A Physics-Based Model Reduction Approach for Node-to-Segment Contact Problems in Linear Elasticity

Abstract: The paper presents a new reduction method designed for dynamic contact problems. Recently, we have proposed an efficient reduction scheme for the node-to-node formulation, that leads to Linear Complementarity Problems (LCP). Here, we enhance the underlying contact problem to a node-to-segment formulation. Due to the application of the dual approach, a Nonlinear Complementarity Problem (NCP) is obtained, where the node-to-segment condition is described by a quadratic inequality and is approximated by a sequence of LCPs in each time step. These steps are performed in a reduced approximation space, while the contact treatment itself can be achieved by the Craig-Bampton method, which preserves the Lagrange multipliers and the nodal displacements at the contact zone. We think, that if the contact area is small compared to the overall structure, the reduction scheme performs very efficiently, since the contact shape is entirely recovered. The performance of the resulting reduction method is assessed on two 2D computational examples