Mathematical Fitting
Mathematical algorithms decompose experimental stress relaxation data into linear combinations of decaying exponential terms. Executing prony series extraction yields discrete relaxation times and modulus weights for viscoelastic constitutive equations. The mathematical model fits measured relaxation modulus curves across multiple decade time scales under isothermal conditions.
Applicability stops when material deformation exceeds linear viscoelastic limits or when experimental noise corrupts exponential fitting routines. Resulting exponential coefficients represent discrete relaxation modes within the internal polymer network.
Relaxation Spectrum
Time constants selected for the series determine the spectral resolution of calculated material response functions. Evenly spaced logarithmic relaxation times ensure smooth representation across broad time windows. Optimizing weight coefficients matches total dynamic response without introducing unphysical positive relaxation spikes.
Calculated coefficients feed directly into finite element software for structural stress simulations.
Numerical Stability
Collinearity among exponential terms can cause fitting algorithms to yield non-unique or negative coefficient values. Tikhonov regularization constrains coefficient magnitudes to enforce physically realistic positive series values. Pre-filtering experimental force data removes high-frequency electrical noise before algorithm execution.
Poor choice of relaxation time bounds leads to oscillations in predicted relaxation modulus curves.
Material Application
Extrapolated viscoelastic models allow structural analysis under complex dynamic thermal and mechanical loading profiles. Polymer component designers use extracted series parameters to predict long-term stress relaxation in sealing gaskets. Verification compares model predictions against independent creep or dynamic frequency sweep test results.
Certification requires validation across the full thermal range expected during product deployment.
