The influence of equivalent contact area computation in extended node to surface contact elements

This article aims at extending the node to surface formulation for contact problems with
an area regularization as proposed by [1]. For that purpose, two methods are proposed to compute the equivalent contact area attributed to each slave node. The first method, which is based on a geometrical approach through force equivalence, is an original extension of the one proposed in [1] for two-dimensional contact problems, i.e. plane stress and plane strain state, to the axisymmetric modelling context. The second method relies on an energy consistent way obtained through the virtual work principle and the same expression for the equivalent contact area as the one originally cited in [2] is then recovered. First, the node to surface strategy with area regularization is introduced and the aforementioned methods for the equivalent contact area are presented in detail and compared. Afterwards a consistent linearization technique is applied to achieve a quadratic convergence rate in the Newton Raphson iterative procedure used to solve the non-linear equilibrium equations of the underlying finite element model. Finally, two axisymmetric numerical examples are provided in order to compare the aforementioned equivalent contact area evaluations and to demonstrate the performance and the robustness of the consistent approach especially in the neighbourhood the revolution axis.