PSI- Issue 9

Riccardo Fincato et al. / Procedia Structural Integrity 9 (2018) 136–150 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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horizontal load on the positive side but they tend to overestimate the load on the negative side. Moreover, after the fifth cycle, there is a general overestimation of the material performances. This drawback can be corrected accounting for the additional contribution triggered by the tangential components of the stress rate that allows the numerical response overlapping the experimental results in the last cycles. The material parameter T 3 was set to be equal to 0.6. The same behavior can be observed in Figure 5a, where the peaks of the horizontal load are plotted against the corresponding maximum lateral displacements for the positive side of the loading.

b)

a)

c) Figure 4 a) Hysteresis loops for the pier in Figure 2a (proportional and non-proportional damage laws), b) hysteresis loops for the pier in Figure 2a (without damage), c) example of the absorbed energy during the first cycle. All the curves overestimate the initial elastic response of the pier, probably due to some uncertainties on the elastic constants and the assumption adopted in the FE for modeling the real geometry of the pier. However, the degree of approximation of the peak of the horizontal load can be considered as satisfactory. The post-peak behavior is overestimated by the red and green curves but is very well described by the solution that considers the non-proportional damage evolution law. Nishikawa et al. (1998) evaluated the horizontal load-carrying capacity with an energy-based criterion, investigating the work done per loop by the horizontal force, as schematically displayed in Figure 4c. The normalization factor E 0 is represented by the elastic work done by the horizontal force up to the point when the pier starts to yield:   0 / 2 y y E H   (10) Figure 5b shows the results obtained with the DSS model that point out, once again, that the simulation, carried out without considering the damage, cannot be assumed as reliable for the description of the structural behavior. The