Application of XFEM to Hermite Element

概要

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The extended finite element method (XFEM) has an advantage that an arbitrary shaped crack and its extension can be treated easily. But it is also pointed out that the results of the fracture parameter have significant errors that come from the existence of 'blending elements'. In the standard formulation of XFEM, the nodes in the element including the crack tip have enriched additional degrees of freedom. The nodes in the outer region have usual degrees of freedom, i.e. 2 in the two dimensional problem. The elements in the region surrounding the crack site have nodes with enriched freedom at the crack side and normal freedom at the outer region side. These elements are called 'blending elements'. In this paper, a new Hermite element with three nodes has been formulated and applied to a crack problem with XFEM. Errors of fracture parameters calculated by the M-integral method were discussed from the point of view of the effect of the blending elements. Stress intensity factor of CCT specimen has a 10% of error with a simple formulation. It decreases down to 0.5% by considering the improvement of XFEM proposed by Shibanuma et. al.