  In this paper, a thermodynamic analysis of Bouc-Wen models endowed with both
strength and stiffness degradation is provided. It 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 (Erlicher and Point, 2008).
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.
