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The modeling of large deformation fracture mechanics has been a challengingproblem regarding the accuracy of numerical methods and their ability to dealwith considerable changes in deformations of meshes where having the presenceof 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 torepresent space of the present numerical technique in advance, and then a localrefinement of structured meshes at the vicinity of the discontinuities isadditionally established. Due to differences in the size and type of elementsat the boundaries of those two regions, hanging nodes produced in the modifiedmesh are considered as normal nodes in an arbitrarily polygonal element.Conforming these special elements becomes straightforward by the flexible useof basis functions over polygonal elements. Results of this study are shownthrough several numerical examples to prove its efficiency and accuracy throughcomparison with former achievements.

An extended polygonal finite element method for large deformation fracture analysis