Zener Model with General Fractional Calculus: Thermodynamical Restrictions

Abstract

We studied a Zener-type model of a viscoelastic body within the context of general fractional calculus and derived restrictions on coefficients that follow from the dissipation inequality, which is the entropy inequality under isothermal conditions. We showed, for a stress relaxation and a wave propagation, that the restriction that follows from the entropy inequality is sufficient to guarantee the existence and uniqueness of the solution. We presented numerical data related to the solution of a wave equation for several values of parameters.

Keywords

• general fractional calculus
• viscoelasticity
• Zener model
• restrictions