Partition-of-unity generalized node method based on isolated blocks for simulating multiple cracks

•A partition-of-unity generalized node method (PUGNM) is developed for simulating multiple cracks.•The PUGNM is a new implementation of the “path-connectivity” concept in NMM.•The PUGNM unifies the NMM and XFEM within a same framework.•The PUGNM has the advantages of strong robustness and convenient numerical implementation.