Contact problems in the framework of dynamic substructuring

Typical applications of dynamic substructuring deal with time-invariant systems. An interesting extension of the dynamic substructuring can be to consider, among time-variant systems, those built from time-invariant component subsystems subjected to time-variant coupling conditions, such as those encountered in contact problems. Specifically, a time-varying interface due to a frictional sliding contact is considered. The link between substructuring and contact problems can lead to interesting perspectives, for instance, in the macroscopic analysis of the time-frequency behaviour of bodies in relative sliding with friction. The problem can be tackled in time domain using both primal and dual assembly. In the former case classical numerical time integration techniques can be used; in the latter case to avoid singularities forward increment Lagrange multiplier method can be adapted to dual assembly. The methods are applied to discrete models of substructures. In both cases, the assumption of sliding contact can be verified at the end of the computation.