Stress Singularities in Viscoelastic Media and Related Problems

  • C. Atkinson
Part of the International Centre for Mechanical Sciences book series (CISM, volume 356)


Stress singularities at sharp notch and crack tips in viscoelastic media are considered for both homogeneous and inhomogeneous media (particularly bimaterials). In Lecture 1 various invariants for elastic media are briefly reviewed and extended to the viscoelastic case. Some useful asymptotic results for both Laplace and Mellin transforms are also briefly reviewed. In Lecture 2 near crack tip behaviour is derived and a problem of a crack in an inhomogeneous viscoelastic strip treated by means of one of the invariants derived in Lecture 1. Dual variational principles are also derived for use in this problem. In Lecture 3 the problem of a crack meeting a viscoelastic bimaterial interface is considered and it is shown how the nature of the stress singularity evolves with time depending on the relaxation moduli of the bimaterial components. A partial interpretation of these results is given in terms of the force on a dislocation interacting with the biomaterial interface. In Lecture 4 the time evolution of the singular stress field at a wedge or notch tip in plane strain is discussed. Finally in Lecture 5 we consider the problem of interpreting a crack extent and location from measurements on the inside of a hole from which the crack is initiated.


Stress Singularity Viscoelastic Medium Bimaterial Interface Singular Stress Field Real Time Behaviour 
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  1. 1.
    Akinson, C. (1975), Int. J. Engng. Sci., 13, 31–44.Google Scholar
  2. 2.
    Atkinson, C. and Appleby, S. (1994), Int. J. Engng. Sci., 32, 955–977.Google Scholar
  3. 3.
    Atkinson, C. (1977), Int. J. Fracture, 13, 807–820.CrossRefGoogle Scholar
  4. 4.
    Atkinson, C. and Bourne, J.P. (1989), Quart. J. Mechs. Appl. Math. 42, 385–412.Google Scholar
  5. 5.
    England, A.H. (1971), Int. J. Engng. Sci., 9, 571–585.Google Scholar
  6. 6.
    Williams, M.L. (1959), Bulletin Seismological Society of America, 49, 199–204.Google Scholar
  7. 7.
    Achenbach and Chao (1962), J. Mech. Phys. Solids, 10, 245–252.Google Scholar
  8. 8.
    Christensen, R.M. (1971), Theory of viscoelasticity. An Introduction, Academic Press (1971).Google Scholar
  9. 9.
    Bourne, J.P. and Atkinson, C. (1990), IMA Jnl. Appl. Maths, 4, 163–180.Google Scholar
  10. 10.
    Atkinson, C. and Bourne, J.P. (1990), Int. J. Engng. Sci., 28, 615–630.Google Scholar
  11. 11.
    Eftaxiopulos, D.A. and Atkinson, C. (1991), Int. J. Engng. Sci., 29, 1569–1584.Google Scholar
  12. 12.
    Atkinson, C. and Craster, R.V. (1994), To appear in Jnl. Aerospace Science.Google Scholar
  13. 13.
    Atkinson, C. and Hiercelin, M. (1993), Int. J. Frac., 59, 23–40.Google Scholar
  14. 14.
    Atkinson, C. and Aparicio, N.D. (1994), Proc. Roy. Soc. A445, 637–652.Google Scholar
  15. 15.
    Sagami, T. et al. (1990), Trnas. J. S. M. E., 56, 27–32.Google Scholar
  16. 16.
    Santosa, F. and Vogelius, M. (1992), Technical Report No. 90–3, Centre for the Mathematics of Waves, University of Delaware, USA.Google Scholar
  17. 17.
    Nishimura, N. and Kobayashi, S. (1991), Boundary Elements XII, Vol. 2, 425–434, Southampton, Computational Mechanics.Google Scholar

Copyright information

© Springer-Verlag Wien 1995

Authors and Affiliations

  • C. Atkinson
    • 1
  1. 1.Imperial CollegeLondonUK

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