High-speed simulation of axially symmetric contacts

Axially symmetric contacts can be simulated rapidly with the Method of Dimensionality Reduction (MDR). Within its range of application, the method is highly accurate and several orders of magnitude faster than conventional finite element, or even boundary element approaches. The low computational complexity of the method is due to the low number of degrees of freedom, and it is due to the fact that these degrees of freedom are decoupled. The method was first proposed by V. L. Popov and S. Psakhie in 2007.

From a numerical perspective, the integral transformations which have to be performed as part of this method are a challenge. In the following paper, a simple method for the implementation of these transformations is proposed:

Fast numerical implementation of the MDR transformations
J. Benad
Facta Universitatis, Series: Mechanical Engineering, vol. 16, no. 2, pp. 127-138, 2018

With such a technique, demanding wear simulations can be implemented with the MDR. For special kinds of wear simulations one may further improve the implementation with additional techniques proposed in the following study:

Numerical implementation of fretting wear in the framework of the MDR
Q. Li, F. Forsbach, J. Benad
Facta Universitatis, Series: Mechanical Engineering, vol. 17, no. 1, pp. 87-93, 2019

The implementation technique has also been included in a book about the MDR by V. L. Popov, M. Heß and E. Willert.

It can be found here on ResearchGate.