Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 160

shows elastic or viscous behaviour when the stress is below the yield level depending on
the time scale (see Sect. 5.1 ).
The original plastic drift ice rheology was the elastic-plastic model developed in the
AIDJEX (Arctic Ice Dynamics Joint Experiment) -programme for Arctic sea ice (Coon
et al. 1974; Pritchard 1975). A few years later, Hibler (1979) introduced a viscous-plastic
rheology, which is more feasible for long-term sea ice simulations. These rheologies have
served the basis of later plastic models, where the main concern has been the shape of the
yield curve. Because of computational reasons, ideal plastic models have not been used
but the stress inside yield curve has been taken either as a linear elastic (Coon et al. 1974)
or linear viscous law (Hibler 1979).
The strength of the ice is taken as a function of thickness and compactness as

P ¼ P n h n exp

½ C 1 A ð Þ ð 5 : 36 Þ

where P n and n are the compressive strength parameters, and C is the strength reduction
for lead opening. In the original version n was equal to one, but in general we can allow
the power to vary between ½ and 2 (see Sect. 5.2.1 ). Physically C − 1 is the e-folding value
of strength for changes in compactness, and, due to the high sensitivity, C

≫

1. The normal
parameter values are P n h n = 25 kPa for h = 1 m and C = 20. In a research effort of landfast
ice in the Baltic Sea, Leppäranta (2013) found n = 2 as a good representative value.
Two-dimensional plastic yielding is specified with a yield curve F( σ 1 , σ 2 ) = 0, where σ 1
and

s postulate for stable materials states that the
yield curve serves as the plastic potential, and consequently the failure strain is directed
perpendicular to the yield curve, known as the normal, or associated

σ 2 are the principal stresses. Drucker '

flow rule (e.g., Davis

and Selvadurai 2002). Consequently, we have

e k ¼ K o F
o r k

ð : Þ

5 37

where is a parameter to be obtained as a part of the solution. Drift ice is strain hardening

in compression, and therefore pressure ice formation may proceed only to a certain limit.
Inside the yield curve, F < 0 and stresses are elastic or viscous, while F > 0 would go
outside the yield curve and is not allowed. The plastic failure criterion tells when the ice
fails, and when it does, the plastic

ʛ

flow is obtained from the equation of motion.
The stability of ice cover was treated in Sect. 5.2.1 . Then, once the ice cover has
become broken into a system of

floes, it does not resist tensile stresses, and the yield curve
must be located in the quadrant where

σ 2 < 0. Different shapes have been used
(Fig. 5.12 ). In the elastic-plastic model, a diamond, triangle (Coulomb) and a teardrop
shape yield curves have been employed. The Hibler viscous-plastic model has an elliptic
yield curve, which has good computational properties.

σ 1 ,