Journal of Materials Science

, Volume 41, Issue 20, pp 6800–6812 | Cite as

Multi-scale modeling in damage mechanics of composite materials



This paper addresses the multi-scale modeling aspects of damage in composite materials. The multiplicity of the scales of the operating mechanisms is discussed and clarified by taking examples of damage in a unidirectional ceramic matrix composite and in a cross ply polymer matrix composite laminate. Two multi-scale modeling strategies––the hierarchical and the synergistic––are reviewed in the context of deformational response. Finally, the “big picture” as it relates to the cost-effective manufacturing of composite structures intended for long-term performance is outlined and desired future direction in multi-scale modeling is discussed.


Representative Volume Element Matrix Crack Damage Mode Continuum Damage Mechanic Debond Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Budiansky B (1983) Comput Struct 16:3CrossRefGoogle Scholar
  2. 2.
    Hashin Z (1990) In: Boehler JP (ed) Yielding, damage, and failure of anisotropic solids, Mechanical Engineering Publications, London, p 3 Google Scholar
  3. 3.
    Jamison RD, Schulte K, Reifsnider KL, Stinchcomb WW (1984) Effects of defects in composite materials, ASTM STP 836. American Society for Testing and Materials, Philadelphia, p 21Google Scholar
  4. 4.
    Kachanov LM (1958) Izv. AN SSSR, Ofd. Tekhn. Nauk. 8:26 (in Russian)Google Scholar
  5. 5.
    Pyrz R (2000a) In: Chou T–W (Volume ed), Kelly A, Zweben C (eds-in-Chief), Comprehensive composite materials, vol 1. Elsevier, Oxford, p 465Google Scholar
  6. 6.
    Pyrz R (2000b) In: Talreja R, Månson J-AE (Volume eds), Kelly A, Zweben C (Eds-in-Chief), Comprehensive composite materials, vol 2. Elsevier, Oxford, p 553Google Scholar
  7. 7.
    Sørensen BF, Talreja R (1993) Int J Damage Mech 2:246Google Scholar
  8. 8.
    Talreja R (1990) In: Boehler JP (ed) Yielding, damage and failure of anisotropic solids. Mechanical engineering publications, London, p 509Google Scholar
  9. 9.
    Talreja R (1991) Mech Mat 12:165–180CrossRefGoogle Scholar
  10. 10.
    Talreja R (1996) In: Cardon AH et al (eds) Progress in durability analysis of composite systems. A.A. Balkema, Rotterdam, p 117Google Scholar
  11. 11.
    Varna J, Joffe R, Talreja R (2001) Compos Sci Technol 61:657CrossRefGoogle Scholar
  12. 12.
    Varna J, Krasnikovs A, Kumar RS, Talreja R (2004) Int J Damage Mech 13:301CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringTexas A&M UniversityCollege StationUSA

Personalised recommendations