A Bouc–Wen model compatible with plasticity postulates

The versatile Bouc–Wen model has been used extensively to describe hysteretic phenomena in various fields of engineering. Nevertheless, it is known that it exhibits displacement drift, force relaxation and nonclosure of hysteretic loops when subjected to short unloading–reloading paths. Consequently, it locally violates Drucker's or Ilyushin's postulate of plasticity. In this study, an effective modification of the model is proposed which eliminates these problems. A stiffening factor is introduced into the hysteretic differential equation which enables the distinction between virgin loading and reloading. Appropriate reversal points are utilized effectively to guide the entire process. It is shown that the proposed modification corrects the nonphysical behavior of the model under short unloading–reloading paths without affecting its response in all other cases. It is further demonstrated that the original and modified model exhibit significantly different response under seismic excitation.