A generalized class of uniaxial rate-independent models for simulating asymmetric mechanical hysteresis phenomena

We extend a recently developed class of uniaxial symmetric rate-independent models to simulate complex asymmetric mechanical hysteresis phenomena. The main features of the novel formulation, that allows for the evaluation of the generalized force by solving a scalar equation and employing only one history variable, are illustrated by developing two specific instances of the class, namely the Asymmetric Bilinear and Exponential Models. The former is presented to better illustrate the meaning of the quantities entering the proposed formulation; the latter, representing a more sophisticated model able to simulate a wide range of asymmetric hysteretic behaviors, is illustrated to demonstrate the potentialities of the class in terms of accuracy and computational efficiency. To validate the Asymmetric Exponential Model, some experimental hysteresis loops, selected from the literature, are numerically simulated. Then, some nonlinear time history analyses are performed on a single degree of freedom mechanical system and the numerical results obtained by means of the proposed model are compared to those obtained by employing a modified version of the Bouc-Wen model.