Phenomenological rate-independent uniaxial hysteretic models: A mini-review

A great variety of phenomenological models has been proposed over the years to model rate-independent hysteretic forces in structural mechanics. The classification of such models is usually based on the type of equation that needs to be solved to evaluate the output variable. In particular, we distinguish among algebraic, transcendental, differential and integral models. For algebraic (transcendental) models, an algebraic (a transcendental) equation needs to be solved to compute the output variable; conversely, differential equations are employed for differential models, whereas equations expressed in integral form characterize integral models. This paper provides a mini-review of the most adopted phenomenological rate-independent uniaxial hysteretic models. Such models are selected in order to provide a complete overview of the four types of previously mentioned models, currently available in the literature. In particular, we illustrate the fundamental characteristics of each model and discuss their peculiarities in terms of 1) number of adopted parameters and variables, 2) physical interpretation of parameters and related calibration procedures, 3) type of hysteresis loop shapes that can be simulated.