Asymptotic modelling of interfaces taking contact conditions into account: asymptotic expansions and numerical implementation

Frédéric Lebon (1) , Fouad Zaittouni (2)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 M3 - Modélisation Mathématique en Mécanique

In the present theoretical and numerical study on thin layers, a method is presented for modelling bonding processes and interfaces. When the thickness and the rigidity of the layer tend to zero, the asymptotic problem leads to a limit problem with a mechanical constraint on the surface, to which the layer shrinks. The formulation of the limit problem includes the mechanical and geometrical properties of the layer. The contact and pseudo-friction conditions between the adhesive and the adherents are also taken into account. Theoretical results are obtained using asymptotic expansions and numerical data. The asymptotic laws are implemented in a finite element software. Numerical algorithms are detailed and numerical examples are presented.

Mots clés: Thin layer; Contact; Friction; Asymptotic expansions

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

Frédéric Lebon, Fouad Zaittouni. Asymptotic modelling of interfaces taking contact conditions into account: asymptotic expansions and numerical implementation. International Journal of Engineering Science, 2010, 48 (2), pp.111-127. ⟨10.1016/j.ijengsci.2009.07.005⟩. ⟨hal-00459511⟩