Non-normal flow rules affect fracture angles in sea ice viscous–plastic rheologies

• Published in: The Cryosphere
• Main Authors: D. Ringeisen, L. B. Tremblay, M. Losch
• Format: Article in Journal/Newspaper
• Language: English
• Published: Copernicus Publications 2021
• Subjects: Environmental sciences; GE1-350; Geology; QE1-996.5; Arctic; Arctic Ocean; Sea ice; The Cryosphere
• Online Access: https://doi.org/10.5194/tc-15-2873-2021; https://doaj.org/article/01363a9d2acf431b8e1c9ead619c8f68

The standard viscous–plastic (VP) sea ice model with an elliptical yield curve and a normal flow rule has at least two issues. First, it does not simulate fracture angles below 30 ∘ in uni-axial compression, in contrast with observations of linear kinematic features (LKFs) in the Arctic Ocean. Second, there is a tight, but unphysical, coupling between the fracture angle, post-fracture deformation, and the shape of the yield curve. This tight coupling was identified as the reason for the overestimation of fracture angles. In this paper, these issues are addressed by removing the normality constraint on the flow rule in the standard VP model. The new rheology is tested in numerical uni-axial loading tests. To this end, an elliptical plastic potential – which defines the post-fracture deformations, or flow rule – is introduced independently of the elliptical yield curve. As a consequence, the post-fracture deformation is decoupled from the mechanical strength properties of the ice. We adapt Roscoe's angle theory, which is based on observations of granular materials, to the context of sea ice modeling. In this framework, the fracture angles depend on both yield curve and plastic potential parameters. This new formulation predicts accurately the results of the numerical experiments with a root-mean-square error below 1.3 ∘ . The new rheology allows for angles of fracture smaller than 30 ∘ in uni-axial compression. For instance, a plastic potential with an ellipse aspect ratio smaller than 2 (i.e., the default value in the standard viscous–plastic model) can lead to fracture angles as low as 22 ∘ . Implementing an elliptical plastic potential in the standard VP sea ice model requires only small modifications to the standard VP rheology. The momentum equations with the modified rheology, however, are more difficult to solve numerically. The independent plastic potential solves the two issues with VP rheology addressed in this paper: in uni-axial loading experiments, it allows for smaller fracture angles, which fall ...