On the application of the Method of Dimensionality Reduction to two-dimensional contacts

TL;DR

This paper investigates extending the Method of Dimensionality Reduction (MDR) from point contacts to line contacts in contact mechanics, analyzing whether an approximate formulation is feasible for contacts with unbounded contact areas in one dimension.

Contribution

It explores the possibility of adapting MDR to two-dimensional line contacts, expanding its applicability beyond point contacts in contact mechanics.

Findings

Analysis of MDR applicability to line contacts

Potential approximate formulations for 2D contact problems

Extension of MDR framework to unbounded contact areas

Abstract

The conventional formulation of the Method of Dimensionality Reduction (MDR) in contact mechanics is only applicable two "point contacts", that is to contacts of two unbounded three-dimensional bodies over final contact area. We analyze here if it is possible to find an at least approximate formulation of the MDR for "line contacts", that is contacts which contact area is unbounded in one direction. In this case the problem can be formulated as contact of two two-dimensional half-"spaces".