The Extended Finite Element Method for Dynamic Fractures

Abstract

A method for modelling arbitrary growth of dynamic cracks without remeshing is presented. The method is based on a local partition of unity. It is combined with level sets, so that the discontinuities can be represented entirely in terms of nodal data. This leads to a simple method with clean data structures that can easily be incorporated in general purpose software. Results for a mixed-mode dynamic fracture problem are given to demonstrate the method.

Extended meshfree methods without branch enrichment for cohesive cracks

“…Only one crack occurs that is travelling from the end of the notch. A similar result was shown in Zi et al [52], also. …”

An explicit dynamics extended finite element method. Part 1: Mass lumping for arbitrary enrichment functions

“…We consider here only the brittle propagation with an impact velocity of 20m.s −1 . As in Belytschko et al [3], Zi et al [39] and Menouillard et al [24], we model the experiment in plane strain and consider only the upper half of the plate with the appropriate symmetry boundary conditions. The material properties are those of a 18Ni1900 maraging type steel and are given in The left part of Figure 32 shows the crack path obtained with the proposed method and with an X-FEM implicit mean acceleration time integrator with a full singular enrichment basis with the same mesh (from Menouillard et al [24]).…”

A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks

“…This method has been successfully applied to static problems in two and three dimensions, (see e.g. [22,31,32,45,47]) and to dynamic problems ( [6,46]) in two dimensions.…”