Fractal crushing of ice and brittle solids

• Published in: Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
• Format: Article in Journal/Newspaper
• Language: English
• Published: The Royal Society 1991
• Subjects: Sea ice
• Online Access: http://dx.doi.org/10.1098/rspa.1991.0060; https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1991.0060

A significant ‘scale effect’ is observed when sea ice forces on structures are measured at field scale: the force per unit contact area is not independent of area, but decreases with increasing area. Fragments of broken materials are found to have a fractal size distribution, with a fractal dimension close to 2.5 over a remarkably wide range of fragment size. The research described in this paper brings these two observations together, and shows that they can be explained by a simple model of crushing, which incorporates the relation between fragment size and splitting force predicted by linear elastic fracture mechanics. The model indicates a special role for the fractal dimension of 2.5, and predicts a relation between force and area, consistent with field observations.