A contact smoothing method for arbitrary surface meshes using Nagata patches

• A new 3D contact surface smoothing approach for large deformation contact problems between deformable bodies is proposed.
• The local Nagata patch interpolation is used to smooth arbitrary surface meshes.
• The original curvature of the master surface is recovered using a relatively coarse mesh.
• The non-physical contact force oscillations usual in the faceted surface representation are eliminated.
• The accuracy, robustness and performance of the numerical simulations is improved adopting the surface smoothing method.

This paper presents a contact surface smoothing method combined with the node-to-segment discretization technique to solve large deformation frictional contact problems between deformable bodies. The Nagata patch interpolation is used to smooth the surface mesh, providing a master surface with quasi  -G1G1 continuity between patches. Moreover, the local support of the interpolation method allows to deal with surface meshes of arbitrary topology (regular and irregular finite element discretizations), as well as hybrid meshes. The non-physical oscillations in the contact force evolution, induced by the faceted contact surface representation, are reduced using the proposed smoothing method. Furthermore, the smooth representation of the master surface allows a more accurately evaluation of the resulting stresses and forces, while providing an important improvement in convergence behaviour. Four representative numerical examples are used to demonstrate the advantages of the proposed contact smoothing method. The results show a significant improvement in the accuracy, robustness and performance of the numerical simulations using the smoothing approach, when compared with the piecewise faceted contact surface description.