Hysteretic models with damage and flexibility increase

The need to accurately describe nonlinear degrading phenomena in both modern and classical complex materials that exhibit hysteretic behavior is a relevant task for the analysis of their response. In the present study an enrichment to an existing formulation to describe strength and stiffness degradation is proposed. The description of damage, that reduces the hysteretic force, is then accompanied by the introduction of flexibility increase, which increments the elastic displacement experienced by the system. Both effects influence the energy dissipated by the system. The condition of thermodynamic admissibility in presence of damage and flexibility increase is derived, entailing constraints on system parameters. Additional constraints arise from consistency conditions on the transformation of the pure hysteretic system into the system with damage and flexibility increase. A numerical solution involving the forward Euler method is presented to evaluate the response quantities. The formulation is eventually applied to the elastic–plastic and Bouc Wen hysteresis models, and the influence of the degrading parameters is presented. The presented Bouc-Wen model with damage and flexibility increase is applied to study the cyclic response of a masonry panel experimentally tested to validate the numerical model and prove its capability of describing the structural response.