The thermorheologically complex material

The material dispersion and attenuation of acoustic waves in a linear viscoelastic medium are uniquely described by its frequency-dependent complex moduli. Traditionally, the moduli master curves are constructed using the time-temperature superposition hypothesis that leads to the thermorheologically ‘‘simple’’ material model. Recent research indicates that the time-superposition hypothesis should be modified to account for temperature-dependent shape changes observed in some moduli curves. This modified hypothesis leads to the thermorheologically ‘‘complex’’ material model. The complex model is based on an approximation of quantum mechanical energy transitions in intramolecular bonds and a simple notion of viscoelastic relaxation. The complex model is shown to be related to a fractal time process describing stress relaxation, also to use fractional order time derivations to relate stress fields to strain fields, and to be practical for rheological and engineering analyses.