Formulation of thermodynamically consistent fractional Burgers models

Abstract

The approach of viscoelastic body constitutive equation fractionalization using rheological representation of the classical Burgers model and considering the Scott–Blair (fractional) elements instead of the dash-pot elements is adopted. The obtained fractional Burgers model is further generalized by considering arbitrary model parameters: multiplicative constants and orders of fractional differentiation. Thermodynamical consistency of the fractional Burgers model is analyzed, resulting in formulation of eight thermodynamically consistent fractional Burgers models.