研究了采用扩展有限元法分析接触摩擦问题的方法。该方法基于单位分解思想，在位移插值形式中引入不连续函数和裂尖渐近位移场函数分别反映接触面的不连续性和接触面端点的奇异性；根据虚功原理建立有限元支配方程，接触面不连续函数积分采用分区高斯积分的方法。扩展有限元法在分析接触问题时不需要引入接触面单元，接触面可以位于单元内任意位置。因此该方法在分析接触摩擦问题以及压剪裂纹的开裂扩展时有显著的优势。

A new method for modeling frictional contact problem by extended finite element method (XFEM) is researched. On the basis of the idea of partition of unity, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the displacement interpolation formula to account for discontinuity of the contact surface and stress singularity near the contact surface tip respectively. Governing equations are deduced by virtual work principle and the integral of the discontinuous functions are calculated by Gauss integral through sub-elements cut by discontinuous surface. Thus it is unnecessary for using contact element in contact analysis by XFEM compared with FEM, and the element can be meshed without considering the location of the contact surface. So XFEM is promising in modeling frictional contact problem and the crack growth of compression-shear mixed mode crack.