A Maxwell elasto-brittle rheology for sea ice modelling

Abstract

Abstract. A new rheological model is developed that builds on an elasto-brittle (EB) framework used for sea ice and rock mechanics, with the intent of representing both the small elastic deformations associated with fracturing processes and the larger deformations occurring along the faults/leads once the material is highly damaged and fragmented. A viscouslike relaxation term is added to the linear-elastic constitutive law together with an effective viscosity that evolves according to the local level of damage of the material, like its elastic modulus. The coupling between the level of damage and both mechanical parameters is such that within an undamaged ice cover the viscosity is infinitely large and deformations are strictly elastic, while along highly damaged zones the elastic modulus vanishes and most of the stress is dissipated through permanent deformations. A healing mechanism is also introduced, counterbalancing the effects of damaging over large timescales. In this new model, named Maxwell-EB after the Maxwell rheology, the irreversible and reversible deformations are solved for simultaneously; hence drift velocities are defined naturally. First idealized simulations without advection show that the model reproduces the main characteristics of sea ice mechanics and deformation: strain localization, anisotropy, intermittency and associated scaling laws.

Wave–ice interactions in the neXtSIM sea-ice model

“…In particular, extending the Coulomb branches into the third quadrant in principal stress space (see Fig. 2 of Dansereau et al, 2016, who instead apply tensile failure criteria σ 1 , σ 2 ≥ −σ c /q) could be seen as theoretically suspect (since there should be no friction under tension), but the observations of Weiss et al (2007;see Fig. 2) seem to support this approach. In practice, using σ N ≥ σ N,min or σ 1 , σ 2 ≥ −σ c /q was found to make little difference to large-scale simulations.…”

“…Similarly, σ N,max is set large enough that it is not reached in simulations, which is reasonable since few examples of large biaxial compressive stresses have been observed (Weiss et al, 2007). Note that Dansereau et al (2016) chose not to close the failure envelope at all for this same reason.…”

“…See space of principal stresses (Schulson et al, 2006;Dansereau et al, 2016) correspond to the lines |τ | − µσ N = τ 0 , so the material fails when the applied shear force |τ | reaches the sum of the frictional force inside the material (µσ N ) and the cohesion of the material (τ 0 ). Now (Schulson et al, 2006), where ϑ is the angle between the maximum principal stress (taken as the most compressive stress), σ 1 and the failure plane.…”

Ice bridges and ridges in the Maxwell-EB sea ice rheology

“…In this paper, these unique flow and ice coverage conditions are used as a benchmark for testing a new rheological framework developed as an alternative to the traditional viscous-plastic (VP) rheology to represent accurately the deformation and drift of sea ice in continuum models at regional (∼ 100 km) to global (∼ 1000 km) scales (Dansereau et al, 2016). This framework, called Maxwell elasto-brittle (Maxwell-EB), combines the concepts of elastic memory, viscous-like relaxation of the internal stress and progressive damage mechanics.…”

Relationships between Arctic sea ice drift and strength modelled by NEMO-LIM3.6

“…9). This shows the limitations of the parameterization from Hibler (1979) and could support the use of new sea ice rheologies, such as the elasto-brittle rheology (Girard et al, 2011;Dansereau et al, 2016).…”