Classification and unified phenomenological modeling of complex uniaxial rate-independent hysteretic responses

The number and nature of hysteretic responses typically exhibited by mechanical systems and materials are so huge that their modeling and identification are usually carried out on an ad-hoc basis. Thus, with the aim of proposing a unified approach to the modeling of rate-independent hysteretic behavior, we first perform a detailed classification of complex generalized force- displacement hysteresis loops, ranging from the asymmetric, pinched, S-shaped, flag-shaped ones to those obtained by their arbitrary combination, since they typically span the vast majority of loops obtained experimentally. Subsequently, we formulate a novel rate-independent hysteretic model, having an exponential nature, that offers a series of advantages over other hysteretic models available in the literature. Indeed, it adopts closed form expressions for evaluating the output variable, with important benefits in terms of computational efficiency and implementation ease, and it allows for an uncoupled modeling of the generic loading and unloading phases by means of two different sets of eight parameters. In addition, it requires the use of a simple identification procedure thanks to the clear theoretical and/or experimental interpretation of the adopted parameters. The accuracy of the proposed model is experimentally and numerically validated and its computational efficiency is demonstrated. In particular, the experimental validation is carried out by reproducing four different types of complex experimental hysteresis loops retrieved from the literature, whereas the numerical validation is performed by running some nonlinear time history analyses on a single degree of freedom mechanical system and comparing the results with those obtained by using a modified version of the celebrated Graesser-Cozzarelli model.