Utilising the eXtended Finite Element Method (XFEM) to model failure of thin-walled structures

The eXtended Finite Element Method (XFEM), exploring the partition of unity concept in terms of an enriched FE-space in order to represent strong (e.g. discontinuity in the field itself) and/or weak (e.g. discontinuity in the spatial derivative) discontinuities, has been extensively used in the literature ever since it was presented by Belytschko and co-workers in 1999. Interesting applications are mesh independent representation of cracks and crack propagation, holes, inclusions, evolving grain and phase boundaries etc. The current contribution will aim at giving an overview of XFEM and the developments thereof with the application to modelling of crack propagation and failure, focusing on the work performed at the Department of Applied Mechanics at Chalmers. Starting from the basics of XFEM, specifics related to robustness and efficiency, extensions of the XFEM concept and applications to industrial relevant loading conditions and materials will be discussed. Currently, the developments are made within two parallel projects on XFEM representation of crack propagation, from which numerical results will be presented. The first project focuses on ductile failure of thin and large metal structures addressing issues related both to the modelling of the ductile failure process as to robustness and computational efficiency of the structural representation. The second project is devoted to crashworthiness of structural composites with the aim of developing a shell element formulation that can simultaneously handle multiple delaminations (within one shell element) and through-thickness cracking (splitting), both being important mechanisms in the modelling of composite crushing. As a first step, a shell element formulation has been established that is able to represent multiple delaminations. The basic features of this formulation and some preliminary results will be presented