A degrading Bouc–Wen model for the hysteresis of reinforced concrete structural elements

This paper presents a smooth hysteresis model for reinforced concrete (RC) structural elements based on the differential equation of the Bouc–Wen model. Stiffness degradation and strength degradation are defined by introducing a damage index that includes both dissipated energy and maximum displacement. The pinching effect acts directly on the stiffness of the system and is controlled by an activation energy. The degrading functions are connected to the actual processes with which the damage occurs, thereby giving each parameter a physical meaning. The simple formulation of the model allows a straightforward identification of the best-fitting parameters and an easy interpretation of the results. Applications to the cyclic behaviour of RC structural elements demonstrate that the model is well capable of describing complex hysteretic behaviours involving degradation and pinching effects.