Issue 47

R. Fincato et alii, Frattura ed Integrità Strutturale, 47 (2019) 231-246; DOI: 10.3221/IGF-ESIS.47.18 238 (13) or (15)), pointing out the necessity to include the additional inelastic stretching contribution for a more realistic description of the material behavior. Nishikawa et al. [32] conducted a series of experiments on thin steel piers in order to analyze the horizontal load-carrying capacity of the structures subjected to an increasing unidirectional horizontal load. The schematic of the pier is reported in Fig. 3a together with its FE modeling. The loading sequence is instead reported in Fig. 3b. In order to save computational time, just half of the column was considered, applying symmetric boundary conditions. Moreover, the experimental results showed that the plastic deformations, and the buckling, appear in a region close to the base of the pier. Therefore, the structure was modeled according to its real geometry until a height equal to two times the internal diameter from the bottom and the remaining part was modeled with a beam element. A similar strategy was adopted by Gao et al. [34] and by Ucak and Tsopelas [35]. The geometric specifications are reported in Tab. 1. a) b) Figure 3: a) Model and geometry of the bridge pier; b) Loading sequence. The lower part of the pier has a mesh of eight-node hexahedral elements with reduced integration (i.e. Abaqus C3D8R elements) and the nodes of the top cross section were connected to the beam with rigid links. A mesh refinement was considered close to the base of the pier, where the maximum accumulation of plastic deformation is expected. The minimum element size is 9.8 mm (circumference) x 2.25 mm (thickness) x 15 mm (axial), comparable with the minimum element size used by Van Do et al. [36], who conducted a mesh size sensitivity analysis on the same study case. The total number of elements amount to 51841. The structure is subjected to two types of loads: a compressive load P, constant and kept for the whole duration of the experiment, and a horizontal load H, directed along the x-direction and with an increasing amplitude. The idea of Nishikawa et al. was to reproduce the conditions of a seismic solicitation hitting a bridge pier, where P represented the dead load of the infrastructure over the steel column and H represented a simplify shock wave. The magnitude of P was set to be 0.124 the squash load P y . The parameters H y and δ y in Tab. 1 represent the horizontal load and horizontal displacement when the specimen yields close to the base. A preliminary characterization of the material parameters for the DSS and the material parameters for the definition of the MC failure envelope was carried out by reproducing the uniaxial tensile behavior of a smooth bar reported in [36,37]. Few material parameters such as: the Young’s modulus, the Poisson’s ratio and the yield stress F 0 were assumed directly from [32], the kinematic hardening parameters C 1 , B 1 , C 2 , B 2 and the threshold for the strain plateau H p were assumed as in Van Do et al. [36]. The threshold for the damage evolution d 1 was chosen to be equal to strain plateau threshold H p . The remaining damage parameters in Tab. 3, together with the isotropic hardening parameters K , h 1 , h 2 were obtained by minimizing the difference between the numerical and experimental curves reported by Goto et al. [37], as shown in Fig. 4. Two aspects have to be mentioned. Firstly, the calibration of the damage parameters based on a single uniaxial tensile test cannot guarantee to identify the correct set of variables for the description of the ductile behavior of the material. Therefore, the