Mapping of Two-Dimensional Contact Problems on a Problem with a One-Dimensional Parametrization


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We discuss a possible generalization of the ideas of the method of dimensionality reduction (MDR) for the mapping of two-dimensional contact problems (line contacts). The conventional formulation of the MDR is based on the existence and uniqueness of a relation between indentation depth and contact radius. In two-dimensional contact problems, the indentation depth is not defined unambiguously, thus another parametrization is needed. We show here that the Mossakovskii-Jäger procedure of representing a contact as a series of incremental indentations by flat-ended indenters can be carried out in two-dimensions as well. The only available parameter of this process is, however, the normal load (instead of indentation depth as in the case of threedimensional contacts). Using this idea, a complete solution is obtained for arbitrary symmetric two-dimensional contacts with a compact contact area. The solution includes both the relations of force and half-width of the contact and the stress distribution in the contact area. The procedure is generalized for adhesive contacts and is illustrated by solutions of a series of contact problems.

作者简介

V. Popov

Technische Universität Berlin; National Research Tomsk Polytechnic University; National Research Tomsk State University

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Email: v.popov@tu-berlin.de
德国, Berlin, 10623; Tomsk, 634050; Tomsk, 634050

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