A generalized stress correction scheme for the Maxwell elasto-brittle rheology: impact on the fracture angles and deformations

Abstract

The Maxwell elasto-brittle (MEB) rheology uses a damage parameterization to represent the brittle fracture of sea ice without involving plastic laws to constrain the sea ice deformations. The conventional MEB damage parameterization is based on a correction of super-critical stresses that binds the simulated stress to the yield criterion but leads to a growth of errors in the stress field. A generalized damage parameterization is developed to reduce this error growth and to investigate the influence of the super-critical stress correction scheme on the simulated sea ice fractures, deformations and orientation of linear kinematic features (LKFs). A decohesive stress tensor is used to correct the super-critical stresses towards different points on the yield curve. The sensitivity of the simulated sea ice fractures and deformations to the decohesive stress tensor is investigated in uniaxial compression experiments. Results show that the decohesive stress tensor influences the growth of residual errors associated with the correction of super-critical stresses, the orientation of the lines of fracture and the short-term deformation associated with the damage, but it does not influence the long-term post-fracture sea ice deformations. We show that when ice fractures, divergence first occurs while the elastic response is dominant, and convergence develops post-fracture in the long term when the viscous response dominates – contrary to laboratory experiments of granular flow and satellite imagery in the Arctic. The post-fracture deformations are shown to be dissociated from the fracture process itself, an important difference with classical viscous plastic (VP) models in which large deformations are governed by associative plastic laws. Using the generalized damage parameterization together with a stress correction path normal to the yield curve reduces the growth of errors sufficiently for the production of longer-term simulations, with the added benefit of bringing the simulated LKF intersection half-angles closer to observations (from 40–50 to 35–45∘, compared to 15–25∘ in observations).