Wagner model - Alchetron, The Free Social Encyclopedia

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:

σ ( t ) = − p I + ∫ − ∞ t M ( t − t ′ ) h ( I 1 , I 2 ) B ( t ′ ) d t ′

where:

σ ( t ) is the Cauchy stress tensor as function of time t,

p is the pressure

I is the unity tensor

M is the memory function showing, usually expressed as a sum of exponential terms for each mode of relaxation:

M ( x ) = ∑ k = 1 m g i θ i exp ⁡ ( − x θ i ) , where for each mode of the relaxation, g i is the relaxation modulus and θ i is the relaxation time;

h ( I 1 , I 2 ) is the strain damping function that depends upon the first and second invariants of Finger tensor B .

The strain damping function is usually written as:

h ( I 1 , I 2 ) = m ∗ exp ⁡ ( − n 1 I 1 − 3 ) + ( 1 − m ∗ ) exp ⁡ ( − n 2 I 2 − 3 ) ,

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.

References

Wagner model Wikipedia

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