Dynamic response of masonry panels based on a modified Bouc-Wen hysteresis with strength and stiffness degradation

Masonry is one of the most traditional materials, and is still now extensively studied due to the fact that it constitutes a large part of the world historical and architectural heritage. Numerous methods are employed in literature to reproduce its nonlinear behavior and complex mechanisms, considering the uncertainty level during both static and dynamic loading conditions. The Bouc-Wen model is still a valid model for the representation of the cyclic behavior of a large variety of materials including masonry, although its formulation is dated in early ’70s [1]. Different authors have proposed various modifications to the original hysteresis model, including the introduction of damage by means of a scalar variable that affects the hysteretic component of the force [2, 3]. In this study, to reproduce more accurately the stiffness degradation during the loading and unloading branches of the cyclic response, the hysteretic formulation with damage presented in [2] is properly enriched by introducing flexibility increase. The latter produces an expansion of the elastic displacement depending on a parameter that regulates the rate of the flexibility increase itself. The enriched hysteretic formulation with damage and flexibility increase is, then, used to model the nonlinear behavior of masonry panels within the framework of a macroelement procedure relying on the force-based approach for beams. The nonlinearity of masonry is lumped in two flexural hinges and a shear link. In the case of the flexural components, a nonlinear elastic device is considered in parallel with the modified Bouc-Wen hysteresis and, in series with both, a linear elastic negative device is arranged. This allows to reproduce two peculiarities of the behavior of slender panels, namely pinching and the high initial stiffness. A lumped mass approach, according to the force-based approach, and the classical Rayleigh damping are included to explore the dynamic response field. An extended study is carried on focused on the dynamic behavior of the macroelement with hysteresis, considering the influence of damage and flexibility increase separately, with respect to the classical Bouc- Wen hysteresis and elastic cases. Different loading conditions are considered, in order to highlight the interaction of the evolution of degradation with the masonry dynamic characteristics. Different geometric configurations are then examined and results are discussed.