Skip to main content

Full text: 29: The Operational Circulation Model of BSH (BSHcmod)

47 
In contrast to engineering plastics, for which elastoplastic models are commonly used, 
Hibler's model is viscous-plastic and treats the ice as a kind of isotropic fluid. The 
constitutive law is cast in terms of its viscosity which is made highly dependent on strain 
rate so as to incorporate plastic yield. Here a concise exposition is given since it is 
required for reference. 
Again in spherical co-ordinates, the tensor of strain rates is given by 
1 du i tan 7 
£ il “ * 
R cos q> dX R 
1 
£¡2 =—( 
1 
ôv. 1 du, tan co 
+ —+ —^u,) 
£22 
2 R cos#? dX R dcp 
1 3v ( . 
R dcp 
R 
The constitutive equations read 
<J n = %(£u + £22) + TJ (£\\~ £22) — P/2 
cr 12 = 2rj£\2 
<J22 = ¿¡(£22 + £u) + ^{.£22 — in) - P/2 
where bulk viscosity Ç and shear viscosity rj depend on strain rate. (As a typical feature 
of Hibler’s model the hydrostatic pressure P/2 is related to the compressive yield 
strength P and shear strength P/(2e).) The non-linear constitutive law is stated in terms 
of the following invariants of the strain rate tensor. 
£ I ~ ^11 + £ 22 
£ I1 ~ i( £ U~ £ 22) 2 + (2 £ n) 2 ) U2 
A = (£ 1 2 + (£ II /e) 2 ) m 
While Hibler’s model is perfectly plastic, we employ viscoplasticity for régularisation. Let 
us introduce a small non-negative parameter m and put for bulk viscosity and shear 
viscosity 
_ l + crmax(A/A 0 -1,0) P 
max(A,A 0 ) 2 
(As is easily seen, Hibler’s constitutive law is recovered as the special case m = 0.) 
The entire ice dynamics problem, or system of equations, is highly non-linear. There are 
three types of non-linearity originating from dynamics, constitutive response and 
transport, by far the stiffest of which is attributable to plasticity.
	        
Waiting...

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.