Master curve of viscoelastic solid: Using causality to determine the optimal shifting procedure, and to test the accuracy of measured data

Viscoelastic solids such as rubber exhibit a complex elastic modulus E(ω), which depends on the frequency ω of the applied stress or strain. The modulus E(ω) can often be determined in a wide frequency range by performing measurements in a limited frequency range for many different temperatures, and then shift the frequency segments horizontally along the frequency axis to obtain a continuous master curve. We show that one can use the spectral representation of E(ω) (or 1/E(ω)), which obeys causality, to determine the optimal shifting procedure, and to test the accuracy of the measured data and the calculated master curve.