An extended polygonal finite element method for large deformation fracture analysis

TL;DR

This paper introduces an extended polygonal finite element method integrated with XFEM for improved large deformation fracture analysis in hyper-elastic materials like rubber, emphasizing mesh flexibility and accuracy.

Contribution

It develops a novel polygonal mesh-based XFEM approach with local refinement for large strain fracture simulation, handling mesh discontinuities effectively.

Findings

Demonstrates high accuracy in fracture simulation results.

Shows efficiency of polygonal elements in complex deformations.

Validates method through numerical examples.

Abstract

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.