
,
M.
, and
He
,
P.
,
2001
, “
A Multi-Scale Approach for the Response of a 3D Carbon/Carbon Composite Under Shock Loading
,”
Compos. Sci. Technol.
,
61
(3), pp.
409
415
.
7.
Hashin
,
Z. V. I.
, and
Rosen
,
B. W.
,
1964
, “
The Elastic Moduli of Fiber-Reinforced Materials
,”
ASME J. Appl. Mech.
,
31
(
2
), pp.
223
232
.
8.
Mori
,
T.
, and
Tanaka
,
K.
,
1973
, “
Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions
,”
Acta Metall.
,
21
(
5
), pp.
571
574
.
9.
Zhang
,
D.
, and
Waas
,
A. M.
,
2014
, “
A Micromechanics Based Multiscale Model for Nonlinear Composites
,”
Acta Mech.
,
225
(
4–5
), pp.
1391
1417
.
10.
Patel
,
D. K.
,
Hasanyan
,
A. D.
, and
Waas
,
A. M.
,
2017
, “
N -Layer Concentric Cylinder Model (NCYL): An Extended Micromechanics-Based Multiscale Model for Nonlinear Composites
,”
Acta Mech.
,
228
(
1
), pp.
275
306
.
11.
Nemat-Nasser
,
S.
,
Iwakuma
,
T.
, and
Hejazi
,
M.
,
1982
, “
On Composites With Periodic Structure
,”
Mech. Mater.
,
1
(
3
), pp.
239
267
.
12.
Aboudi
,
J.
,
1982
, “
A Continuum Theory for Fiber-Reinforced Elastic-Viscoplastic Composites
,”
Int. J. Eng. Sci.
,
20
(
5
), pp.
605
621
.
13.
Paley
,
M.
, and
Aboudi
,
J.
,
1992
, “
Micromechanical Analysis of Composites by the Generalized Cells Method
,”
Mech. Mater.
,
14
(2), pp.
127
139
.
14.
Aboudi
,
J.
,
Pindera
,
M.-J.
, and
Arnold
,
S. M.
,
2001
, “
Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials
,”
ASME J. Appl. Mech.
,
68
(5), pp.
697
707
.
15.
Haj-Ali
,
R.
, and
Aboudi
,
J.
,
2009
, “
Nonlinear Micromechanical Formulation of the High Fidelity Generalized Method of Cells
,”
Int. J. Solids Struct.
,
46
(
13
), pp.
2577
2592
.
16.
Pineda
,
E. J.
,
Bednarcyk
,
B. A.
,
Waas
,
A. M.
, and
Arnold
,
S. M.
,
2013
, “
Progressive Failure of a Unidirectional Fiber-Reinforced Composite Using the Method of Cells: Discretization Objective Computational Results
,”
Int. J. Solids Struct.
,
50
(
9
), pp.
1203
1216
.
17.
Bednarcyk
,
B. A.
,
Aboudi
,
J.
, and
Arnold
,
S. M.
,
2010
, “
Micromechanics Modeling of Composites Subjected to Multiaxial Progressive Damage in the Constituents
,”
AIAA J.
,
48
(
7
), pp.
1367
1378
.
18.
Haj-Ali
,
R.
, and
Aboudi
,
J.
,
2010
, “
Formulation of the High-Fidelity Generalized Method of Cells With Arbitrary Cell Geometry for Refined Micromechanics and Damage in Composites
,”
Int. J. Solids Struct.
,
47
(
25–26
), pp.
3447
3461
.
19.
Sun
,
C. T.
, and
Vaidya
,
R. S.
,
1996
, “
Prediction of Composite Properties From a Representative Volume Element
,”
Compos. Sci. Technol.
,
56
(
2
), pp.
171
179
.
20.
González
,
C.
, and
LLorca
,
J.
,
2007
, “
Mechanical Behavior of Unidirectional Fiber-Reinforced Polymers Under Transverse Compression: Microscopic Mechanisms and Modeling
,”
Compos. Sci. Technol.
,
67
(
13
), pp.
2795
2806
.
21.
D'Mello
,
R. J.
,
Maiaru
,
M.
, and
Waas
,
A. M.
,
2016
, “
Virtual Manufacturing of Composite Aerostructures
,”
Aeronaut. J.
,
120
(
1223
), pp.
