X-FEM in isogeometric analysis for linear fracture mechanics

The extended finite element method (X‐FEM) has proven to be an accurate, robust method for solving problems in fracture mechanics. X‐FEM has typically been used with elements using linear basis functions, although some work has been performed using quadratics. In the current work, the X‐FEM formulat...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2011-08, Vol.87 (6), p.541-565
Main Authors: De Luycker, E., Benson, D. J., Belytschko, T., Bazilevs, Y., Hsu, M. C.
Format: Article
Language:English
Subjects:
Asymptotic properties
Basis functions
Convergence
Degrees of freedom
Engineering Sciences
Exact sciences and technology
Finite element method
Fracture mechanics
Fracture mechanics (crack, fatigue, damage...)
Fundamental areas of phenomenology (including applications)
isogeometric analysis
linear fracture mechanics
Mathematical analysis
Mathematical models
Mathematics
Mechanics
Mechanics of materials
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
NURBS
Physics
Sciences and techniques of general use
Solid mechanics
Structural and continuum mechanics
X-FEM
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Summary:The extended finite element method (X‐FEM) has proven to be an accurate, robust method for solving problems in fracture mechanics. X‐FEM has typically been used with elements using linear basis functions, although some work has been performed using quadratics. In the current work, the X‐FEM formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics. In comparison with X‐FEM with conventional finite elements of equal degree, the NURBS‐based isogeometric analysis gives equal asymptotic convergence rates and equal accuracy with fewer degrees of freedom (DOF). Results for linear through quartic NURBS basis functions are presented for a multiplicity of one or a multiplicity equal the degree. Copyright © 2011 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
1097-0207
DOI:10.1002/nme.3121