A consistent degrading Bouc–Wen model

In this work, a consistent smooth Bouc–Wen-type degrading hysteretic model is presented which incorporates stiffness degradation, strength deterioration, pinching, asymmetric hysteresis and strain-hardening characteristics. The smooth rate-independent model originally proposed by Bouc [1] and later extended by Wen [2] was further developed by Sivaselvan and Reinhorn [3] to incorporate degradation phenomena. This is extended herein to incorporate two specific modifications; one accounting for the loading history effect in stiffness degradation, pointed out by Wang and Foliente [4], and another related to compatibility with plasticity postulates. The latter is independently enforced based on the method developed by Charalampakis and Koumousis [5], eliminating the model’s displacement drift, force relaxation and non-closure of hysteretic loops when subjected to short unloading–reloading paths. Numerical examples are presented for a single-degree-of-freedom system demonstrating the effect of the modifications, particularly for seismic excitations.