A dual mortar-based contact formulation applied to finite plastic strains – Complas XI

Abstract

Significant progress has been made on computational contact mechanics over the past decade. Many of the drawbacks that were inherent to the standard node-tosegment element strategy, such as locking/over-constraint and non-physical jumps in the contact forces due to the discontinuity of the contact surface, have been systematically overcome. In particular, the formulation of the mortar finite element method [1], which has allowed the establishment of efficient segment-to-segment approaches [2, 3] when applied to the discretization of a contact surface, has promoted significant advance. However, the regularization schemes used with the mortar element (e.g. the Penalty method, the Lagrange multipliers method or combination of them) still cause unwanted side-effects such as: ill-conditioning, additional equations in the global system or a significant increase in the computational time for solution. In order to circumvent these shortcomings, Wohlmuth [4] has proposed the use of dual spaces for the Lagrange multipliers allowing the local elimination of the contact constraints. As a consequence, the Lagrangian multipliers can be conveniently condensed and no additional equations are needed for the solution of the global system of equations. H´’ueber et al. [5], Hartmann et al. [6], Popp et al.[7] and Gitterle et al [8]. have later combined this methodology with an active set strategy and obtained improved results in terms of convergence rate. Despite the successful application of the dual mortar formulation to contact problems, the advances presented in the literature have, to the authors knowledge, only been employed for the simulation of elastic problems. However, contact between bodies has a strong influence in many applications (e.g., metal forming and cutting) where finite inelastic strains play a crucial role. Therefore, the main goal of the present work is both the application and assessment of the dual mortar method in problems where contact takes place coupled with finite plastic strains.