Asymptotic Homogenisation in Strength and Fatigue Durability Analysis of Composites

  • S. E. Mikhailov
  • J. Orlik
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)


Asymptotic homogenisation technique and two-scale convergence is used for analysis of macro-strength and fatigue durability of composites with a periodic structure under cyclic loading. The linear damage accumulation rule is employed in the phenomenological micro-durability conditions (for each component of the composite) under varying cyclic loading. Both local and non-local strength and durability conditions are analysed. The strong convergence of the strength as the structure period tends to zero is proved and its limiting value is estimated.


Periodic structures two-scale convergence local strength conditions non-local strength conditions cyclic loading S-N durability diagram linear damage accumulation 


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  1. [1]
    Allaire, G (1992) Homogenisation and Two-Scale Convergence, SIAM J. Math. Anal., 23, 1482–1518.CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    Bakhvalov, N and Panasenko, G (1984) Homogenisation: Averaging Processes in Periodic Media. Mathematical Problems in the Mechanics of Composite Materials, Dordrecht-Boston-London: Kluwer.Google Scholar
  3. [3]
    Cioranescu, D and Donato, P (1999) An Introduction to Homogenization. New York: Oxford University Press.Google Scholar
  4. [4]
    Kolmogorov, A N and Fomin, S B (1957) Elements of the theory of functions and functional analysis. Rochester, N.Y.: Graylock Press.Google Scholar
  5. [5]
    Mikhailov, S E (1995) A Functional Approach to Non-local Strength Conditions and Fracture Criteria: I. Body and Point Fracture, Eng. Fract. Mech., 52, 731–743.CrossRefGoogle Scholar
  6. [6]
    Pobedrya, B E (1984) Mechanics of Composite Materials, Moscow State University Publishing.Google Scholar
  7. [7]
    Trenogin, V A (1980) Functional Analysis, Moscow: Nauka.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • S. E. Mikhailov
    • 1
  • J. Orlik
    • 2
  1. 1.Div. of MathematicsGlasgow Caledonian UniversityGlasgowUK
  2. 2.Fraunhofer Institut für Techno-und WirtschaftsmathematikKaiserslauternGermany

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