Applying Nagata patches to smooth discretized surfaces used in 3D frictional contact problems

The accurate solution of large deformation frictional contact problems using the finite element method is still a challenging task due to the strong nonlinearities involved. This paper presents a smoothing method applicable to 3D contact surfaces discretized with an arbitrary mesh topology. The quadratic Nagata patch interpolation is adopted to define the smooth surface. The resulting contact surface passes through all nodes of the mesh while providing a smooth description, with at least G1 continuity at the nodes and quasi-G1 continuity between the patches. Thus, the proposed method avoids the non-physical oscillations in the contact force, which are induced by the traditionally used faceted contact surfaces description, when slave nodes slide over several master segments. Moreover, it allows the accurate evaluation of kinematic variables, leading to important improvements in terms of convergence rate within the Newton–Raphson iteration loop. The developed global and local contact search algorithms, designed for contact surfaces described by Nagata patches, are described in detail. Three numerical examples were selected to illustrate the advantages of the proposed smoothing method, including a complex industrial example of sheet metal forming process. The results show the significant improvements attained with the proposed approach, in terms of efficiency, robustness and accuracy, when compared with the traditional faceted contact surfaces description.