An asymptotic approach to thin film adhesion

Frédéric Lebon (1) , Raffaella Rizzoni (2)

1 M&S - Matériaux et Structures
2 Dipartimento di Ingegneria

A common approach to the modeling of very thin adhesive films is their replacement with an equivalent contact law, prescribing the jumps in the displacement and traction vector fields at the limit interface as the film thickness goes to zero. From the geometrical point of view, the adhesive film is eliminated, although it is accounted for mechanically. Recently, we analyzed several cases to obtain the equivalent contact laws: soft films [17, 18]; adhesive films governed by a non convex energy [12]; linearly elastic adhesive films having stiffness comparable with the adherents [19, 13]; imperfect adhesion between flat adhesive films and the adherents [14]; joints with mismatch strain between the adhesive and the adherents [16]. In this paper, we extend the results obtained in [13, 14] to the case of a thin curvilinear elastic anisotropic adhesive undergoing plane deformations. The asymptotic method proposed in [14] and based on the energy minimization is used. After obtaining the contact law in a general system of curvilinear coordinates, we analyze the gluing between two circular adherents (figure 2), a case of significant importance for composite materials which often contain fibers or particles.

Mots clés: thin film; elasticity; asymptotic analysis

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Frédéric Lebon, Raffaella Rizzoni. An asymptotic approach to thin film adhesion. Eleventh International Conference on Computational Structures Technology, Sep 2012, Dubrovnik, Croatia. ⟨10.4203/ccp.99.144⟩. ⟨hal-00740766⟩