PSI - Issue 61

Igor Gribanov et al. / Procedia Structural Integrity 61 (2024) 89–97 I.Gribanov et al. / Structural Integrity Procedia 00 (2024) 000–000

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and spreads out the fragments. The wind force is not su ffi cient to initiate new cracks, but may propagate the existing cracks, especially between the large fragments. The mesh resolution is uniform across the whole sheet, with each element corresponding to approximately 15 cm. Such resolution is about 10 times higher than what is su ffi cient to resolve the action of the waves. The simulation result is shown in Figure 10.

5. Experimental validation

The above-mentioned test cases can be compared with the Hamburg Ship Model Basin experiments (Hamburgische Schi ff bau-Versuchsanstalt, HSVA), where the uniform ice sheet breaks up under standing waves Herman et al. (2018). Qualitatively, the experimental results are similar to the simulation results in the current work. The formation of fragments was observed at HSVA by Marchenko et al. (2019). During the experiment, the ice broke up into strips and, subsequently, into small floes. The floes then rotated and became rounded. Water spilled through the cracks onto the surface of the ice, causing wave dissipation. While the current work does not model the hydrodynamic e ff ects and fragment collisions, the initial breakup stage is qualitatively similar to the experimentally observed results.

6. Discussion and conclusions

The proposed numerical model reproduces several ice fracture patterns observed in nature and during laboratory experiments. While the current results are mostly qualitative, the fracture model shows potential for the application in ice mechanics. The advantage of the proposed approach is its relative simplicity and versatility – the model ad dresses various loading scenarios without fine-tuning any parameters. Instead, a single fracture criterion is based on the established Rankine theory, with the tensile strength being a measurable mechanical property. This work proposes a fracture algorithm for uniform sheets of brittle material. Mindlin-Reissner plate theory is used to model the sheet’s elastic behavior, allowing the representation of materials with high Young’s modulus. The formulation of the normal component of traction is modified to make it a continuous function of the tentative fracture angle. The function continuity simplifies the algorithm for determining the direction of the fracture, because compu tationally inexpensive methods of root finding may be applied to such functions. The proposed fracture model was applied to several test cases relevant to ice mechanics including floe breakup by wind and waves, waterfall crossing, and mixed forces. The proposed fracture model may present interest in investigating spring breakup of ice, the formation of jams, intentional ice clearing with ice breaking vessels, and other situations. River ice usually has a uniform thickness, and fracture processes are driven by collisions between floes, obstacles, and bending due to water level variations. Ice breakup often occurs when massive floes cross waterfalls or cascades along their way. While the simulation cannot predict each floe’s exact shape and trajectory, it may provide an overall understanding of the fragments’ velocities and sizes, which may help assess potential jams’ locations. The proposed method will simulate ice action forces on bridge piers and other human-made structures if combined with a collision algorithm. Ice fracture is a complex process that is hard to model accurately. Modeling full-scale scenarios like the river ice breakup and ice-structure interaction requires high-resolution geometry, while the technical aspects of FEM limit the size of this geometry. The use of a two-dimensional mesh to represent floating ice is a compromise between the accuracy and the computational complexity, leading to a hybrid modeling technique. We demonstrated that the proposed method reproduced several natural fracture phenomena. The development of the proposed technique into a fully functional simulator of floating ice would be an exciting avenue for future work.

Acknowledgements

This project has received funding from the Natural Sciences and Engineering Research Council (NSERC) of Canada and Mitacs.ca.