How to Make the Stress Relaxation Experiment for Polymers More Informative

Area of Science:

• Polymer Science
• Materials Science
• Rheology

Background:

• Polymer mechanical properties are described by viscoelastic models like the Maxwell and Kohlrausch-Williams-Watts models.
• Accurate identification of these models from experimental data is crucial but challenging due to data dependency and noise.

Purpose of the Study:

• To develop a method for identifying polymer relaxation modulus models that is independent of sampling instants.
• To ensure the stability and accuracy of model identification from noise-corrupted rheological data.

Main Methods:

• Weighted least-squares approximation for relaxation modulus.
• Application of Tikhonov regularization to address ill-posed identification problems.
• Stochastic convergence analysis and numerical studies with randomized sampling instants.

Main Results:

• An identification algorithm was developed that yields approximate optimal model parameters.
• The method demonstrated strong consistency and exponential convergence rates for noise-corrupted data.
• Numerical studies confirmed the recovery of asymptotically time-instant-independent models.

Conclusions:

• The proposed identification method, incorporating randomization and regularization, accurately determines polymer viscoelastic models.
• This approach offers robustness against measurement noise and independence from sampling strategies.
• It advances the reliable characterization of polymer mechanical behavior.