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

Abstract

A partition-of-unity generalized node method (PUGNM) based on isolated blocks was developed to model multiple cracks. This study accommodates the extended finite element method (XFEM) and the numerical manifold method (NMM) within the same framework using the “path-connectivity” concept. In the PUGNM, (1) a cracked body is discretized by a structured square mesh; (2) the pre-assumed isolated blocks (or square elements) are partitioned into isolated sub-blocks by cracks and geometric boundaries; (3) the generalized nodes associated with each square node are defined on the isolated blocks; (4) the generalized nodes with actual independent deformations are obtained by merging all initial generalized nodes on the continuous blocks; (5) the displacement approximation based on the partition-of-unity (PU) method is constructed by a product of the standard quadrilateral finite element (FE) shape functions with the local functions associated with independently deformed generalized nodes. It was demonstrated that almost identical formulations can be derived for the classic XFEM, NMM, and PUGNM from the perspective of generalized nodes. Thus, construction of generalized nodes based on isolated blocks in the PUGNM is actually another implementation of the NMM based on the “path-connectivity” concept. The excellent numerical results show that the PUGNM can model multiple cracks.