Reformulation of a phenomenological model for symmetric rate-independent hysteresis

The present paper enhances, both theoretically and numerically, a recent uniaxial phenomenological model aiming to reproduce complex hysteretic behaviors of seismic isolation devices, including steel- and fiber-reinforced elastomeric bearings, presenting smooth hysteresis loops with hardening and/or softening regions. The investigated constitutive model is based on five parameters that can be directly related to the experimentally observed hysteresis loops. Moreover, because of its analytical nature, the presented formulation is capable of computing in closed form the generalized response relevant to any displacement increment starting from a known equilibrium state. Hence, differently from the original differential formulation of the investigated model as well as from popular materials such as the celebrated Bouc–Wen, the presented formulation does not require any iterative strategy for computing the hysteretic force. Finally, the investigated model is validated by numerical simulations compared with experimental tests selected from the literature.