Comput Mech DOI 10.1007/s00466-017-1423-2 ORIGINAL PAPER Virtual gap element approach for the treatment of non-matching interface using three-dimensional solid elements Yeo-Ul Song 1 · Sung-Kie Youn 1 · K. C. Park 2 Received: 7 March 2017 / Accepted: 8 May 2017 © Springer-Verlag Berlin Heidelberg 2017 Abstract A method for three-dimensional non-matching interface treatment with a virtual gap element is developed. When partitioned structures contain curved interfaces and have different brick meshes, the discretized models have gaps along the interfaces. As these gaps bring unexpected errors, special treatments are required to handle the gaps. In the present work, a virtual gap element is introduced to link the frame and surface domain nodes in the frame work of the mortar method. Since the surface of the hexahedron element is quadrilateral, the gap element is pyramidal. The pyramidal gap element consists of four domain nodes and one frame node. Zero-strain condition in the gap element is utilized for the interpolation of frame nodes in terms of the domain nodes. This approach is taken to satisfy the momentum and energy conservation. The present method is applicable not only to curved interfaces with gaps, but also to flat interfaces in three dimensions. Several numerical examples are given to describe the effectiveness and accuracy of the proposed method. Keywords Gap elements · Mortar method · Brick element · Non-matching interfaces · Localized Lagrange multipliers B Sung-Kie Youn skyoun@kaist.ac.kr 1 Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Republic of Korea 2 Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, CO 80309-429, USA 1 Introduction Large-scaled systems such as automobiles and aircrafts are normally partitioned into multiple subsystems for efficient parallel computation. The subsystems are independently dis- cretized for individual target accuracy [1–3]. If the mesh sizes of the divided structures are different, the meshes do not match at the shared boundary [4–8]. It is rela- tively straightforward to apply interface constraints when the shared boundary is flat. However, in practical applications many curved interfaces are involved. Non-matching inter- faces and gaps are produced along the curved interfaces when the neighboring subsystems employ low order elements and different sizes of mesh. Many studies try to deal with the dis- similar interfaces [9–11]. An interface method is required to properly handle linear and angular momentum conservation. As the single pass form of interface constraints does not pass the patch test, the mortar method is widely implemented to the interface problems in which constraints are enforced in a weak sense [12–16]. The surface-to-surface contact approach in the mor- tar method generally utilizes surface projection procedures [9, 17–19]. The constraint integral of the mortar method is evaluated in the segment that represents the overlap of the projected slave element with the connected master ele- ment. Inappropriate evaluation of the mortar integrals hinders angular momentum conservation [20, 21]. To reduce this issue, Song et al. [22] proposed a family of gap element concepts with zero strain condition based on the localized Lagrange multiplier method [22–24]. Gap elements connect the interface without surface projection. This is advanta- geous in three-dimensional cases. Also, one of the features of this method is the freedom to designate master and slave because it employs two weak forms of compatibil- ity between the frame-slave and frame-master interfaces. 123