Comparison of Lagrange Multiplier Method Implementation for Solving Two-Dimensional Contact Problems

We consider a two-dimensional contact problem involving two deformable solids. We used the finite element method based on quadrilateral bilinear elements to approximate our elastic problem. Three implementations of the Lagrange multiplier method account for contact conditions: node-to-surface, surface-to-surface and surface-to-surface employing sub-segments. We carried out test calculations, solving the Hertz problem and comparing our results to the analytical solution. A comparative analysis of these methods shows that the two surface-to-surface contact implementations are more accurate than the node-to-surface implementation. The surface-to-surface contact method that employs sub-segments makes it possible to smooth out stress field fluctuations, but this effect only works for a limited number of problems

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