Advertisement

Numerical Analysis of Two Non-linear Soft Thin Layers

  • Frédéric Lebon
  • Raffaella Rizzoni
  • Sylvie Ronel-Idrissi
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 61)

Abstract

In a first part, we consider a bar with extremities subject to a given displacement and made by two elastic bodies with linear stress-strain relation separated by an adhesive layer of thickness h. The material of the adhesive is characterized by a non convex (piecewise quadratic) strain energy density with elastic modulus k. After considering the equilibrium problem of the bar and determining the stable and metastable solutions, we let (h,k) tending to zero and we obtain the corresponding asymptotic contact laws, linking the stress to the jump of the displacement at the adhesive interface. The second part of the paper is devoted to the bi-dimensional problem of two elastic bodies separated by a thin soft adhesive. The behaviour of the adhesive is non associated elastic-plastic. As in the first part, we study the asymptotic contact laws.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lebon, F., Ould-Khaoua, A., Licht, C.: Numerical study of soft adhesively bonded joints in finite elasticity. Comp. Mech. 21, 134–140 (1997)CrossRefGoogle Scholar
  2. 2.
    Licht, C., Michaille, G.: A modelling of elastic adhesive bonded joints. Adv. Math. Sci. Appl. 7, 711–740 (1997)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Lebon, F., Rizzoni, R.: Aymptotic analysis of soft thin layers with nonconvex energy. In: Proc. 16th AIMETA Italian Congress, Ferrara (2003)Google Scholar
  4. 4.
    Lebon, F., Rizzoni, R.: Asymptotic Study on a Soft Thin Layer: The Non-Convex Case. Mech. Adv. Mater. Struct. 15, 12–20 (2008)CrossRefGoogle Scholar
  5. 5.
    Aberayatne, R., Knowles, J.K.: On the driving traction acting on a surface of strain discontinuity in a continuum. J. Mech. Phys. Solid 38, 345–360 (1990)CrossRefGoogle Scholar
  6. 6.
    Aberayatne, R., Knowles, J.K.: Kinetic relations and the propagation of phase boundaries in solids. Arch. Rational Mech. Anal. 114, 119–154 (1991)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Aberayatne, R., Bhattacharya, K., Knowles, J.K.: Strain-energy functions with multiple local minima: Modeling phase transformations using finite thermoelasticity. In: Fu, Y.B., Ogden, R.W. (eds.) Nonlinear Elasticity: Theory and Applications. London Mathemathical Society Lecture Notes Series, vol. 283, pp. 433–490. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  8. 8.
    Lebon, F., Ronel-Idrissi, S.: Asymptotic analysis of Mohr-Coulomb and Drucker-Prager soft thin layers. Steel Comp. Struct.: Int. J. 4, 133–148 (2004)Google Scholar
  9. 9.
    Aberayatne, R., Chu, C., James, R.D.: Kinetics of materials with wiggly energies: Theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy. Phil. Mag. A73, 457–497 (1996)Google Scholar
  10. 10.
    Dacorogna, B.: Direct methods in the calculus of variations. Springer, Berlin (1989)zbMATHGoogle Scholar
  11. 11.
    Sagan, H.: An introduction to the calculus of variations. Dover, New York (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Frédéric Lebon
    • 1
  • Raffaella Rizzoni
    • 2
  • Sylvie Ronel-Idrissi
    • 3
  1. 1.Laboratoire de Mécanique et d’AcoustiqueUniversité de ProvenceMarseille Cedex 20France
  2. 2.Dipartimento di IngegneriaUniversitá di FerraraFerraraItaly
  3. 3.Laboratoire Mécanique, Matériaux, StructuresUniversité Claude BernardVilleurbanne CedexFrance

Personalised recommendations