A multiscale method for fracturing solids

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Many materials exhibit micro cracks, which strongly influence the propagation behavior of macro cracks and thus are vitally important for the overall load-carrying capacity of a material. Using a singlescale analysis for this class of problems is not feasible, as the incorporation of micro cracks requires a very fine discretization, which results in a high computational effort. As micro cracks only need to be accounted for in the vicinity of a macro crack front, a multiscale approach is proposed as an elegant and efficient alternative to singlescale analysis. The multiscale method is implemented in context of the three-dimensional eXtended Finite Element Method (XFEM). Special measures are taken to improve robustness and accuracy of the XFEM. A crack face contact formulation is proposed, which prevents the faces of a crack from penetrating each other and thus provides for physically meaningful results.