Abo Bibliothek: Guest
Digitales Portal Digitale Bibliothek eBooks Zeitschriften Referenzen und Berichte Forschungssammlungen
International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i1.60
pages 69-80

Multiscale Transformation Field Analysis of Progressive Damage in Fibrous Laminates

Yehia Bahei-El-Din
The British University in Egypt
Ritesh Khire
Prabhat Hajela
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA


As part of an ongoing effort to model uncertainty propagation across multiple scales in fibrous laminates, this paper presents a deterministic transformation field analysis for modeling damage progression under membrane forces and bending moments. In this approach, equivalent eigenstresses are computed in the phases and/or plies such that their respective stress components that satisfy the underlying failure criteria are reduced to zero. Superposition of the solutions found for the undamaged laminate under applied loads and under the eigenstress field provide the entire response. Failure criteria are based on stress averages in the fiber and matrix. Damage mechanisms considered are frictional sliding and splitting on matrix planes that are parallel to the fiber direction, and fiber breakage. Model predictions correlate well with published experimental measurements for the stress-strain response as well as failure envelope.


  1. Bahei-El-Din, Y. A., Uniform fields, yielding, and thermal hardening in fibrous composite laminates. DOI: 10.1016/0749-6419(92)90008-Z

  2. Bahei-El-Din, Y. A., Finite element analysis of viscoplastic composite materials and structures. DOI: 10.1080/10759419608945852

  3. Bahei-El-Din, Y. A. and Botrous, A. G., Analysis of progressive fiber debonding in elastic laminates. DOI: 10.1016/S0020-7683(03)00353-6

  4. Bahei-El-Din, Y. A. and Dvorak, G. J., Micromechanics of Inelastic Composite Materials. DOI: 10.1016/B0-08-042993-9/00051-6

  5. Bahei-El-Din, Y. A., Mullur, A. A., Hajela, P., Peters, J., and Dvorak, G. J., Nondeterministic Modeling of Progressive Failure in Laminated Composites.

  6. Bahei-El-Din, Y. A., Rajendran, A. M., and Zikry, M. A., A Micromechanical Model for Damage Progression in Woven Composite Systems. DOI: 10.1016/j.ijsolstr.2003.12.006

  7. Chaboche, J. L., Kruch, S., Maire, J. F., and Pottier, T., Towards a Micromechanics Based Inelastic and Damage Modeling of Composites. DOI: 10.1016/S0749-6419(00)00056-5

  8. Chuang, S.-N., Probabilistic Analysis in Unidirectional Fiber-Reinforced Composite Material Design Screening.

  9. Dvorak, G. J., Plasticity Theories for Fibrous Composite Materials.

  10. Dvorak, G. J., Transformation Field Analysis of Inelastic Composite Materials. DOI: 10.1098/rspa.1992.0063

  11. Dvorak, G. J., Bahei-El-Din, Y. A., and Wafa, A. M., Implementation of the Transformation Field Analysis for Inelastic Composite Materials. DOI: 10.1007/BF00370073

  12. Dvorak, G. J. and Benveniste, Y., On Transformation Strains and Uniform Fields in Multiphase Elastic Media. DOI: 10.1098/rspa.1992.0062

  13. Dvorak, G. J. and Sejnoha, M., Initial Failure Maps of Fibrous CMC Laminates. DOI: 10.1111/j.1151-2916.1995.tb08384.x

  14. Dvorak, G. J. and Zhang, J., Transformation field analysis of damage evolution in composite materials. DOI: 10.1016/S0022-5096(01)00066-7

  15. Fish, J., Yu, Q., and Shek, K. L., Computational damage mechanics for composite materials based on mathematical homogenization. DOI: 10.1002/(SICI)1097-0207(19990820)45:11<1657::AID-NME648>3.0.CO;2

  16. Hill, R., Elastic properties of reinforced solids: some theoretical principles. DOI: 10.1016/0022-5096(63)90036-X

  17. Hill, R., Theory of mechanical properties of fiber-strengthened materials: I. elastic behaviour.

  18. Hill, R., A self-consistent mechanics of composite materials. DOI: 10.1016/0022-5096(65)90010-4

  19. Khire, R., Bahei-El-Din, Y. A., and Hajela, P., Uncertainty propagation in multiscale transformation field analysis of laminated composites.

  20. Khire, R., Hajela, P., and Bahei-El-Din, Y., Handling uncertainty propagation in laminated composites through multiscale modeling of progressive failure.

  21. Levin, V. M., Thermal expansion coefficients of heterogeneous materials.

  22. Michel, J. C. and Suquet, P., Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis. DOI: 0.1016/j.cma.2003.12.071

  23. Mori, T. and Tanaka, K., Average stress in matrix and average elastic energy of materials with misfitting inclusions. DOI: 10.1016/0001-6160(73)90064-3

  24. O'Brien, T. K., An Evaluation of Stiffness Reduction as a Damage Parameter and Criterion for Fatigue Failure in Composite Materials.

  25. Oskay, C. and Fish, J., Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. DOI: 10.1016/j.cma.2006.08.015

  26. Soden, P. D., Hinton, M. J., and Kaddour, A. S., Lamina properties, lay-up configurations loading conditions for a range of fibre-reinforced composite laminates. DOI: 10.1016/S0266-3538(98)00078-5

  27. Soden, P. D., Hinton, M. J., and Kaddour, A. S., Biaxial test results for strength and deformation of a range of e-glass and carbon fibre reinforced composite laminates: Failure exercise benchmark data. DOI: 10.1016/S0266-3538(02)00093-3

  28. Tsai, S. W. and Wu, E. M., A general theory of strength for anisotropic materials. DOI: 10.1177/002199837100500106

Articles with similar content:

Friction factors and Nusselt numbers for fully developed laminar flow in annuli
International Heat Transfer Conference 12, Vol.10, 2002, issue
Charl G. Jat Du Toit
Blast Analysis of Enclosure Masonry Walls Using Homogenization Approaches
International Journal for Multiscale Computational Engineering, Vol.7, 2009, issue 2
Gabriele Milani, Paulo B. Lourenco
Nonlinear viscoelastic analysis of statistically homogeneous random composites
International Journal for Multiscale Computational Engineering, Vol.2, 2004, issue 4
Michal Sejnoha, R. Valenta, Jan Zeman
Telecommunications and Radio Engineering, Vol.71, 2012, issue 2
Sven-Erik Sandstrom
Olivier F. Balima, Daniel Marceau, Joan Boulanger, Andre Charette