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Discontinuous enrichment in finite elements with a partition of unity method
Authors:John Dolbow  Nicolas Moës  Ted Belytschko
Institution:

a Department of Civil and Environmental Engineering, Duke University, Box 90287, Durham NC 27708-0287, USA

b Mechanical Engineering, Northwestern University, USA

c Mechanical Engineering, Northwestern University, USA

Abstract:A technique is presented to model arbitrary discontinuities in the finite element framework by locally enriching a displacement-based approximation through a partition of unity method. This technique allows discontinuities to be represented independently of element boundaries. The method is applied to fracture mechanics, in which crack discontinuities are represented using both a jump function and the asymptotic near-tip fields. As specific examples, we consider cracks and crack growth in two-dimensional elasticity and Mindlin–Reissner plates. A domain form of the J-integral is also derived to extract the moment intensity factors. The accuracy and utility of the method is also discussed.
Keywords:Discontinuous enrichment  Partition-of-unity  Fracture
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