The extension of the method of dimensionality reduction to non-compact and non-axisymmetric contacts

Abstract

The Hertz-type three-dimensional frictionless contact problem with a single controlling parameter is considered through a prism of the method of dimensionality reduction (MDR). The corresponding MDR formalism has been developed with respect to the main contact parameters (contact force and contact approach). It is shown that the half-length of the 1D contact interval can be uniquely interpreted as the harmonic radius of the original contact area. Also, the case of self-similar contact is studied in detail, and the obtained relations are applied to this case.