The Partition of Unity Finite Element Method for the simulation of waves in air and poroelastic media

2014 ◽  
Vol 135 (2) ◽  
pp. 724-733 ◽  
Author(s):  
Jean-Daniel Chazot ◽  
Emmanuel Perrey-Debain ◽  
Benoit Nennig
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Partition Of Unity ◽  
Poroelastic Media ◽  
Element Method

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.

Assessment of a Method to Model 2D Discontinuities with Enriched Finite Elements and Level Sets

2016 ◽  
Vol 846 ◽  
pp. 391-396
Author(s):  
Patrick Schmidt ◽  
D.M. Pedroso ◽  
Hans Mühlhaus ◽  
Alexander Scheuermann
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Level Set ◽  
Partition Of Unity ◽  
Extended Finite Element ◽  
Material Interfaces ◽  
Discontinuous Elements ◽  
Element Enrichment ◽  
Enriched Finite Elements ◽  
Element Method

The computational treatment of discontinuities within the framework of the finite element method (FEM) is a requirement for simulations of fracturing of solids and has become a challenging topic in computational mechanics. Particularly popular amongst the advanced schemes is the extended finite element method (XFEM) which is based on enrichment of shape functions and falls within the framework of the partition of unity method. Because there is no simple way to track the interface of discontinuities, the computer implementation of the XFEM is not as straightforward as the FEM. One method to solve the interface tracking problem is the level set method (LSM) which introduces another partial differential equation. The level set equation describes the change of an interface due to a known velocity field. To obtain its solution, the FEM can also be employed. This contribution investigates the XFEM-LSM technique with element enrichment and the integration of discontinuous elements for the modelling of cracks or material interfaces. Numerical experiments illustrate the capabilities and accuracy of the resulting formulation.

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