The thermorheologically complex material

An approximate quantum mechanical description of molecular energy transitions leads to fractional order time derivative descriptions of linear viscoelastic stress relaxation in polymers. The resulting fractional calculus stress-strain constitutive laws are mathematically compact and suitable for rheological and engineering analyses. The mathematical form of the models suggests a modification to the thermorheologically simple material that enables the description of temperature-dependent changes to the shape of curves representing a material's modulus in the transition region. The fractional calculus models are seen to be extensions of the traditional exponential models of stress relaxation.