Partitioned formulation of frictional contact problems using localized Lagrange multipliers

Abstract

Interface treatment methods for the contact problem between non-matching meshes have traditionally been based on a direct coupling of the contacting solids employing a master–slave strategy or classical Lagrange multipliers. These methods tend to generate strongly coupled systems that is dependent on the discretization characteristics on each side of the contact zone. In this work a displacement frame is intercalated between the interface meshes. The frame is then discretized so that the discrete frame nodes are connected to the contacting substructures using the localized Lagrange multipliers collocated at the interface nodes. The resulting methodology alleviates the need for master–slave book-keeping and provides a partitioned formulation which preserves software modularity, facilitates non-matching mesh treatment and passes the contact patch test. Frictional contact problems are used to demonstrate the salient features of the proposed method.

Full Document