Modeling crack micro-branching using finite elements with embedded strong discontinuities

The emphasis of this work lies in the development of a numerical method which is capable of representing the complex physical phenomena arising in the case of crack branching in brittle materials. In particular, the formation of crack micro-branches needs to be accounted for when it comes to the prediction of the propagation pattern of crack macro-branches which will ultimately lead to the failure of the material. This is achieved by numerically modeling the failure zones within the individual finite elements based on the concept of the embedded finite element method, where all the information with regard to the geometry of the failure zone is stored locally on the element level leading to a very efficient methodology capable of discretely resolving the failure zone. The main feature of the current work is the redundancy of the branching criterion based on crack tip velocity and that both, micro- as well as macro-branches can be modeled. Whether a micro-crack develops into a macro-crack solely depends on the local state of the material as it is outlined based on the application of the proposed numerical scheme on a rectangular block with a pre-existing notch set under tension. A comparison of the oscillatory behavior of the obtained crack tip velocity every time a micro-crack develops with experimental results from the literature is provided. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)