Soft imperfect interface models accounting for inertial effects, viscosity, and damage

This paper presents new results on the modeling of interfaces in viscoelastic media, taking into account inertial effects and damage evolution. The approach relies on an asymptotic expansion method to derive effective interface models from full three-dimensional descriptions of a stratified composite, as the thickness of the intermediate adhesive layer tends to zero. The asymptotic analysis highlights the combined influence of the viscoelastic properties of the constituent materials, inertial contributions, and damage processes. Appropriate scaling laws for the physical parameters of the adhesive layer are introduced, and the corresponding limit configurations are derived. Three distinct regimes are considered: (1) constant mass density of the adhesive, with low stiffness and very low viscosity; (2) constant mass density, with low stiffness and low viscosity; (3) very high mass density, scaling as the inverse of the layer thickness, with low stiffness and viscosity. These different regimes give rise to specific asymptotic behaviors. In the first two cases, the inertial contribution vanishes in the limit, yielding a classical equation for the damage variable at the interface, in the elastic and viscoelastic setting, respectively. In the third case, the limit configuration acquires a nonlocal character and keeps track of the dynamics in the adhesive layer.