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A multiscale method for frictionless contact mechanics of rough surfaces.pdf

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A multiscale method for frictionless contact mechanics of rough surfaces.pdf

Tribology International 96 (2016) 109–121 Contents lists available at ScienceDirect Tribology International journal homepage: /locate/triboint A multiscale method for frictionless contact mechanics of rough surfaces Y. Waddad a,b,c,n, V. Magnier a,b,c, P. Dufrénoy a,b,c, G. De Saxcé a,b,c a Université Lille Nord de France, F-59000 Lille, France b Lille1-LML, F-59655 Villeneuve dAscq, France c CNRS, UMR 8107, F-59655 Villeneuve dAscq, France article info Article history: Received 26 June 2015 Received in revised form 23 November 2015 Accepted 20 December 2015 Available online 29 December 2015 Keywords: Surface roughness Hertz theory Contact mechanics Finite element method abstract An ef?cient methodology is proposed for the analysis of frictionless contact between rough surfaces. The surface is described by parabolic asperities which deform according to Hertz Theory. The problem is solved considering interactions between elliptic contact zones. Such analysis provides interface laws that are incorporated into a macroscopic numerical model where contact surfaces are ?at. This operation is done by means of Love solution for elastic half spaces and the penalty method. A numerical example of this multiscale method is presented to show its robustness. In comparison with a purely numerical model where roughness is explicitly described, the proposed strategy provides good results and saves a considerable amount of time. 2015 Elsevier Ltd. All rights reserved. 1. Introduction Contact mechanics is a fundamental problem in mechanical engineering. It provides necessary information to design safely many systems that involve two or more bodies that are contacting each other, such as braking systems, blade-abradable seals and many others. The ?rst work in this domain dates back to 1882 with the pioneering Hertz theory. This theory describes the frictionless contact between two elastic curved surfaces. However, real surfaces are rough, thus the real contact area is very small compa