Curve-Fitting the Linear Viscoelastic Model Parameters for Three Modes

Add two more viscoelastic modes and enter the parameters for them. This improves the fit with experimental data, at a computational cost for the added modes.

In general, to find initial values for the relaxation time in multi-mode cases, take the mode specified in the previous section as the main mode, then specify relaxation time values one decade above and below for the other two modes. For initial value for the polymer viscosity, use the same value as before for all three modes.

To curve-fit the linear model parameters for three modes:

  1. Select the Continua > Extended PomPom > Models > Viscoelastic model node and set Number of Modes to 3.
  2. Right-click the Material Calibration node and select Fitting Tool....
  3. Enter Viscosity and Lambda values for viscoelastic Modes 1, 2 and 3. For Viscosity, use the same values as for Mode 1 in the previous section. For Lambda, set Mode 2 one decade below Mode 1 and Mode 3 one decade above Mode 1, as follows:
    Parameter Material Property Value Minimum Maximum
    Viscosity Viscoelastic mode 1 16 Pa-s 1.6 Pa-s 160 Pa-s
    Lambda Viscoelastic mode 1 0.00025 s 0.000025 s 0.0025 s
    Viscosity Viscoelastic mode 2 16 Pas 1.6 Pas 160 Pas
    Lambda Viscoelastic mode 2 0.000025 s 0.0000025 s 0.00025 s
    Viscosity Viscoelastic mode 3 16 Pas 1.6 Pas 160 Pas
    Lambda Viscoelastic mode 3 0.0025 s 0.00025 s 0.025 s
  4. Start the multi-mode curve-fitting with polymer viscosity. Activate curve-fitting for viscosity, one mode at a time, starting from the smallest relaxation time. This leads to the order 2, 1, 3. As you add modes and recalculate results, note how the results come closer each cycle to the input data.
    Parameter Material Property Action
    Viscosity Viscoelastic mode 2 Click Active, then click Execute Fit.

    Note the result curves, then click Clear Results.

    Viscosity Viscoelastic mode 1 Click Active, then click Execute Fit.

    Note the result curves, then click Clear Results.

    Viscosity Viscoelastic mode 3 Click Active, then click Execute Fit.

    Note the result curves, then click Clear Results.

  5. While Viscosity remains Active, activate curve-fitting for λ , one mode at a time, in the order 2, 1, 3. Note the results continue to approximate the input data.
    Parameter Material Property Action
    Lambda Viscoelastic mode 2 Click Active, then click Execute Fit.

    Note the result curves, then click Clear Results.

    Lambda Viscoelastic mode 1 Click Active, then click Execute Fit.

    Note the result curves, then click Clear Results.

    Lambda Viscoelastic mode 3 Click Active, then click Execute Fit.

    Note the result curves, then click Clear Results.

    End result:


  6. Click Close.
  7. Save the simulation.