A spline-based enrichment function for arbitrary inclusions in extended finite element method with applications to finite deformations

2013 ◽  
Vol 95 (5) ◽  
pp. 361-386 ◽  
Author(s):  
Brett A. Benowitz ◽  
Haim Waisman
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Finite Deformations ◽  
Extended Finite Element ◽  
Enrichment Function ◽  
Element Method

scholarly journals Research on Extended Finite Element Method for Axisymmetric Electrostatic Field Based on Liquid Nitrogen with Bubbles

2021 ◽  
Vol 11 (11) ◽  
pp. 5214
Author(s):  
Nana Duan ◽  
Shaocong Lu ◽  
Xinyu Ma ◽  
Weijie Xu ◽  
Fuquan Jin ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Liquid Nitrogen ◽  
Electrostatic Field ◽  
Extended Finite Element Method ◽  
Shape Function ◽  
Computational Accuracy ◽  
Extended Finite Element ◽  
Enrichment Function ◽  
Element Method

In this paper, the extended finite element method (XFEM) is first applied to account for the weak discontinuity of the axisymmetric electrostatic field. Firstly, the interface between two materials in an element is described by the level set method. The enrichment function is used to modify the shape function of enrichment elements. Secondly, to illustrate the feature of the enrichment function, the distribution diagrams of enrichment functions in sub-elements are drawn. The 3D field can be simplified to an axisymmetric field, which can reduce the difficulty of calculation. Finally, models with bubbles in liquid nitrogen in the axisymmetric field are used to prove the reliability of XFEM. Compared with the conventional finite element method (CFEM), XFEM costs lower computing resources with almost the same computational accuracy.

scholarly journals A mesh-independent framework for crack tracking in elastodamaging materials through the regularized extended finite element method

2021 ◽  
Author(s):  
Elena Benvenuti ◽  
Nicola Orlando
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Damage Evolution ◽  
Extended Finite Element Method ◽  
Mesh Adaptivity ◽  
Extended Finite Element ◽  
Evolution Law ◽  
Crack Paths ◽  
Original Crack ◽  
Element Method

AbstractWe propose a formulation for tracking general crack paths in elastodamaging materials without mesh adaptivity and broadening of the damage band. The idea is to treat in a unified way both the damaging process and the development of displacement discontinuities by means of the regularized finite element method. With respect to previous authors’ contributions, a novel damage evolution law and an original crack tracking framework are proposed. We face the issue of mesh objectivity through several two-dimensional tests, obtaining smooth crack paths and reliable structural results.

scholarly journals An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 507
Author(s):  
K. Yakoubi ◽  
S. Montassir ◽  
Hassane Moustabchir ◽  
A. Elkhalfi ◽  
Catalin Iulian Pruncu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Internal Pressure ◽  
Extended Finite Element Method ◽  
Research Study ◽  
Extended Finite Element ◽  
T Stress ◽  
Cracked Structures ◽  
Element Method

The work investigates the importance of the K-T approach in the modelling of pressure cracked structures. T-stress is the constant in the second term of the Williams expression; it is often negligible, but recent literature has shown that there are cases where T-stress plays the role of opening the crack, also T-stress improves elastic modeling at the point of crack. In this research study, the most important effects of the T-stress are collected and analyzed. A numerical analysis was carried out by the extended finite element method (X-FEM) to analyze T-stress in an arc with external notch under internal pressure. The different stress method (SDM) is employed to calculate T-stress. Moreover, the influence of the geometry of the notch on the biaxiality is also examined. The biaxiality gave us a view on the initiation of the crack. The results are extended with a comparison to previous literature to validate the promising investigations.

Application of Extended Finite Element Method (XFEM) to Stress Intensity Factor Calculations

2015 ◽  
Author(s):  
Do-Jun Shim ◽  
Mohammed Uddin ◽  
Sureshkumar Kalyanam ◽  
Frederick Brust ◽  
Bruce Young
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Partition Of Unity ◽  
Extended Finite Element ◽  
Element Method

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.

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