A multiscale contact homogenization technique for the modeling of third bodies in the contact interface

In this work, a contact homogenization technique is developed to extract the macroscopic coefficient of friction (CF) from a three-body frictional system. The particular frictional system under consideration consists of rigid particles embedded between a finitely deformable elastic solid and a rigid surface. The challenge of the problem lies in modeling the interaction between the particles with the finite element mesh, as well as in the dynamic nature of the problem. In order to extract the macroscopic CF, a microscopic sample is analyzed in a time-adaptive dynamic setting and the macroscopic CF is identified as the ratio of tangential force to normal force applied to the sample. In order to alleviate dynamic effects, time averaging is employed. The identification of a representative contact element (RCE) and the application of proper boundary conditions are discussed for periodic and random arrangements of the particles in the interface with a particular emphasis on the nature of the micro-to-macro transition procedure. Finally, the implementation of the model in a coupled micro–macro simulation using a RCE is discussed in the context of multiscale analysis.