Curve-Fitting the Non-Linear Model Parameters

Now you fit the non-linear model parameters Q , 1 / ϵ , and α using the experimental uniaxial elongational viscosity versus time curve. To obtain an initial value for the relaxation time, you invert the extension rate at which the uniaxial elongational viscosity versus time curve is measured.

To curve-fit the non-linear model parameters:

  1. Right-click the Material Calibration node and select Fitting Tool....
  2. Deactivate all parameters in the Parameters list.
  3. Select the Log Graph tab on the ElongationalViscosity Table pane.
  4. Find the viscoelastic mode that has the most influence on the shape of the curve:
    1. Invert the value of the extension rate ϵ ˙ = 1000 /s. This gives a first estimate of the relaxation time λ 1 / ϵ ˙ = 0.001 s.
    2. Search for the value of Lambda that comes closest to 0.001 s. In this case, it is viscoelastic Mode 3.
    3. Activate the non-linear parameters Alpha, Q, and 1/eps for Mode 3.
    4. Enter reasonable inital, minimum, and maximum values for the non-linear parameters:
      Parameter Material Property Value Minimum Maximum
      Alpha Viscoelastic mode 3 0.01 0 0.1
      Q Viscoelastic mode 3 10 1 100
      1/eps Viscoelastic mode 3 10 1 100
    5. Click Execute Fit.


      Note that the Result 1 fitting curve coincides very closely with the elongational_velocity curve.
  5. Click Save Parameters.
  6. Click Close.
  7. Examine the values under Polymer > Material Properties > Viscoelastic mode n > Extended PomPom and note the changes from the initial values.
  8. Save the simulation.