On Applications of Semi-Analytical Methods of Contact Mechanics

This paper is concerned with possible applications of semi-analytical methods of frictional contact mechanics. The semi-analytical solutions, such as the Method of Memory Diagrams, enable the load-displacement relationship for contact of two axisymmetric bodies with friction to be written as an analytical expression with parameters calculated via a numerical procedure. As a result, a complex history-dependent solution is obtained for an arbitrary loading history in a computationally efficient way. This fact allows one to calculate hysteretic responses to extremely complex loading histories, such as random vibrations. Another case when complex loading histories appear is in a harmonic excitation of a dynamic contact system in which inertia is taken into account. Both examples are considered here. The random excitation case can be used as a basis for modeling for wear in frictional contacts while the second one may be extended to describe coupled dynamic contact systems, stick-slip phenomena, or friction-induced instabilities.