1. Teardrop and Parabolic Lens Yield Curves for Viscous‐Plastic Sea Ice Models: New Constitutive Equations and Failure Angles.
- Author
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Ringeisen, Damien, Losch, Martin, and Tremblay, L. Bruno
- Subjects
YIELD curve (Finance) ,SEA ice ,ANGLES ,STRAINS & stresses (Mechanics) ,BULK viscosity ,DEFORMATIONS (Mechanics) ,PLASTICS ,MATERIAL point method - 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. Plain Language Summary: Sea ice is a complicated dynamical system. It consists of many individual floes that interact in many ways. A sea‐ice model must contain many simplifying assumptions, sacrificing some observed properties. It is common to treat sea ice as an unusual fluid that behaves like an ideal plastic material and deforms permanently under high external loading (e.g., strong winds). The law that describes how the material yields to high loading contains a yield curve. This curve is usually an ellipse, a mathematically simple and acceptable approximation to the real yield curve. However, this yield curve cannot reproduce the orientation of conjugate failure lines when sea ice breaks. This paper discusses alternative yield curve shapes, the teardrop and parabolic lens yield curves, to reflect the sea ice's granular nature more accurately. We present improved constitutive equations that solve three issues in the original formulation that led to poor numerical and nonphysical behavior. Simple numerical experiments show that the improved formulation leads to a reduction of the computing time and large improvements in the representation of stresses and deformation within the sea‐ice model. The new formulation creates pairs of failure lines with smaller and more realistic angles than with the elliptical yield curve. Key Points: The constitutive equation of the elliptical yield curve is not applicable to yield curves such as the teardrop (TD) or parabolic lens (PL)We present new constitutive equations for the TD and PL that solve this problem and improve numerical convergenceThe TD and PL yield curves lead to failure angles that better agree with observations [ABSTRACT FROM AUTHOR]
- Published
- 2023
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