An Algebraic Model for Hysteretic Responses Exhibiting Cyclic Hardening and Softening Phenomena: Preliminary Results

In this chapter, a newly formulated model called the algebraic model is extended to simulate the cyclic hardening and softening phenomena observed in hysteretic mechanical systems and materials. The proposed approach consists in analytically expressing the model parameters as functions of the generalized work. To this end, we first provide closed-form expressions to evaluate the generalized work done by a generalized rate-independent hysteretic force over a generic generalized displacement interval. Subsequently, to prove the effectiveness of the methodology, two different experimental hysteretic responses retrieved from the literature and characterized by cyclic hardening and softening phenomena, respectively, were reproduced.