Robust and Efficient NURBS Enrichment Strategies for Large Deformation Contact Problems

Abstract

The present work develops a robust, accurate, and computationally efficient isogeometric analysis (IGA) framework for large deformation contact problems, including self-contact. Contact problems are characterized by non-smooth kinematics and strong nonlinear behavior, which make their numerical solution highly sensitive to contact surface discretization. Although IGA provides accurate geometric representation and smoother contact response, conventional refinement strategies often rely on uniform mesh discretization over the entire computational domain, which is inefficient because contact interactions usually occur only in localized regions. To address this limitation, the present work first extends the varying-order (VO) NURBS discretization technique, previously developed for three-dimensional frictionless contact, to frictional contact problems. This is achieved by increasing the interpolation order only along the contact interface, while maintaining a lower-order discretization in the bulk domain. The performance of the VO discretization is evaluated in terms of accuracy and computational efficiency under large deformation and sliding conditions. Building on this approach, the adaptive NURBS contact enrichment technique is proposed, in which surface enrichment is dynamically concentrated within active contact regions, adapting to the continuously changing contact area. This technique avoids unnecessary refinement of inactive contact regions and achieves improved accuracy at a lower computational cost compared to uniform and VO discretizations. Finally, these enrichment techniques are extended to large deformation self-contact problems. The resulting formulation enables efficient and reliable simulation of complex self-contact interactions. Overall, the developed framework provides a robust and computationally efficient approach for large deformation contact and self-contact analysis within the IGA paradigm.