A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method

NURBS-based isogeometric analysis is applied to 3D frictionless large deformation contact problems. The contact constraints are treated with a mortar-based approach combined with a simplified integration method avoiding seg- mentation of the contact surfaces, and the discretization of the continuum is performed with arbitrary order NURBS and Lagrange polynomial elements. The contact constraints are satisfied exactly with the augmented Lagrangian formula- tion proposed by Alart and Curnier, whereby a Newton-like solution scheme is applied to solve the saddle point prob- lem simultaneously for displacements and Lagrange mul- tipliers. The numerical examples show that the proposed contact formulation in conjunction with the NURBS dis- cretization delivers accurate and robust predictions. In both small and large deformation cases, the quality of the con- tact pressures is shown to improve significantly over that achieved with Lagrange discretizations. In large deformation and large sliding examples, the NURBS discretization pro- vides an improved smoothness of the traction history curves. In both cases, increasing the order of the discretization is either beneficial or not influential when using isogeometric analysis, whereas it affects results negatively for Lagrange discretizations.