An LCP based approach for the contact mechanics of elastic half spaces

Abstract eng:
The Contact Mechanics (CM) problem can be considered a complementarity problem. If assuming linearly elasticity of the contacting bodies, the discretised system of equations as a Linear Complementarity Problem (LCP). The contact mechanics model is first formulated in continuous form by posing a complementarity relation between the gap of the deformed surfaces and the contact pressure. The LCP is then obtained after a linearisation and discretisation of the equations. An advantage of posing the CM problem as a strict LCP formulation, is that this allows for the application of well-established numerical solution techniques, such as Lemke’s pivoting algorithm. In addition, Lemke’s pivoting algorithm has the advantage that it finds the numerically exact solution, within a finite number of iterations. This type of LCP based contact mechanics approach is applied here to solve the Hertzian line contact problem, with and without the addition of surface roughness, to demonstrate it’s applicability.

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