A fatigue damage model for seismic response of RC structures

Numerous damage models have been developed in order to analyze seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of continuum damage mechanics are more consistent with the definition of damage as a phenomenon with mechanical consequences because they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, most of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Cipollina et al. [Cipollina A, López-Hinojosa A, Flórez-López J. Comput Struct 1995;54:1113–26] is made in order to include the low cycle fatigue. Such a model employs in its formulation irreversible thermodynamics and internal state variable theory.

Modelization of low cycle fatigue damage in frames

Damage models based on the Continuum Damage Mechanics (CDM) include explicitly the coupling between damage and mechanical behavior and, therefore, are consistent with the definition of damage as a phenomenon with mechanical consequences. However, this kind of models is characterized by their complexity. Using the concept of lumped models, possible simplifications of the coupled models have been proposed in the literature to adapt them to the study of beams and frames. On the other hand, in most of these coupled models damage is associated only with the damage energy release rate which is shown to be the elastic strain energy. According to this, damage is a function of the maximum amplitude of cyclic deformation but does not depend on the number of cycles. Therefore, low cycle effects are not taking into account. From the simplified model proposed by Flórez-López, it is the purpose of this paper to present a formulation that allows to take into account the degradation produced not only by the peak values but also by the cumulative effects such as the low cycle fatigue. For it, the classical damage dissipative potential based on the concept of damage energy release rate is modified using a fatigue function in order to include cumulative effects. The fatigue function is determined through parameters such as the cumulative rotation and the total rotation and the number of cycles to failure. Those parameters can be measured or identified physically through the haracteristics of the RC. So the main advantage of the proposed model is the possibility of simulating the low cycle fatigue behavior without introducing parameters with no suitable physical meaning. The good performance of the proposed model is shown through a comparison between numerical and test results under cycling loading.

A damage model for seismic retrofitting of structures

Numerous damage models have been developed in order to analyse the seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of Continuum Damage Mechanics are more consistent with the definition of damage like a phenomenon with mechanical consequences as they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, many of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Flórez is made in order to include the low cycle fatigue. Such model employs in its formulation irreversible thermodynamics and internal state variable theory.

Health monitoring of web plastifying dampers subjected to cyclic loading through vibration tests

This article investigates experimentally the application of health monitoring techniques to assess the damage on a particular kind of hysteretic (metallic) damper called web plastifying dampers, which are subjected to cyclic loading. In general terms, hysteretic dampers are increasingly used as passive control systems in advanced earthquake-resistant structures. Nonparametric statistical processing of the signals obtained from simple vibration tests of the web plastifying damper is used here to propose an area index damage. This area index damage is compared with an alternative energy-based index of damage proposed in past research that is based on the decomposition of the load?displacement curve experienced by the damper. Index of damage has been proven to accurately predict the level of damage and the proximity to failure of web plastifying damper, but obtaining the load?displacement curve for its direct calculation requires the use of costly instrumentation. For this reason, the aim of this study is to estimate index of damage indirectly from simple vibration tests, calling for much simpler and cheaper instrumentation, through an auxiliary index called area index damage. Web plastifying damper is a particular type of hysteretic damper that uses the out-of-plane plastic deformation of the web of I-section steel segments as a source of energy dissipation. Four I-section steel segments with similar geometry were subjected to the same pattern of cyclic loading, and the damage was evaluated with the index of damage and area index damage indexes at several stages of the loading process. A good correlation was found between area index damage and index of damage. Based on this correlation, simple formulae are proposed to estimate index of damage from the area index damage.