关键词: 多裂纹, 扩展有限元法, 广义形函数, 接触条件, 砂浆法, 增广型Lgrange乘子

Abstract: 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.

Key words: multiple cracks, extended finite element method, generalized shape functions, contact conditions, mortar method, augmented Larange multipliers