A consistent partly cracked XFEM element for cohesive crack growth

Abstract

SUMMARYPresent 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 non-linear 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.

The extended/generalized finite element method: An overview of the method and its applications

“…Cohesive models in the XFEM/GFEM framework have been discussed by de Borst et al [29,30]. Other interesting developments for cohesive cracks can be found in [112,11,5].…”

An embedded crack in a constant strain triangle utilizing extended finite element concepts

“…At any state of deformation we may calculate V d as a function of V c by iteratively solving (11), and stresses in the continuum as well as in the crack may be established. Also, at any state of deformation we may, analogously to (14), establish a relation between the variations given by δV d = Z δV c , keeping in mind that Z is a function of V d .…”

“…The results are compared with a reference simulation with the commercially available finite element programme DIANA. This simulation by [11] was considered to be sufficiently accurate, and it was made by applying 48 standard interface elements with a quadratic displacement interpolation along the crack path, predefined to follow the midsection of the beam. The midpoint deflection is measured as the difference between downward deformation of the midsection and the downward deformation of a point at mean height in the beam end above the support.…”

“…In recent years partly cracked elements have been formulated, the first by Zi and Belytschko [10]. Lately, formulations with additional parameters in the enrichment have been presented by Asferg et al [11] and Mougaard et al [12]. In the latest developments by Mougaard et al [12] reasonable accuracy is obtained with coarse element meshes, e.g.…”

Untitled

“…al. [20], used XFEM to create a technique for simulating crack propagation in two dimensions without remeshing the domain, while the extension to three dimensions was begun by Sukumar et al [21], where they used the two dimensional enrichment functions for planar cracks, and then extended in [22][23][24][25][26]. XFEM has demonstrated more accurate and stable solutions while the conventional finite element results were rough or highly oscillatory [27,28].…”