Transmission Conditions for Thin Elasto-Plastic Pressure-Dependent Interphases

  • Gennady MishurisEmail author
  • Wiktoria  Miszuris
  • Andreas Öchsner
  • Andrea Piccolroaz
Part of the Engineering Materials book series (ENG.MAT.)


A thin soft elasto-plastic interphase between two different media is under consideration. The intermediate layer is assumed to be of infinitesimal thickness and is modeled by nonlinear transmission conditions which incorporate the elasto-plastic material behavior of the layer. The case of pressure-independent (von Mises) as well as pressure-dependent yield condition is theoretically treated. Finite element analysis of a bimaterial structure with such an imperfect elasto-plastic interface (von Mises) shows the efficiency of the approach and illustrates some restrictions of its application.


Interface Inhomogeneous Nonlinear Deformation theory von Mises material Drucker-Prager material 



GM and WM thank to FP7 IAPP project PARM-2 (PIAPP-GA-2011-284544) for support of this research. WM gratefully acknowledges facilities and hospitality of the industrial partner, EUROTECH, during her secondment there in the framework of the project.


  1. 1.
    Antipov, Y.A., Avila-Pozos, O., Kolaczkowski, S.T., Movchan, A.B.: Mathematical model of delamination cracks on imperfect interfaces. Int. J. Solids Struct. 38, 6665–6697 (2001)CrossRefzbMATHGoogle Scholar
  2. 2.
    Avila-Pozos, O., Klabring, A., Movchan, A.B.: Asymptotic model of ortotropic highly inhomogeneous layered structure. Mech. Mater. 31, 101–115 (1999)CrossRefGoogle Scholar
  3. 3.
    Bigoni, D.: Nonlinear Solid Mechanics Bifurcation Theory and Material Instability. Cambridge University Press, Cambridge (2012)CrossRefzbMATHGoogle Scholar
  4. 4.
    Benveniste, Y., Miloh, T.: Imperfect soft and stiff interfacses in two-dimentional elasticity. Mech. Mater. 33, 309–323 (2001)CrossRefGoogle Scholar
  5. 5.
    Benveniste, Y.: The effective mechanical behaviour of composite materials with imperfect contact between the constituens. Mech. Mater. 4, 197–208 (1985)CrossRefGoogle Scholar
  6. 6.
    Chen, W.F., Han, D.J.: Plasticity for Structural Engineers. Springer, New York (1988)CrossRefzbMATHGoogle Scholar
  7. 7.
    Chen, W.F.: Constitutive Equations for Engineering Materials. Elsevier, Amsterdam (1994)Google Scholar
  8. 8.
    Erdogan, F.: Fracture mechanics of interfaces. In: Balkoma, A.A. (ed.) Proceedings of the First International Conference on Damage and Failure of Interfaces DFI-I/Vienna/22-24 September 1997, Rotterdam-Brookfield, pp 3–36 (1997)Google Scholar
  9. 9.
    Hashin, Z.: Thermoeleastic properties of fiber composites with imperfect inyterface. Mech. Mater. 8, 3333–3348 (1990)Google Scholar
  10. 10.
    Hashin, Z.: Thin interphase/imperfect interface in elasticity with application to coated fiber composites. J. Mech. Phys. Solids 50, 2509–2537 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hassanipour, M., Öchsner, A.: Implementation of a pressure sensitive yield criterion for adhesives into a commercial finite element code. J. Adhesion 87, 1125–1147 (2011)CrossRefGoogle Scholar
  12. 12.
    Hatheway, A.E.: Evaluating stresses in adhesive bond lines. In: MSC/NASTRAN Users’ Conference March 13–17, 1989, Universal City (1989)Google Scholar
  13. 13.
    Hencky, H.: Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen. Z. Angew Math. Mech. 4, 323–334 (1924)CrossRefGoogle Scholar
  14. 14.
    Hill, R.: The Mathematical Theory of Plasticity. Oxford University Press, Oxford (1950)zbMATHGoogle Scholar
  15. 15.
