A virtual interface-coupled extended finite element method for three-dimensional contact problems

In this article, we propose a virtual interface-coupled technique to model the arbitrary discontinuous interface based on the three-field dual mortar method. The computational domain is divided into several subdomains and the enriched nodes are individually introduced to construct the approximation of the displacement field. This method provides a flexible way to describe the multiple-body contact with nonconforming mesh in the extended finite element method (XFEM). An independent virtual interface is employed to replace the XFEM discontinuous interface. The connect condition between the virtual interface and discontinuous interface is imposed using the dual Lagrange multiplier method. Due to the bi-orthogonality condition, the Lagrange multipliers can be locally eliminated at a very low computational cost. The resulting system matrix is symmetric positive definite and well-conditioned. Furthermore, the contact and natural boundary conditions can be directly imposed on the virtual interface. Several numerical experiments are performed and the results show that the proposed method provides an effective, robust, and fast way to simulate three-dimensional contact behaviors of nonconforming interfaces.

Automated summary

In this article, a virtual interface-coupled technique is proposed for modeling three-dimensional contact behaviors of nonconforming interfaces. The method constructs an approximation of the displacement field by introducing enriched nodes and imposes the connection between virtual interface and discontinuous interface using the dual Lagrange multiplier method. The proposed method provides an effective, robust, and fast way to simulate arbitrary discontinuous interfaces in XFEM.