Index

Phan Thien-Tanner model

Ver: 1
 
 

DESCRIPTION

For the Phan Thien-Tanner model, the extra-stress tensor T can be written as
  T = T1 + T2


where both T1 and T2 are tensors which obey the following constitutive equations :
 

exp [ eps * trelax / visc1 * tr(T1) ] * T1 + trelax * [ (1-xi/2) * T1up + xi/2 * T1low ] = 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, eps and xi are material constants; and the subscripts "up" and "low" denote the upper- and lower-
convected derivative operators, respectively.
 

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 )


The default values of trelax and visc are both unity; the default values of eps, xi and ratio are all zero.

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

  OPTIONS
 
-1
 Upper level menu
1
 Modification of visc
2
 Modification of trelax
3
 Modification of eps
4
 Modification of xi
5
 Modification of ratio
NOTES A large relaxation time leads to strong non-linearities. The use of a non-linear strategy is recommended
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 the material parameters, as well as for T and D are :
 
Parameter
Mass
Length
Time
Temperature
    visc
1
-1
-1
-
    trelax
-
-
1
-
    eps, xi, ratio
-
-
-
-
    T
1
-1
-2
-
    D
-
-
-1
-

SEE ALSO