Mathematical analysis of a bonded joint with a soft thin adhesive

This paper considers the problem of two adherents joined by a soft thin adh esive along their common surface. Using the asymptotic expansion method, th e authors obtain a simplified model in which the adhesive is treated as a m aterial surface and is replaced by returning springs. The authors show weak and strong convergence of the exact solution toward the solution of the li mit problem. The singularities of the limit problem are analyzed, and it is shown that typically they are logarithmic. Furthermore, the authors invest igate the phenomenon of boundary layer by studying the correctors, the extr a terms, which must be added to the classical asymptotic expansion to verif y the boundary conditions. The correctors show that, contrary to the adhere nts, in the adhesive there are power-type singularities, which are at the b ase of the failure of the assemblage.