Research Papers

Micromechanical Progressive Failure Analysis of Fiber-Reinforced Composite Using Refined Beam Models

[+] Author and Article Information
I. Kaleel

MUL2 Group,
Department of Mechanical and
Aerospace Engineering,
Politecnico di Torino Turin,
Turin 10129, Italy
e-mail: ibrahim.kaleel@polito.it

M. Petrolo

MUL2 Group,
Department of Mechanical and
Aerospace Engineering,
Politecnico di Torino Turin,
Turin 10129, Italy
e-mail: marco.petrolo@polito.it

A. M. Waas

Boeing-Egtvedt Chair
William E. Boeing Department of Aeronautics
and Astronautics,
University of Washington Seattle,
Seattle, WA 98195
e-mail: awaas@aa.washington.edu

E. Carrera

MUL2 Group,
Department of Mechanical and
Aerospace Engineering,
Politecnico di Torino,
Turin 10129, Italy
e-mail: erasmo.carrera@polito.it

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 12, 2017; final manuscript received November 28, 2017; published online December 12, 2017. Assoc. Editor: George Kardomateas.

J. Appl. Mech 85(2), 021004 (Dec 12, 2017) (8 pages) Paper No: JAM-17-1501; doi: 10.1115/1.4038610 History: Received September 12, 2017; Revised November 28, 2017

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.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


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. [CrossRef] [PubMed]
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.
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. [CrossRef]
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
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Zhang, D. , and Waas, A. M. , 2014, “ A Micromechanics Based Multiscale Model for Nonlinear Composites,” Acta Mech., 225(4–5), pp. 1391–1417. [CrossRef]
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. [CrossRef]
Nemat-Nasser, S. , Iwakuma, T. , and Hejazi, M. , 1982, “ On Composites With Periodic Structure,” Mech. Mater., 1(3), pp. 239–267. [CrossRef]
Aboudi, J. , 1982, “ A Continuum Theory for Fiber-Reinforced Elastic-Viscoplastic Composites,” Int. J. Eng. Sci., 20(5), pp. 605–621. [CrossRef]
Paley, M. , and Aboudi, J. , 1992, “ Micromechanical Analysis of Composites by the Generalized Cells Method,” Mech. Mater., 14(2), pp. 127–139. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
D'Mello, R. J. , Maiaru, M. , and Waas, A. M. , 2016, “ Virtual Manufacturing of Composite Aerostructures,” Aeronaut. J., 120(1223), pp. 61–81. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
Carrera, E. , Cinefra, M. , Zappino, E. , and Petrolo, M. , 2014, Finite Element Analysis of Structures Through Unified Formulation, John Wiley & Sons, West Sussex, UK. [CrossRef]
Carrera, E. , and Petrolo, M. , 2012, “ Refined Beam Elements With Only Displacement Variables and Plate/Shell Capabilities,” Meccanica, 47(3), pp. 537–556. [CrossRef]
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. [CrossRef]
Carrera, E. , and Petrolo, M. , 2012, “ Refined One-Dimensional Formulations for Laminated Structure Analysis,” AIAA J., 50(1), pp. 176–189. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
Bazant, Z. , and Oh, B. H. , 1983, “ Crack Band Theory for Fracture of Concrete,” Mater. Struct., 16(3), pp. 155–177.
Carrera, E. , and Giunta, G. , 2010, “ Refined Beam Theories Based on a Unified Formulation,” Int. J. Appl. Mech., 2(1), pp. 117–143. [CrossRef]
Bathe, K. J. , 1996, Finite Element Procedures, Prentice Hall, Upper Saddle River, NJ.
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. [CrossRef]
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. [CrossRef]
Hinton, M. J. , Soden, P. D. , and Kaddour, A. S. , 2004, Failure Criteria in Fibre-Reinforced-Polymer Composites, Elsevier, Oxford, UK.


Grahic Jump Location
Fig. 2

Coordinate frame of reference of a generic beam

Grahic Jump Location
Fig. 1

Cross section L9 element in natural coordinate system

Grahic Jump Location
Fig. 4

Formation of transverse cracks in static tensile tests of cross-ply laminates: (a) fiber-matrix debonding and (b) coalescence into longer transverse cracks [37]

Grahic Jump Location
Fig. 5

CW discretization of the cross section of RVE with 13 randomly distributed fibers

Grahic Jump Location
Fig. 3

An illustration of a CW modeling of composite microstructure with arbitrary constituents: (a) a triply periodic composite microstructure with three different phases, (b) CW idealization of a triply periodic RVE with individual components modeled as separate components, and (c) assembled cross section with Lagrange elements along with the beam for the RVE

Grahic Jump Location
Fig. 6

Transverse tensile stress versus transverse tensile strain for randomly distributed fiber composite under transverse tension

Grahic Jump Location
Fig. 7

Damage progression in the randomly distributed fiber composite under transverse tension at global strains (a) 0.00225, (b) 0.00275, (c) 0.0035, and (d) 0.004



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In