The Influence of Equivalent Contact Area Computation in 3D Extended Node to Surface Contact Elements

This paper extends the frictionless penalty-based node to contact formulation with area regularization to a 3D framework. Based on our previous work [1] focused on axisymmetric modeling, two computational methods are also considered for the determination of the slave node area. The first method, named as the geometrical approach, is based on a force equivalence system, while the second one, named as the consistent approach, is derived from a more sophisticated scheme elaborated upon the virtual work principle. Then, the extended contact elements are derived for the contact formulations with geometrical and consistent area regularization and a consistent linearization is provided accordingly, which guarantees a quadratic rate of convergence of the global Newton Raphson iterative procedure. Finally, two numerical examples assess the performance of both contact formulations with area regularization and demonstrates the robustness and the efficiency of the node to surface contact formulation with consistent area regularization in reproducing a constant contact pressure distribution across the interface between a deformable body and a analytically-defined rigid body, irrespective of
the mesh. Our findings will certainly encourage further developments towards the design of a penalty based node to surface contact algorithm passing the contact patch test, as was already done successfully in 2D contact problems [2].