Issue 31

H.F.S.G. Pereira et alii, Frattura ed Integrità Strutturale, 31 (2015) 54-66; DOI: 10.3221/IGF-ESIS.31.05 59 The adopted CDP model used a yield surface that was defined as the loading function proposed by Lubliner et al. [30], see Fig. 8. The evaluation of the yield surface was controlled by the two hardening variables, namely, the plastic strain in tension ( pl t   ) and the plastic strain in compression ( pl c  ~ ). Tab. 2 includes the mechanical properties of concrete and steel used in the numerical simulations. Regarding the steel tensile behaviour an elastic – perfectly plastic relationship 1 n  was considered with a yield stress of 567 MPa. On the other hand, Tab. 3 includes the constitutive parameters of the CDP model used to simulate the nonlinear behaviour of concrete when considered. Material Density, ρ [kg/m 3 ] Young Modulus, E [GPa] Poisson ratio,  [-] Steel 7800 200 0.30 Concrete 2400 30 0.20 Table 2 : Mechanical properties adopted in the numerical simulations. Dilatation angle [º] Eccentricity [-] σ bo /σ co [-] Kc [-] 40.0 0.1 1.16 0.667 Table 3 : The constitutive parameters of CDP model. P ARAMETRIC STUDY his section presents the parametric study that was carried out to calibrate the numerical model for the pullout tests. This study evolves the analysis of the influence of distinct parameters on the numerical responses, such as: the mesh refinement, the cohesive element thickness and the viscosity coefficient. Mesh refinement To analyse the influence of the mesh refinement, it was considered in a first stage a linear elastic behaviour for concrete. For the interface behaviour it was used the relationship depicted in Fig. 7. For this task, four meshes similar to the one presented in Fig. 4 were considered. Tab. 4 presents several parameters for mesh characterization, such as number of elements and nodes, and respective computational time for completing the numerical simulation of the pullout test. Mesh Element quantity Nodes quantity Computational Time 1 2100 2790 48min 21s 2 3100 3945 49min 10s 3 4100 5100 61min 21s Table 4 : Mesh parameters. The parameters to define the behaviour of the cohesive elements layer in terms of nominal stresses are presented in Tab. 5. The adopted damage evolution was of the type displacement with linear softening and maximum degradation. Moreover, two values for displacement at failure, namely, 5 and 1000 mm were adopted. In the last case, it corresponds practically to assuming no degradation of the bond stresses with the increment of slip. Nominal Stress Normal-only Mode [MPa] Nominal Stress First Direction [MPa] Nominal Stress Second Direction [MPa] 0 10.26 0 Table 5 : Nominal Stress. Fig. 9 and 10 depict the results obtained in the numerical simulations considering an elastic behaviour for concrete and the local bond stress – slip relationship defined by Fig. 7 for the interface elements behaviour. As it was expectable the T