scholarly journals Optimal convergence analysis for the extended finite element method

2011 ◽  
Vol 86 (4-5) ◽  
pp. 528-548 ◽  
Author(s):  
Serge Nicaise ◽  
Yves Renard ◽  
Elie Chahine
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Convergence Analysis ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Optimal Convergence ◽  
Optimal Convergence Analysis ◽  
Element Method

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.

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