Issue 47

R. Fincato et alii, Frattura ed Integrità Strutturale, 47 (2019) 231-246; DOI: 10.3221/IGF-ESIS.47.18 237 a) b) c) Figure 2: a) sketch of the plate subjected to two loading steps; b) ductile damage evolution depending on the material parameter T 3 . c) cumulative inelastic strain H i , cumulative plastic strain H D and cumulative tangential plastic strain H T vs. angular distortion. For sake of convenience, the material parameters adopted in this first study case are the same of the ones used for the numerical analysis of the thin wall steel pier. The calibration and the discussion of their values will be dealt in the next sub- section. The actual values of the material constants are relatively important in this study case, since the primary goal is to show the characteristic of the ductile damage evolution law described in Eqn. (14) 1 . Fig. 2b reports the damage evolution through the step 1 and the step 2 for different values of the parameter T 3 . During the first loading step, the damage evolves in the same way, independently from the value of the T 3 constant, since the load is proportional. However, at the beginning of step 2 the damage evolution accelerate proportionally to T 3 , as a consequence of the rotation of the directions of the principal stresses, triggered by the sudden change of loading conditions. Experimental results, reported by Roscoe [33] for granular materials, also confirm the non-coaxiality of the principal stresses and the principal plastic strains directions for the simple shear test. However, this tendency tends to disappear at large strains where the proportionality of the load tends to be re-established. This phenomenon can be seen in Fig. 2b, after the initial acceleration of the damage accumulation, the evolution rate slows down and the blue lines became parallel to the black one. Therefore, the damage evolution accelerates whenever the loading conditions trigger a rotation of the directions of the principal stresses, whereas it proceeds with the same rate as in Eqn.(13) when the proportionality is re-established. Fig. 2c reports the cumulative inelastic strain H i , cumulative plastic strain H D and cumulative tangential plastic strain H T (see Eqn. (15)) against the angular distortion for the second loading step. The contribution of the tangential plastic strain is around the 20% of the total cumulative inelastic strain. Thin wall steel column under cyclic loading This second numerical analysis focuses the attention on reproducing the structural response of a steel column subjected to unidirectional cyclic loading. The damage evolution was monitored considering or not the tangential plasticity term (i.e. Eq