Wagner model
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Wagner model is a rheological model developed for the prediction of the viscoelastic properties of polymers. It might be considered as a simplified practical form of the Bernstein-Kearsley-Zapas model. The model was developed by German rheologist Manfred Wagner.
For the isothermal conditions the model can be written as:
where:
- mathbfσ(t) is the stress tensor as function of time t,
- p is the pressure
- \mathbf{I} is the unitity tensor
- M is the memory function showing, usually expressed as a sum of exponential terms for each mode of relaxation:
-
, where for each mode of the relaxation, gi is the relaxation modulus and θi is the relaxation time;
- h(I1,I2) is the strain damping function that depends upon the first and second invariants of Finger tensor
.
The strain damping function is usually written as:
,
The strain hardening function equal to one, then the deformation is small and approaching zero, then the deformations are large.
The Wagner equation can be used in the non-isothermal cases by applying time-temperature shift factor.
[edit] References
- M.H. Wagner Rheologica Acta, v.15, 136 (1976)
- M.H. Wagner Rheologica Acta, v.16, 43, (1977)
- B. Fan, D. Kazmer, W. Bushko, Polymer Engineering and Science, v44, N4 (2004)
