A consistent partly cracked XFEM element for cohesive crack growth.

*(English)*Zbl 1194.74359Summary: Present extended finite element method (XFEM) elements for cohesive crack growth may often not be able to model equal stresses on both sides of the discontinuity when acting as a crack-tip element. The authors have developed a new partly cracked XFEM element for cohesive crack growth with extra enrichments to the cracked elements. The extra enrichments are element side local and were developed by superposition of the standard nodal shape functions for the element and standard nodal shape functions for a sub-triangle of the cracked element. With the extra enrichments, the crack-tip element becomes capable of modelling variations in the discontinuous displacement field on both sides of the crack and hence also capable of modelling the case where equal stresses are present on each side of the crack. The enrichment was implemented for the 3-node constant strain triangle (CST) and a standard algorithm was used to solve the nonlinear equations. The performance of the element is illustrated by modelling fracture mechanical benchmark tests. Investigations were carried out on the performance of the element for different crack lengths within one element. The results are compared with previously obtained XFEM results applying fully cracked XFEM elements, with computational results achieved using standard cohesive interface elements in a commercial code, and with experimental results. The suggested element performed well in the tests.

##### Keywords:

XFEM; fracture mechanics; cohesive cracks; crack propagation; discontinuity; partition of unity
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\textit{J. L. Asferg} et al., Int. J. Numer. Methods Eng. 72, No. 4, 464--485 (2007; Zbl 1194.74359)

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