Zener Model with General Fractional Calculus: Thermodynamical Restrictions
Teodor M. Atanacković, Stevan Pilipović
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.
Topics & Concepts
Standard linear solid modelUniquenessFractional calculusViscoelasticityMathematicsContext (archaeology)DissipationEntropy (arrow of time)Isothermal processZener diodeCalculus (dental)Mathematical analysisApplied mathematicsPhysicsThermodynamicsMedicineVoltageBiologyPaleontologyDentistryQuantum mechanicsResistorThermoelastic and Magnetoelastic PhenomenaFractional Differential Equations SolutionsElasticity and Wave Propagation