Isogeometric analysis (IGA) offers significant improvement in geometric accuracy over finite element analysis (FEA) by utilizing non-uniform rational B-spline (NURBS) basis functions, which allow a precise representation of complex geometries. Within the IGA framework, the robustness and efficiency of contact formulations can be further improved by refining contact surfaces using higher-order NURBS functions. This paper presents a contact surface enrichment strategy based on a varying-order NURBS discretization for three-dimensional (3D) frictional large deformation contact problems. The strategy enhances contact surface resolution, keeping the overall computational cost low by avoiding unnecessary refinement in non-contact regions. It also achieves better accuracy and efficiency in capturing complex contact behavior, making it a promising framework for solving general 3D frictional large deformation contact problems. A detailed algorithm is provided to facilitate user implementation. A comprehensive set of numerical examples is also presented to show the effectiveness of the strategy.
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