Simultaneous Characterization of Relaxation, Creep, Dissipation, and Hysteresis by Fractional-Order Constitutive Models

We considered relaxation, creep, dissipation, and hysteresis resulting from a six-parameter fractional constitutive model its particular cases. The storage modulus, loss factor, as well their characteristics based on the thermodynamic requirements, were investigated. It was proved that for Maxwell model, modulus increases monotonically, while has symmetrical peaks curve against logarithmic scale log(?), Zener monotonically factor have curves log(?). peak values corresponding stationary points analytically given. relaxation creep compliance given in terms of Mittag–Leffler functions. Finally, stress–strain loops simulated by making use derived model. These results show models could characterize phenomena viscoelastic bodies, orders ? ? be used to real-world physical properties well.