Mathematical Analysis of a Bonded Joint with a Soft Thin Adhesive

Author:

Geymonat Giuseppe1,Krasucki Francoise2,Lenci Stefano3

Affiliation:

1. Laboratoire de Mécanique et Technologie, ENS Cachan, CNRS, Université Pierre et Marie Curie, 94235 Cachan Cedex, France

2. Laboratoire de Modélisation en Mecanique, Université Pierre et Marie Curie, CNRS, 75252 Paris Cedex 05, France

3. Istituto di Scienza e Tecnica delle Costruzioni, Università di Ancona, 60131 Ancona, Italy

Abstract

This paper considers the problem of two adherents joined by a soft thin adhesive along their common surface. Using the asymptotic expansion method, the authors obtain a simplified model in which the adhesive is treated as a material surface and is replaced by returning springs. The authors show weak and strong convergence of the exact solution toward the solution of the limit problem. The singularities of the limit problem are analyzed, and it is shown that typically they are logarithmic. Furthermore, the authors investigate the phenomenon of boundary layer by studying the correctors, the extra terms, which must be added to the classical asymptotic expansion to verify the boundary conditions. The correctors show that, contrary to the adherents, in the adhesive there are power-type singularities, which are at the base of the failure of the assemblage.

Publisher

SAGE Publications

Subject

Mechanics of Materials,General Materials Science,General Mathematics

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