Numerical conversion of transient to harmonic response functions for linear viscoelastic materials

Area of Science:

• Materials Science
• Rheology
• Numerical Analysis

Background:

• Viscoelastic material behavior is typically measured using creep, stress-relaxation, or dynamic sinusoidal tests.
• Analyzing data from different test types, especially in the Laplace domain, presents numerical challenges.

Purpose of the Study:

• To develop a two-stage numerical method for representing creep and stress-relaxation data in the Laplace domain.
• To enable direct comparison of data from transient tests and facilitate model fitting.

Main Methods:

• A two-stage numerical method was developed to convert temporal stress and strain data to the stiffness function G(s) on the real axis in the Laplace domain.
• A polynomial fitting technique maps G(s) to the imaginary axis, yielding the dynamic stiffness G(jω).
• The method was validated using poroelasticity model functions and applied to experimental stress relaxation data.

Main Results:

• The numerical method successfully transformed transient test data (creep, stress-relaxation) into the Laplace domain.
• The transformed data allowed direct comparison with dynamic sinusoidal test results.
• The method demonstrated accuracy even with noisy and unequally spaced data.

Conclusions:

• The two-stage numerical method provides a robust way to analyze viscoelastic material behavior from transient tests.
• It facilitates the comparison of data from different experimental methods and aids in curve-fitting routines.
• This approach enhances the analysis of both linear and nonlinear viscoelastic material properties.