On Contact Modelling in IsoGeometric Analysis

Abstract

IsoGeometric Analysis (IGA) has proved to be a reliable numerical tool for the simulation of structural behaviour and uid mechanics. The main reasons for this popularity are essentially due to: i) the possibility of using higher order polynomials for the basis functions; ii) the high convergence rates possible to achieve; iii) the possibility to operate directly on CAD geometry without the need to resort to a mesh of elements. The major drawback of IGA is the non-interpolatory characteristic of the basis functions, which adds a di culty in handling essential boundary conditions and make it particularly challenging for contact analysis. In this work, the IGA is expanded to include frictionless contact procedures for sheet metal forming analyses. Non-Uniform Rational B-Splines (NURBS) are going to be used for the modelling of rigid tools as well as for the modelling of the deformable blank sheet. The contact methods developed are based on a two-step contact search scheme, where during the rst step a global search algorithm is used for the allocation of contact knots into potential contact faces and a second (local) contact search scheme where point inversion techniques are used for the calculation of the contact penetration gap. For completeness, elasto-plastic procedures are also included for a proper description of the entire IGA of sheet metal forming processes.