Representative contact element size determination for micromechanical contact analysis of self-affine topographies. (1st December 2020) - Couto Carneiro, A.M.; Pinto Carvalho, R.; Andrade Pires, F.M.
Abstract: A generic and straightforward numerical strategy for the determination of the size of Representative Contact Elements (RCEs), which are employed in finite element contact homogenization procedures, is proposed in this contribution. The approach enables the determination of the length, height and mesh discretisation of RCEs that provide a good statistical representation of the contact interface, described by a given set of topography properties. The case of Gaussian self-affine and elastic rough profiles under normal, frictionless and non-adhesive contact is analysed in detail. A collection of conditions has been derived for two-dimensional problems, based on a trade-off between the convergence of the real contact area and the computational cost. With the increasing width of the roughness power spectrum, the restrictions imposed on the length and mesh size can be relaxed, allowing to reduce the size of numerical models. The corresponding class of problems in three-dimensions has also been studied. In this case, the influence of the numerical scheme adopted for the evaluation of the contact area has been analysed leading to the identification of two bounds, which converge for the same value with progressively finer meshes. State-of-the-art numerical results fall within the bounded region, and the application of the area correction technique proposed by Yastrebov et al . to the upper node-based bound, accelerates the convergence of the mesh and renders a good agreement with reference data.