Numerical Simulation of Crack Growth

In recent years the X-FEM based on the partition of unity method and the strong discontinuity approach (SDA) have shown to be powerful tools to model crack growth. Both methods model the crack surface by introducing additional d.o.f.. In the X-FEM the nodes in the mesh around a crack are globally enhanced with new d.o.f. while in in the SDA the new d.o.f. are commonly introduced as internal ones. Thus the jump displacement fields are constant across elements. Therefore the d.o.f. can be condensed on element level which results in jumps in the displacement field at element edges. In this contribution the strong discontinuity approach is used approximating the displacement jump linearly across the crack length similar as e.g. in 3]. New additional nodes of the cracked elements that lie on the element edges are introduced but are not considered as internal nodes but remain global. Thus crack path continuity is automatically given. These global d.o.f. approximate the discontinuous part of the displacement field. The sum of the aforementioned part and the continuous displacement field represent the total displacement field including a possible jump. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)