Accurate and efficient analysis of stationary and propagating crack problems by meshless methods

- Novel numerical strategies for efficient analysis of propagating cracks are proposed.
- The method can be used with enrichment techniques or nodal refinement strategies.
- A robust integration technique is used for evaluation of the domain integrals.
- The crack trajectory path can be predicted with a high accuracy and efficiency.

New numerical strategies based on meshless methods for the analysis of linear fracture mechanics problems with minimum computational labor are presented. Stationary as well as propagating cracks can be accurately modeled and analyzed by these proposed meshless techniques. For numerical analysis of the problem, meshless methods based on global weak-form are used. In order to capture the singular stress field near the crack tip, two different approaches are adopted. In the first approach, the asymptotic displacement fields are added to the basis functions of the meshless method. In the second one, a few nodes are added in the vicinity of the crack tip, while regular basis functions are used. The accuracy and stability of the two methods for determination of the stress intensity factors are then compared. In this work, an accurate integration technique, i.e., the background decomposition method (BDM), is utilized for efficient evaluation of the domain integrals of the weak-form with minimum computational cost. The superior accuracy of the proposed techniques is assessed by virtue of several benchmark problems. Through the presented numerical results it is concluded that the proposed methods are promising for the analysis of linear fracture mechanics problems.