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

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.