Abstract：In computational fracture mechanics, dealing with discontinuous displacement field cross the cracks and the approximation of the singular stress fields around the crack tips are two never-ending difficulties. Especially for the case of multiple cracks, these two issues become more challenging. In this paper, a modified weight function for discontinuous field is developed for meshless method to deal with two-dimensional multi-crack problems. According to the geometric characteristics of the cracks, the local coordinate system of the modified weight function method is established. The derivation process of the formula for the modified weight function is presented. The correction strategies and schemes for different calculation points in the multi-crack calculation domain are proposed with an optimized calculation scheme. Comparing with the traditional methods used for dealing with discontinuity and singular fields in fracture problems, the modified weight function is much simpler to be implemented. Only the weight functions of nodes around each crack segment need to be modified and both the discontinuous displacement fields across multiple cracks and the singular fields at multiple crack tips can be captured simultaneously. In this paper, the element-free Galerkin method (EFGM) based on the modified discontinuous weight function is used to numerically analyze plates with Y-shaped crack, cross-shaped crack and double cracks emanating from a hole, respectively. In these numerical examples, the convergence analysis of different computing parameters is carried out in detail. The results of stress intensity factor and Von-mises stress are given and compared. Numerical results show that without introducing enriched basis function with singular terms, the modified weight function can obtain solutions of stress intensity factor with high accuracy, and can satisfactorily fit the singular fields at multiple crack tips. The meshless simulation strategy for the multi-crack problems based on the modified weight function established in this paper can be further applied to the analysis of multi-crack propagation problems.
2022, Vol. 43 