61
81
.
22.
Vaughan
,
T. J.
, and
McCarthy
,
C. T.
,
2011
, “
Micromechanical Modelling of the Transverse Damage Behaviour in Fibre Reinforced Composites
,”
Compos. Sci. Technol.
,
71
(
3
), pp.
388
396
.
23.
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
.
24.
Kaleel
,
I.
,
Petrolo
,
M.
,
Waas
,
A. M.
, and
Carrera
,
E.
,
2017
, “
Computationally Efficient, High-Fidelity Micromechanics Framework Using Refined 1D Models
,”
Compos. Struct.
,
181
, pp. 358–367.
25.
Carrera
,
E.
,
Cinefra
,
M.
,
Zappino
,
E.
, and
Petrolo
,
M.
,
2014
,
Finite Element Analysis of Structures Through Unified Formulation
, John Wiley & Sons, West Sussex, UK.
26.
Carrera
,
E.
, and
Petrolo
,
M.
,
2012
, “
Refined Beam Elements With Only Displacement Variables and Plate/Shell Capabilities
,”
Meccanica
,
47
(
3
), pp.
537
556
.
27.
Maiarú
,
M.
,
Petrolo
,
M.
, and
Carrera
,
E.
,
2017
, “
Evaluation of Energy and Failure Parameters in Composite Structures Via a Component-Wise Approach
,”
Compos. Part B
,
108
, pp.
53
64
.
28.
Carrera
,
E.
, and
Petrolo
,
M.
,
2012
, “
Refined One-Dimensional Formulations for Laminated Structure Analysis
,”
AIAA J.
,
50
(
1
), pp.
176
189
.
29.
Pagani
,
A.
,
Miguel
,
A. G. D.
,
Petrolo
,
M.
, and
Carrera
,
E.
,
2016
, “
Analysis of Laminated Beams Via Unified Formulation and Legendre Polynomial Expansions
,”
Compos. Struct.
,
156
, pp.
78
92
.
30.
Carrera
,
E.
,
Kaleel
,
I.
, and
Petrolo
,
M.
,
2017
, “
Elastoplastic Analysis of Compact and Thin Walled Structures Using Classical and Refined Beam Finite Element
,”
Mech. Adv. Mater. Struct.
, epub.
31.
Carrera
,
E.
,
Filippi
,
E. M.
, and
Zappino
,
E.
,
2013
, “
Analysis of Rotor Dynamic by One-Dimensional Variable Kinematic Theories
,”
ASME J. Eng. Gas Turbines Power
,
135
(
9
), p.
092501
.
32.
Pagani
,
A.
, and
Carrera
,
E.
,
2017
, “
Large-Deflection and Post-Buckling Analyses of Laminated Composite Beams by Carrera Unified Formulation
,”
Compos. Struct.
,
170
, pp.
40
52
.
33.
Bazant
,
Z.
, and
Oh
,
B. H.
,
1983
, “
Crack Band Theory for Fracture of Concrete
,”
Mater. Struct.
,
16
(3), pp.
155
177
.
34.
Carrera
,
E.
, and
Giunta
,
G.
,
2010
, “
Refined Beam Theories Based on a Unified Formulation
,”
Int. J. Appl. Mech.
,
2
(
1
), pp.
117
143
.
35.
Bathe
,
K. J.
,
1996
,
Finite Element Procedures
,
Prentice Hall
,
Upper Saddle River, NJ
.
36.
Tay
,
T. E.
,
Liu
,
G.
,
Tan
,
V. B. C.
,
Sun
,
X. S.
, and
Pham
,
D. C.
,
2008
, “
Progressive Failure Analysis of Composites
,”
J. Compos. Mater.
,
42
(
18
), pp.
1921
1966
.
37.
Gamstedt
,
E. K.
, and
Sjögren
,
B. A.
,
1999
, “
Micromechanisms in Tension-Compression Fatigue of Composite Laminates Containing Transverse Plies
,”
Compos. Sci. Technol.
,
59
(
2
), pp.
167
178
.
38.
Hinton
,
M. J.
,
Soden
,
P. D.
, and
Kaddour
,
A. S.
,
2004
,
Failure Criteria in Fibre-Reinforced-Polymer Composites
,
Elsevier
,
Oxford, UK
.
You do not currently have access to this content.