An enriched Bouc-Wen model with damage

This paper presents an enriched hysteresis model with damage relying on the Bouc-Wen formulation, in which a single scalar variable is introduced to reproduce effects of strength and stiffness degradation emerging for damaging materials. First, some acknowledged limits of the original Bouc-Wen model are discussed, focusing on its thermodynamic admissibility and compatibility with Drucker's plasticity postulate, and highlighting the effects of the parameters β and γ. Then, a reformulated expression of the dissipated energy is presented, which is consistent from the thermodynamic point of view. This formulation is extended to the case of degrading Bouc-Wen models. Uniaxial validation analyses are proposed, together with some considerations on the physical and thermodynamic admissibility of the model. The effect of pinching is also introduced by means of the arrangement in parallel of a non-dissipative Bouc-Wen and a degrading (damaging)device, resulting in a varied set of hysteresis shapes. Finally, the proposed model is adopted to analyse the cyclic response of masonry structural elements under in-plane horizontal loads. Within the framework of equivalent frame formulation, masonry panels are modelled by an elastic beam arranged in series with nonlinear flexural hinges lumped at the ends and a shear link, whose constitutive relationships are described by means of the enriched hysteretic model with damage.