2019/03/09 by Hai D. Huynh, Huynh, Hai D., Phuong T. Tran +5
Engineering · Mathematics · #Basis (linear algebra) #Classification of discontinuities #Computational Engineering #Computer science #Deformation (meteorology) #Elasticity and Material Modeling #Engineering #Extended finite element method #FOS: Computer and information sciences #FOS: Mathematics #Fatigue and fracture mechanics #Finance #Finite element method #Fracture (geology) #Geology #Geometry #Mathematical analysis #Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Polygon mesh #Structural engineering #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.1903.05160
openalex publication_date 2019/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.