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

Abstract. The standard viscous-plastic (VP) sea ice model with an elliptical yield curve and normal flow rule does not simulate fracture angles below 30° in uni-axial compression, in stark contrast with observations of Linear Kinematic Features (LKFs) in the Arctic Ocean. In this paper, we remove the normality constraint in the standard VP model and study its impact on the fracture angle in a simple uni-axial compressive loading test. To this end, we introduce a plastic potential independent of the yield curve that defines the post-fracture deformations or flow rule. The numerical experiments show that the fracture angle strongly depends on the flow rule details. For instance, a plastic potential with an ellipse aspect ratio smaller than that of the standard ellipse gives fracture angles that are as low as 22°. A newly adapted theory – based on one developed from observations of granular material – predicts numerical simulations of the fracture angles for plastic materials with a normal or non-normal flow rule with a root-mean-square error below 1.3°. Implementing an elliptical plastic potential in the standard VP sea ice model requires only minor modifications. The modified rheology, however, takes longer to solve numerically for a fixed level of numerical convergence. In conclusion, the use of a plastic potential addresses several issues with the standard VP rheology: the fracture angle can be reduced to values within the range of satellite observations and it can be decoupled from the exact shape of the yield curve. Furthermore, a different plastic potential function will be required to change the post-fracture deformation along the fracture lines (convergence or divergence) and to make the fracture angle independent on the confining pressure (as in observations).