    Ikeda, T., Yamashita, A., Lee, D., Miyazaki, N.: Failure of a ductile adhesive layer constrained by hard adherends. Trans. ASME J. Eng. Mater. Technol. 122, 80–85 (2000)CrossRefGoogle Scholar
  16. 16.
    Jones, R.M.: Deformation Theory of Plasticity. Bull Ridge Publishing, Blacksburg (2009)Google Scholar
  17. 17.
    Kachanov, L.M.: Foundations of the Theory of Plasticity. North-Holland, Amsterdam (1971)zbMATHGoogle Scholar
  18. 18.
    Klabring, A., Movchan, A.B.: Asymptotic modelling of adheasive joints. Mech. Mater. 28, 137–145 (1998)CrossRefGoogle Scholar
  19. 19.
    Lakes, R.S.: Negative Poisson’s ratio materials. Science 238, 551 (1987)CrossRefGoogle Scholar
  20. 20.
    Lubarda, V.A.: Deformation theory of plasticity revisited. Proc. Mont. Acad. Sci. Arts 13, 117–143 (2000)Google Scholar
  21. 21.
    Lubliner, J.: Plasticity Theory. Macmillan, New York (1990)zbMATHGoogle Scholar
  22. 22.
    Mahnken, R., Schlimmer, M.: Simulation of strength difference in elasto-plasticity for adhesive materials. Int. J. Numer. Methods Eng. 63, 1461–1477 (2005)CrossRefzbMATHGoogle Scholar
  23. 23.
    Mishuris, G.: Interface crack and nonideal interface approach. Mode III. Int. J. Fract. 107(3), 279–296 (2001)CrossRefGoogle Scholar
  24. 24.
    Mishuris, G., Kuhn, G.: Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface. Z. Angew Math. Mech. 81(12), 811–826 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Mishuris, G., Öchsner, A., Kuhn, G.: Imperfect interfaces in dissimilar elastic body: FEM-analysis. In: Ren, Z., Kuhn, G., Skerget, L., Hribersek, M. (eds.) Advanced Computational Engineering Mechanics. Proc. of the First Workshop, Maribor Slovenia, October 9–11, 2003, University of Maribor Publishers, Maribor (2003)Google Scholar
  26. 26.
    Mishuris, G., Öchsner, A.: Edge effects connected with thin interphases in composite materials. Compos. Struct. 68, 409–417 (2005)CrossRefGoogle Scholar
  27. 27.
    Mishuris, G., Öchsner, A.: 2D modelling of a thin elasto-plastic interphase between two different materials: plane strain case. Compos. Struct. 80, 361–372 (2007)CrossRefGoogle Scholar
  28. 28.
    Movchan, A.B., Movhan, N.V.: Mathematical Modelling of Solids with Nonregular Boundaries. CRC Press, London (1995)Google Scholar
  29. 29.
    Öchsner, A., Winter, W., Kuhn, G.: Damage and fracture of perforated aluminum alloys. Adv. Eng. Mater. 2, 423–426 (2000)CrossRefGoogle Scholar
  30. 30.
    Öchsner, A., Mishuris, G.: A new finite element formulation for thin non-homogeneous heat-conducting adhesive layers. Int. J. Adhes. Adhes. 22, 1365–1378 (2008)Google Scholar
  31. 31.
    Rosselli, F., Carbutt, P.: Structural bonding applications for the transportation industry. SAMPE J. 37(6), 7–13 (2001)Google Scholar
  32. 32.
    Sancaktar, E.: Complex constitutive adhesive models. In: Silva, L.F.M., Öchsner, A. (eds.) Modeling of Adhesively Bonded Joints, pp. 95–130. Springer, Berlin (2008)CrossRefGoogle Scholar
  33. 33.
    Yu, H.H., He, M.Y., Hutchinson, J.W.: Edge effects in thin film delamination. Acta Mater. 49, 93–107 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Gennady Mishuris
    • 1
    Email author
  • Wiktoria  Miszuris
    • 1
  • Andreas Öchsner
    • 2
    • 3
  • Andrea Piccolroaz
    • 1
    • 4
  1. 1.Department of Mathematics and Physics, IMPACS, PenglaisAberystwyth UniversityAberystwythUK
  2. 2.Griffith University, Griffith School of EngineeringSouthportAustralia
  3. 3.The University of NewcastleCallaghanAustralia
  4. 4.University of TrentoTrentoItaly

Personalised recommendations