  The modeling of large deformation fracture mechanics has been a challenging
problem regarding the accuracy of numerical methods and their ability to deal
with considerable changes in deformations of meshes where having the presence
of cracks. This paper further investigates the extended finite element method
(XFEM) for the simulation of large strain fracture for hyper-elastic materials,
in particular rubber ones. A crucial idea is to use a polygonal mesh to
represent space of the present numerical technique in advance, and then a local
refinement of structured meshes at the vicinity of the discontinuities is
additionally established. Due to differences in the size and type of elements
at the boundaries of those two regions, hanging nodes produced in the modified
mesh are considered as normal nodes in an arbitrarily polygonal element.
Conforming these special elements becomes straightforward by the flexible use
of basis functions over polygonal elements. Results of this study are shown
through several numerical examples to prove its efficiency and accuracy through
comparison with former achievements.
