Journal of Engineering Mathematics

, Volume 45, Issue 2, pp 155–168 | Cite as

Slow decay of end effects in layered structures with an imperfect interface

  • Orlando Avila-Pozos
  • Alexander B. Movchan


An asymptotic analysis of a layered structure with an imperfect interface subject to an anti-plane shear deformation and non-homogeneous Dirichlet end conditions is presented in this paper. Two layers of isotropic materials are bonded via a middle interface layer (adhesive joint), which is thin and soft; effectively, this can be described as a discontinuity surface for the displacement. Model fields are constructed to compensate for the error produced by the asymptotic solution for the case when the layered structure is subject to non-homogeneous Dirichlet end conditions. Numerical examples and analytical estimates are presented to illustrate the slow decay of the `boundary-layer' fields.

asymptotic analysis boundary layer imperfect interface 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A.H. Nayfeh. Continuum modelling of low frequency heat conduction in laminated composites with bonds. J. Heat Transfer 102 (1980) 312–319.Google Scholar
  2. 2.
    A.H. Nayfeh. Simulation of the influence of bonding materials on electro-magnetic wave propation in laminated composites. J. Appl. Phys. 51 (1980) 2987–2994.Google Scholar
  3. 3.
    Z. Hashin. Plane anisotropic beams. J. Appl. Mech. (1967) 257–262.Google Scholar
  4. 4.
    Z. Hashin. Thermoelastic properties of fibre composities with imperfect interface. Mechanics of Materials 8 (1990) 333–348.Google Scholar
  5. 5.
    Z. Hashin. Thin interphase/imperfect interface in conduction. J. Appl. Phys. 89 (2001) 2261–2267.Google Scholar
  6. 6.
    D. Bigoni, M. Ortiz and A. Needleman. Effect of interfacial compliance on bifurcation of a layer bonded to a substrate. Int. J. Solids Struct. 34 (1997) 4305–4326.Google Scholar
  7. 7.
    D. Bigoni, S.K. Serkov, M. Valentini and A.B. Movchan. Asymptotic models of dilute composites with imperfectly bonded inclusions. Int. J. Solids Struct. 35 (1998) 3239–3258.Google Scholar
  8. 8.
    C.O. Horgan. Recent developments concerning Saint-Venant's principle: an update. Appl. Mech. Rev. 42 (1989) 295–303.Google Scholar
  9. 9.
    C.O. Horgan. Anti-plane shear deformations in linear and non-linear solid mechanics. SIAM Rev. 37 (1995) 53–81.Google Scholar
  10. 10.
    S.C. Baxter and C.O. Horgan. End effects for anti-plane shear deformations of sandwich structures. Journal of Elasticity 40 (1995) 123–164.Google Scholar
  11. 11.
    S.C. Baxter and C.O. Horgan. Anti-plane shear deformations of anisotropic sandwich structures: end effects. Int. J. Solids Struct. 34 (1997) 79–88.Google Scholar
  12. 12.
    Y. Benveniste. On the decay of end effects in conduction phenomena: A sandwich strip with imperfect interfaces of low or high conductivity. J. Appl. Phys. 86 (1999) 1273–1279.Google Scholar
  13. 13.
    Y. Benveniste and T. Chen. On the saint-venant torsion of composite bars with imperfect interface. Proc. R. Soc. London A 457 (2001) 231–255.Google Scholar
  14. 14.
    A. Klarbring and A.B. Movchan. Asumptotic modelling of adhesive joints. Mechanics of Materials 28 (1998) 137–145.Google Scholar
  15. 15.
    O. Avila-Pozos, A. Klarbring and A.B. Movchan. Asymptotic model of orthotropic highly inhomogeneous layered structure. Mechanics of Materials 31 (1999) 101–115.Google Scholar
  16. 16.
    O. Avila-Pozos. Mathematical models of layered structures with an imperfect interface and delamination cracks. PhD Thesis, University of Bath (1999) 209 pp.Google Scholar
  17. 17.
    R.D. Adams and W.C. Wake. Structural Adhesive Joints in Engineering New York, London: Chapman & Hall (1997) 384 pp.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Orlando Avila-Pozos
    • 1
  • Alexander B. Movchan
    • 2
  1. 1.Instituto de Ciencias Básicas e IngenieríaUniversidad Autónoma del Estado de HidalgoPachucaMexico
  2. 2.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK

Personalised recommendations