Teardrop and Parabolic Lens Yield Curves for Viscous-Plastic Sea Ice Models: New Constitutive Equations and Failure Angles

Abstract

Most viscous-plastic sea ice models use the elliptical yield curve. This yield curve has a fundamental flaw: it excludes acute angles between deformation features at high resolution. Conceptually, the teardrop (TD) and parabolic lens (PL) yield curves offer an attractive alternative. These yield curves feature a non-symmetrical shape, a Coulombic behavior for the low-medium compressive stress, and a continuous transition to the ridging-dominant mode, but their published formulation leads to negative or zero bulk and shear viscosities and, consequently, poor numerical convergence with stress states at times outside the yield curve. These issues are a consequence of the original assumption that the constitutive equations of the commonly used elliptical yield curve are also applicable to non-symmetrical yield curves and yield curves with tensile strength. We derive a corrected formulation for the constitutive relations of the TD and PL yield curves. Results from simple uni-axial loading experiments show that with the new formulation the numerical convergence of the solver improves and much smaller nonlinear residuals after a smaller number of total solver iterations can be reached, resulting in significant improvements in numerical efficiency and representation of the stress and deformation fields. The TD and PL yield curves lead to smaller angles of failure that better agree with observations. They are promising candidates to replace the elliptical yield curve in high-resolution pan-Arctic sea ice simulations.