Available online at www.sciencedirect.com ScienceDirect Comput. Methods Appl. Mech. Engrg. 356 (2019) 407–434 www.elsevier.com/locate/cma A hybrid finite element formulation for large-deformation contact mechanics Manish Agrawal a ,∗ , Arup Nandy b , C.S. Jog c a Department of Mechanical Engineering, Indian Institute of Technology, Ropar, India b Department of Mechanical Engineering, Indian Institute of Technology, Guwahati, India c Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India Received 15 January 2019; received in revised form 8 July 2019; accepted 8 July 2019 Available online xxxx Abstract As is well-known, displacement-based finite elements are prone to the ‘locking’ problem. Thus, employing them for solving contact mechanics problems involving thin structures and almost incompressible materials might require a significant amount of computational effort. Hybrid elements which are based on a two-field Hellinger–Reissner variational principle are known to provide an effective remedy for this locking problem associated with displacement based elements. In this work, we employ the hybrid finite element methodology along with the mortar method towards developing an efficient and robust finite element contact strategy for frictionless two dimensional and axisymmetric problems. The proposed contact formulation can effectively model the contact interaction of thin as well as thick geometries as well as contact between bodies made of almost incompressible materials. Further, for accurate estimation of the contact pressure, a new projection technique is proposed. We demonstrate the excellent coarse mesh accuracy of the proposed formulation through various examples. c ⃝ 2019 Elsevier B.V. All rights reserved. Keywords: Contact mechanics; Mortar method; Hybrid FEM; Nonlinear elasticity 1. Introduction The problem of determining the displacement and stress fields when contact occurs between two deformable bodies has a wide range of applications, ranging from traditional manufacturing processes to modern bio-mechanics problems. Some common applications are the simulation of gear power-train systems, sheet metal forming manufacturing processes, interaction between layers of composite structures and orthopedic mechanics. Thus, it is of great importance to devise a numerical strategy that is both robust and efficient for a wide range of contact mechanics applications. The contact problem is an especially challenging one due to the nonlinear geometric non-penetrability con- straint. For satisfying this geometric constraint, three types of strategies have been proposed in the literature: (1) node-to-node, (2) node-to-segment, and (3) segment-to-segment formulations. Unlike the first two methods where the geometric constraint is satisfied at certain points, in the segment-to-segment formulation, the constraint ∗ Corresponding author. E-mail address: manish.agrawal@iitrpr.ac.in (M. Agrawal). https://doi.org/10.1016/j.cma.2019.07.017 0045-7825/ c ⃝ 2019 Elsevier B.V. All rights reserved.