A stochastic model of rough surfaces for finite element contact analysis

Abstract This paper is concerned with the development of mathematical models for the normal and tangential stiffness of rough flat surfaces. A detailed statistical analysis of a rough surface is performed in terms of peak distribution and the distribution of curvature at the peaks. A random surface model of elasto-plastically yielding asperities with a Gaussian height distribution combined with mechanical description of a single peak based on Hertz theory coupled with the Mindlin friction theory is investigated. The stochastic model is included in an incremetal finite element procedure to make the two-dimensional contact problem solution possible. The influence of the standard deviation of the height asperities on the values of both the tangential and normal stiffness at the joint interface has been found significant. It is an important factor when determining the overall behaviour of the fixed flat joint; the standard deviation of curvatures has been found to have a secondary effect only.

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