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DEVELOPMENTS AND APPLICATIONS IN COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru and M.L. Romero
On Interface Modelling using Asymptotic Techniques
LMA CNRS UPR 7051, University of Provence, Marseille, France
F. Lebon, "On Interface Modelling using Asymptotic Techniques", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru and M.L. Romero, (Editors), "Developments and Applications in Computational Structures Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 5, pp 113-143, 2010. doi:10.4203/csets.25.5
Keywords: thin layer, interface, asymptotic theory.
This chapter is a review of theoretical and numerical asymptotic studies on thin layers. A general method is presented for modelling bonding processes and interfaces. When the thickness and, eventually, the mechanical characteristics of the layer tend to zero, the asymptotic problem leads to a limit problem with a mechanical constraint on the surface, to which the layer shrinks. The formulation of the limit problem includes the mechanical and geometrical properties of the layer. Theoretical results are obtained using Gamma-convergence, variational analysis, asymptotic expansions and numerical studies. An example of a numerical algorithm and numerical examples are given.
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