多裂纹扩展的扩展有限元法分析

建立了求解多裂纹扩展的扩展有限元法。引入裂纹交叉汇合加强函数以分析多裂纹交叉汇合过程；在裂纹附近区域使用广义形函数，并引入线增函数消除混合单元，可有效地提高裂纹附近的精度；用砂浆法（线段-线段接触法）结合增广型Lagrange乘子法处理裂纹段的接触条件，可以精确地模拟裂纹面约束，并方便地求解控制方程。算例分析了两方面内容：（1）计算交叉裂纹体的应力强度因子，结果表明提出的方法精度高；（2）模拟多裂纹扩展及交叉汇合过程，模拟的裂纹扩展路径与试验结果吻合得较好，表明了方法的可靠性。

Analysis of multiple crack growth using extended finite element method

The extended finite element method of multiple crack growth is presented. The crack junction is analyzed using the junction enrichment function; the generalized nodal shape functions are used in a cluster of nodes around the cracks, a ramp function is used to avoid the blending element problem. These techniques can effectively improve the accuracy of stresses in the vicinity of crack. The mortar method (segment-to-segment contact approach) in combination with the augmented Larange method is adopted to establish the contact conditions between crack faces. Thus the contact is modeled precisely; and it is convenient to solve the control equations. Several numerical examples are analyzed as follows: (1) computing the stress intensity factors of the cross crack, the proposed method can obtain higher accuracy; (2) simulating the growth and coalescence of multiple cracks, the numerical results are good in agreement with the experiments; it shows the reliability of the present method.