Bouc–Wen-Type Models with Stiffness Degradation: Thermodynamic Analysis and Applications

In this paper, a thermodynamic analysis of Bouc–Wen models endowed with both strength and stiffness degradation is provided. This analysis is based on the relationship between the flow rules of these models and those of the endochronic plasticity theory with damage, discussed in a companion paper. Using the theoretical framework of that extended endochronic theory, it is shown that an elastic Bouc–Wen model with damage, i.e., without plastic strains, can be formulated. Moreover, a proper definition of the dissipated energy of these Bouc–Wen models with degradation is given and some thermodynamic constraints on the parameters defining the models behavior are emphasized and discussed. In particular, some properties of the energetic linear stiffness degradation rule as well as the so-called pivot rule, well known in the seismic engineering field, are illustrated and commented upon. An improved energetic stiffness degradation rule and a new stiffness degradation rule are proposed.