中文摘要：

建立了三维流形元的点-面接触模型，给出了嵌入准则并应用罚方法强迫接触界面满足不嵌入和无拉伸条件约束求解，详细推导了法向弹簧、切向弹簧和摩擦力子矩阵并给出了接触状态（张开、滑动和固定）的模式变化准则，算例表明该模型的有效性。

英文摘要：

A point-to-face contact model for three-dimensional numerical manifold method is established in this paper. Contact submatrices, including those for the normal spring, shear spring and the frictional forces, are derived by the penalty function method. Also given are the open-close iteration criteria and operations performed for different changes in contact state. An example of the analysis of underground opening stability is provided to demonstrate the capability of the contact model.