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

Abstract

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.

Analysis of Crack Formation and Growth in Tunnel Linings Using Double-K Fracture Criterion

“…The geometry of internal cracks is separated from the finite element mesh, so there is no need to regenerate the mesh as the crack expands. This feature makes XFEM a powerful tool for analyzing crack propagation [32][33][34][35].…”

Convergence Investigation of XFEM Enrichment Schemes for Modeling Cohesive Cracks

“…In contrast to FEM, it relaxes mesh constraints such as mesh conformance to physical discontinuities, mesh refinement around the crack tip, and burdensome adaptive remeshing whenever the crack grows. Various enrichment schemes have been specialized to apply the XFEM in modeling discontinuity problems, such as bi-material [8,9], three-dimensional crack [10,11], inclusion and void [12], microcrack [13,14], two-phase flow [15,16], and frictional contact [17,18] problems. These applications have reached a high degree of robustness and are now being incorporated into general software such as LS-DYNA and ABAQUS.…”