We present a numerical procedure to simulate the dynamic debonding of a thin layer from a rigid substrate. The layer is assumed to behave elastically, whereas the process zone -where dissipation occurs- is modelled through a cohesive softening law. Using a simplified approach, in the case of bending dominated delamination the shear deformation can be disregarded. Thus the Euler-Bernoulli kinematics can be adopted to describe the motion of the specimen.
Under such hypotheses, the governing partial differential equation is characterized by two length scales and two time scales (three time scales when rate-dependency is included in the cohesive model). The first length scale is introduced by the size of the specimen, identified by a macroscopic length l_M; the second length scale is introduced by the presence of a process zone in front of the delamination crack tip. As for the time scales, the first one is related to the propagation of a dilatational wave along the free part of the specimen t_g; the second one is a characteristic time t_c, which accounts for the interplay between the debonding layer inertia of and the mechanical properties of the process zone. Length and time scales can differ of several orders of magnitude, conferring to the problem a space-time multiscale nature.
Introducing a spatial discretization (e.g. by central finite differences), the PDE is transformed into an ordinary differential equation system to be integrated in time. Assuming that the spatial discretization is fine enough to capture everywhere the stress distribution, for the numerical solution of the layer dynamics in the process zone an accurate time integration is impelling. In fact, the process zone is characterized by fast changes of the stress distribution. In this work we present the application of a temporal multiscale approach for the analysis of the dynamic delamination, able to capture the essential mechanical features of the process.

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