A partition of unity formulation referring to the NMM for multiple intersecting crack analysis

A partition of unity method (PUM) is presented for multiple intersecting crack analysis. In the present PUM, the influence domain at each node is defined by a polygon composed of all the elements connected to the node. The nodal influence domain is partitioned by the material discontinuities, e.g. cracks into several sub-domains where the local displacement functions are constructed using the partition of unity (PU). The proposed PUM unifies the continuum analyses and discontinuum analyses within the same framework, which has a straightforward formulation to implement. The developed PUM is capable for modeling complex cracks such as star-shaped cracks and branched cracks. A number of numerical examples indicate the accuracy and robust of the present method.