Index

White-Metzner model

Ver: 1
 

DESCRIPTION

For the White-Metzner model, the extra-stress tensor T can be written as
  T = T1 + T2   where T1 and T2 are tensors which obey the following constitutive equations :   T1 + trelax * T1up = 2 * visc1 * D
T2 = 2 * visc2 * D   Here, D is the symmetric part of the velocity gradient tensor, trelax is the relaxation time, visc1 and visc2 are
partial shear viscosities, and the subscript "up" denotes the upper-convected derivative operator.
  visc1 = (1-ratio)*visc
visc2 = ratio*visc


The parameter ratio of the Newtonian viscosity to the total shear viscosity is defined by:
 

ratio = visc2 / ( visc1 + visc2 )   For this model, the parameters trelax and visc can depend upon the second invariant of the rate of deformation tensor D.
See "Viscosity function" and "Relaxation time function" for more details.

The default values of trelax and visc are both unity; the default valueof ratio is zero.

Selecting an option allows the user to modify the corresponding material parameter.

  OPTIONS
 
 -1
   Upper level menu
  1
   Modify the viscosity function
  2
   Modify the relaxation time function
  3
   Modify the ratio
NOTES A large relaxation time leads to strong non-linearities. A strong dependence of the parameter visc or trelax
upon the second invariant of the rate of deformation tensor can lead to similar difficulties.

The use of a non-linear strategy is recommanded for increasing this parameter: the current task should, therefore,
be of the pseudo-evolution type.

The user should be aware of the system of units, if dimensional values are used.

The units for trelax, visc and ratio, as well as for T and D are :

  
parameter
mass
length
time
temperature
trelax
-
-
 1
 -
visc
1
-1
-1
 -
ratio
-
-
-
 -
T
1
-1
-2
 -
D
-
-
-1
 -
SEE ALSO