| Summary: | Conventional element-based methods for crack modelling suffer from remeshing and mesh distortion, while the cracking particle method is meshless and requires only nodal data to discretise the problem domain so these issues are addressed. This method uses a set of crack segments to model crack paths, and crack discontinuities are obtained using the visibility criterion. It has simple implementation and is suitable for complex crack problems, but suffers from spurious cracking results and requires a large number of particles to maintain good accuracy. In this thesis, a modified cracking particle method has been developed for modelling fracture problems in 2D and 3D. To improve crack description quality, the orientations of crack segments are modified to record angular changes of crack paths, e.g. in 2D, bilinear segments replacing straight segments in the original method and in 3D, nonplanar triangular facets instead of planar circular segments, so continuous crack paths are obtained. An adaptivity approach is introduced to optimise the particle distribution, which is refined to capture high stress gradients around the crack tip and is coarsened when the crack propagates away to improve the efficiency. Based on the modified method, a multi-cracked particle method is proposed for problems with branched cracks or multiple cracks, where crack discontinuities at crack intersections are modelled by multi-split particles rather than complex enrichment functions. Different crack propagation criteria are discussed and a configurational-force-driven cracking particle method has been developed, where the crack propagating angle is directly given by the configuration force, and no decomposition of displacement and stress fields for mixed-mode fracture is required. The modified method has been applied to thermo-elastic crack problems, where the adaptivity approach is employed to capture the temperature gradients around the crack tip without using enrichment functions. Several numerical examples are used to validate the proposed methodology.
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