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.

中文翻译：

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求解三维接触问题的虚拟接口耦合扩展有限元方法

在本文中，我们提出了一种基于虚拟界面耦合的技术，可以基于三场双砂浆法对任意不连续界面建模。计算域分为几个子域，并且分别引入了丰富的节点以构造位移场的近似值。此方法提供了一种灵活的方法，用于描述扩展有限元方法（XFEM）中与不合格网格的多实体接触。采用独立的虚拟接口来代替XFEM不连续接口。虚拟接口和不连续接口之间的连接条件是使用双重Lagrange乘法器方法施加的。由于双正交条件，可以以非常低的计算成本来局部消除拉格朗日乘数。由此产生的系统矩阵是对称正定的且条件良好。此外，可以将接触和自然边界条件直接施加到虚拟界面上。进行了几次数值实验，结果表明，该方法提供了一种有效，鲁棒和快速的方法来模拟不合格界面的三维接触行为。