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

Abstract

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).

Alternative viscous-plastic rheologies for the representation of fracture lines in high-resolution sea ice models

“…The fracture angles correspond to the Arthur angles. Contradicts our previous work (Ringeisen et al, 2020).…”

“…Experimental setup: Uni-axial compression Recent results with the same setup Ringeisen et al (2019) Ellitptical yield curve with normal flow rule (Hibler, 1979) Fracture angles depend on the yield curve slope with a normal flow rule Cannot create angles smaller than 30 • in uni-axial compression Ringeisen et al (2020) Designed a elliptical yield curve with non-normal flow rule.…”

A glacier–ocean interaction model for tsunami genesis due to iceberg calving

“…Snow is a highly porous material, which justified the use of an associative plastic flow rule and a hardening law based on the volumetric plastic strain. In contrast, the failure of ice is not associated with large changes in volume 29 . Hence, a nonassociative plastic flow rule has been developed, and a relevant formulation for the deviatoric plastic strain, α (see definition in Supplementary Note 1 and illustration in Supplementary Figure 1), is used in the hardening rule as follows:…”

“…However, the previously chosen associative flow rule was only adequate owing to the porous nature of snow, allowing for volume change (compaction hardening). Conversely, in the case of a significantly less-porous material such as ice, choosing a non-associative flow rule 29 is key owing to its natural volume-preserving qualities 30 . As such, we adopt a non-associative flow rule 31 coupled with a softening law to model the dynamic ice fracture.…”

Sea Ice Rheology Experiment (SIREx): 2. Evaluating Linear Kinematic Features in High‐Resolution Sea Ice Simulations

“…Experiments with simple geometry and uniform forcing suggest a clear connection between rheology and intersection angles (e.g., Ringeisen et al, 2019Ringeisen et al, , 2020. The SIREx simulations with realistic forcing and realistic geometry produce a large variety of stress states that eventually lead to deformation.…”