Asymptotic study of soft thin layer: the non convex case

Frédéric Lebon (1) , Raffaella Rizzoni (2)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 Dipartimento di Ingegneria [Ferrara]

In this paper, it is proposed to model the adhesive bonding of elastic bodies, taking into account a non convex (piecewise quadratic) strain energy density for the adhesive material. In the ¯rst part of the paper, asymptotic expansions are used to study the asymptotic behavior of the adhesive. In the second part, we study in detail the example of a bar consisting of two elastic bodies, giving linear stress-strain relations, separated by an adhesive layer, the extremities of which undergo a given displacement. The stability and the metastability of the equilibrium configurations are then discussed. Lastly, the limit problem, where the pair thickness and stiffness of the glue tend to zero, is studied.

Mots clés: asymptotic studies; soft thin layers; non-convex energy

Domaines: Mécanique [physics.med-ph]

Frédéric Lebon, Raffaella Rizzoni. Asymptotic study of soft thin layer: the non convex case. Mechanics of Advanced Materials and Structures, 2008, 15 (1), pp.12-20. ⟨10.1080/15376490701410521⟩. ⟨hal-00294891⟩