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

摘要

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 segmentation 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 formulation proposed by Alart and Curnier, whereby a Newton-like solution scheme is applied to solve the saddle point problem simultaneously for displacements and Lagrange multipliers. The numerical examples show that the proposed contact formulation in conjunction with the NURBS discretization delivers accurate and robust predictions. In both small and large deformation cases, the quality of the contact pressures is shown to improve significantly over that achieved with Lagrange discretizations. In large deformation and large sliding examples, the NURBS discretization provides 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.