The eXtended Finite Element Method is a partition of unity based method, particularly suitable for modelling crack propagation phenomena, without knowing a priori the crack path. Its numerical implementation is mostly achieved with stand-alone codes. The implementation of the eXtended Finite Element Method in commercial FEA softwares is still limited, and the most famous one including such capabilities is Abaqus TM.
However, due to its relatively recent introduction, XFEM technique in Abaqus has been proved to provide trustable results only in few simple benchmark problems involving linear elastic material models.In this work, we present an assessment of the applicability of the eXtendend Finite Element Method in Abaqus, to deal with fracture mechanics problems of rubber-like materials. Results are provided for both Neo-Hookean and Arruda-Boyce material models, under plane strain conditions.
In the rst part of this work, a static analysis for the pure Mode-I and for a 45o mixed-Mode load condition, whose objective has been to evaluate the ability of the XFEM technique in Abaqus, to correctly model the stress and displacement fields around a crack tip, has been performed. Outcomes from XFEM analysis with coarse meshes have been compared with the analogous ones obtained with highly refined standard FEM discretizations. Noteworthy, despite the remarkable level of accuracy in analyzing the displacement eld at the crack tip, concerning the stress eld, the adoption of the XFEM provides no benefits, if compared to the standard FEM formulation. The only remarkable advantage is the possibility to discretize the model without the mesh con-forming the crack geometry.
Furthermore, the dynamic process of crack propagation has been analyzed by means of the XFEM. A 45o mixed-Mode and a 30o mixed-Mode load condition are analyzed. In particular, three fundamental aspects of the crack propagation phenomenon have been investigated, i.e. the instant at which a pre-existing crack starts to propagate within the body under the applied boundary conditions, the crack propagation direction and the predicted crack propagation speeds. According to the obtained results, the most inuent parameters are thought to be the elements size at the crack tip hand the applied displacement ratev. Severe diffculties have been faced to attain convergence. Some reasonable motivations of the unsatisfactory convergence behaviour are proposed.
Author: Gigliotti, Luigi