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Meshless Numerical Simulation of Singular Fields at Crack Tips of Branched Crack

One of the most important tasks in the numerical analysis of the fracture problem is to achieve a high-precision approximation of the singular stress fields at crack tips. Partially or fully enriched basis functions are often used as enhancements on the whole problem domain or just near the crack tips when constructing the meshless shape functions to simulate the singularity fields at crack tips, namely: global enhancement with fully enriched basis, global enhancement with partially enriched basis, local enhancement with fully enriched basis and local enhancement with partially enriched basis. The scheme of the enriched basis has been extensively and successfully employed in handling problems with a single crack, but its applicability in the branched crack problem remains to be studied. In this paper, the stress intensity factors, the displacement field and the stress field near crack tip are calculated by these four schemes, respectively, and the singular field at the crack tip of a branching crack is also considered. The numerical results show that: for the problems with a single crack, the accuracy of the stress intensity factor obtained by the meshless method with different kinds of enriched basis is basically the same, but the accuracy of the crack tip field variables is obviously different; for the problems with branched crack, the accuracy of the stress intensity factors differs depending on the problems.

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