13. The Coupling to Macroscopic Dynamics

In practical applications, mechanical models are frequently considered in which macroscopic frictional contacts are present. The typical procedure used to describe frictional contacts is to formulate a suitable law of friction, which is then subsequently applied in a macroscopic simulation of the system dynamics. However, it is often difficult to formulate a useable law of friction, as the frictional force is not only a function of the instantaneous state of motion of the system, but is also dependent on the previous history of the system motion. Here, the method of dimensionality reduction opens up a new path: The simulations using the reduction method are carried out so quickly that one can completely forego the previous formulation of the frictional law. The calculation of the contact and frictional forces is then carried out directly within the framework of the macroscopic simulation of the system dynamics. Models that combine both the macrosimulations and microsimulations into one are termed hybrid models in the following. In this chapter, it will be shown how the method of dimensionality reduction is used for the formulation of hybrid models.