The present study utilises the extended finite element method (XFEM) to model fibre-reinforced composites, with a focus on crack initiation and propagation. Silicon nitride-based ceramics were selected as a model material; they represent a broad class of short fibre ceramics and have received a lot of attention in recent decades. Some peculiarities when using the XFEM, including its selected modifications, are discussed in response to applied external stresses, mainly in the viscoelastic range. Promising approaches are recommended, which lead to a more accurate description of these materials under operating conditions, focusing on the correct calculation of the macroscopic stress ahead of the propagating crack front. The authors draw on years of experience with the material and investigate the possible improvements and modifications to the XFEM.

Institute of Mathematics and Descriptive Geometry Faculty of Civil Engineering Brno University of Technology 613 00 Brno Czech Republic

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