Rheological constitutive equation of solids : a link between models based on irreversible thermodynamics and on fractional order derivative equations Article - Avril 2003

In this paper we focus on the rheological problem of defining a constitutive equation for viscoelastic materials. In this simple case, we show that writing the dissipative component of the observable response to a given excitation as the result of multiple internal processes working for equilibrium recovery (flux of internal hidden variables), can yield a recursive series in time. This can be obtained when use is made of the theorem of created entropy equipartition as a model for fluctuation regression. A distribution (spectrum) for relaxation times naturally follows. The model thus obtained reflects the concept of a hierarchically constrained dynamic behavior. The conclusion is that the operator of non-integer differentiation in time applied to field variables can also be recovered from pure thermodynamic considerations.