A model for hierarchical anisotropic friction, adhesion and wear

Due to a widespread number of examples, biological hierarchical structures have been studied for years, founding that surface properties are strictly correlated to the surface roughness. Since friction appears to be a multiscale phenomenon and hierarchy optimizes the macroscopic mechanical properties of bodies, it may be of great interest to develop a model to predict friction of structures with hierarchical surfaces. Thus, we propose an analytical model to describe anisotropic friction, adhesion and wear of hierarchical surfaces. The model describes friction between two generic rough surfaces in contact, sliding one against the other. Then, it has been extended to adhesion, wear and finally to multiple hierarchical levels to obtain the global frictional response.