Hybrid analytical and extended finite element method (HAX-FEM): A new enrichment procedure for cracked solids

Abstract : A new numerical method is proposed to estimate directly stress intensity factors at the tip of a crack in an elastic body. In the same spirit as for the extended finite element method, the approximation of the displacement field is enriched in the vicinity of the crack tip. Yet the method proposed herein differs by the way the enrichment is introduced. Instead of using partition of unity concepts, a two-description formulation is implemented. The first one uses standard finite elements while the second one, in the vicinity of the crack tip, resorts to a few purely analytical expressions. These two descriptions are then coupled by partitioning the energy with an overlapping zone. The performance of this new enrichment technique is illustrated and compared with existing techniques by means of two examples.
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Julien Réthoré, Stéphane Roux, François Hild. Hybrid analytical and extended finite element method (HAX-FEM): A new enrichment procedure for cracked solids. International Journal for Numerical Methods in Engineering, Wiley, 2010, 81, pp.269-285. ⟨10.1002/nme.2691⟩. ⟨hal-00430488⟩

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