An asymptotic study of the debonding of thin films

Kaushik Bhattacharya
Division of Engineering and Applied
Science, California Institute of Technology
Pasadena, CA 91125, USA
email:nnbhatta@caltech.edu

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213, USA
email: fonseca@andrew.cmu.edu

Gilles Francfort
L.P.M.T.M., Université
Paris-Nord, 93430
Villetaneuse, France
email: francfor@lpmtm.univ-paris13.fr

Abstract:We examine the asymptotic behavior of a bilayer thin film using the notion of Gamma-convergence. We allow for debonding at the interface, but penalize it using an interfacial energy; thus the functional we consider consists of the elastic energy of the two layers and the interfacial energy with penalizes debonding. We show that the asymptotic theory or Gamma-limit depends on the particular form of the interfacial energy, and derive detailed results for both the cohesive and the brittle interface.

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