Virtual tetrahedral gap element to connect three-dimensional non-coincident interfaces Yeo-Ul Song a , Gil-Eon Jeong b , Sung-Kie Youn b, * , K.C. Park c a Central Research Institute, Korea Hydro and Nuclear Power Co., Daejeon, 34101, Republic of Korea b Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 305-701, Republic of Korea c Department of Aerospace Engineering Sciences, University of Colorado at Boulder, CO 80309-429, USA ARTICLE INFO Keywords: Virtual tetrahedral gap elements Mortar method Tetrahedral element Non-matching interfaces Localized Lagrange multipliers ABSTRACT This study introduces a new version of a virtual tetrahedral gap element to connect partitioned structures which are independently discretized with tetrahedral elements. Tetrahedral meshes are widely used for practical en- gineering problems due to their simplicity. The proposed interface method employs the localized Lagrange multiplier method. The virtual tetrahedral gap elements are placed between the frame-slave and frame-master interfaces. The surface of the tetrahedral meshes is triangular; thus, a virtual tetrahedral gap element is devel- oped. A distinct feature of the virtual tetrahedral gap element is that it has a zero-strain condition which provides the exact interface reaction forces at the non-matched interface. The proposed tetrahedral gap element handles three-dimensional interface problems more effectively than conventional segment-to-segment methods. It also provides better accuracy. The validity and robustness of the proposed method are demonstrated by several nu- merical examples. 1. Introduction Interface schemes include domain decomposition, fluid-structure interaction, and contact and crack analyses [1–4]. These analyses generally use triangular elements in two-dimensional(2D) problems and tetrahedral elements in three-dimensional(3D) problems because it is easy to perform the analyses. The main purpose of the interface analysis is to connect structures that contain different meshes at common boundaries to ensure continuity in a consistent manner. This study con- siders mesh-tying constraints for independent tetrahedral meshes of a partitioned structure. An important step in the finite element method is to create a discretization model. When performing a 3D engineering analysis, the tetrahedral element is the preferred mesh to create a finite element model from the computer aided design(CAD) model [13–15]. In addition, tetrahedral meshes are more convenient than hexahedral meshes. Based on these properties, tetrahedral elements are used for various engineering interface problems, such as bulk-forming analysis with large deformation. Moreover, remeshing is essential for large deformation. Using the tetrahedron in the remeshing procedure makes the mesh adaptation easier. In fluid-structure interface problems, tetra- hedral elements provide a better shape representation of structures, such as blades with complex shapes. In the field of biomechanics, virtual surgery uses deformation and contact analysis of nonlinear materials based on the finite element method. The expression of the exact shape of the body part is essential for making accurate medical decisions. To this end, tetrahedral elements are actively used, and the interface analysis for tetrahedral elements is required. Substructures have different sizes of meshes; hence, the interface nodes of each substructure do not match along the shared boundaries. The mortar method, which imposes the interface constraint in a weak sense, is first introduced for the domain decomposition. The mortar method is more robust than the single pass method; thus, it is widely used in interface methods.[20,30-35] Various domain decomposition studies have been performed based on the mortar method to connect the spatial grids. Contact constraints in the variational equations can be applied in several ways. The method of Lagrange multipliers is widely used in the mortar method [5,6,10–12,27,28]. The Lagrangian multipliers act like contact forces between the substructures. The Lagrangian multipliers are approximated by shape functions and impose contact constraints on the corresponding interpolated displace- ments to optimally satisfy contact constraints. In the work of Dohrmann et al. [22,36], mesh tying problems were addressed for the 3D dissimilar interface. However, a major concern of the interface method for 3D surfaces is to accurately and efficiently integrate mortar constraints to conserve momentum and energy [16–19]. * Corresponding author. E-mail address: skyoun@kaist.ac.kr (S.-K. Youn). Contents lists available at ScienceDirect Finite Elements in Analysis and Design journal homepage: www.elsevier.com/locate/finel https://doi.org/10.1016/j.finel.2018.08.005 Received 12 May 2018; Received in revised form 19 August 2018; Accepted 27 August 2018 0168-874X/© 2018 Elsevier B.V. All rights reserved. Finite Elements in Analysis and Design 152 (2018) 18–26