Issue 47

E. Grande et alii, Frattura ed Integrità Strutturale, 47 (2019) 321-333; DOI: 10.3221/IGF-ESIS.47.24 331 - zone 5: 2 5 1 5 2 2 2 5 5 2 2 0 - 0 i i e d s K dx L d x L d s d s dx dx                     (22) The boundary conditions are the same of those accounted for the previous phases and, also in this case, it is necessary to introduce additional boundary conditions for deriving the length of the different zones. Numerical applications for the case with softening Considering the approach based on the step function approximation, numerical applications are performed with reference to the case studies presented in the first part of the paper ([4]). In particular, considering the shear stress-slip law proposed in [4], a bi-linear law has been derived (Fig. 7.a). Subsequently, this law has been approximated throughout a step function and assumed for the behavior of the lower interface (Fig. 7.b). Regarding the upper interface, a linear brittle shear stress-slip law has been considered by assuming a bond strength value equal to 0.9 MPa, which corresponds to the attainment of the tensile strength of the upper mortar layer (see the approach 2). a) b) Figure 7 : Shear stress-slip law accounted for the lower interface in the case of the approach based on the step function approximation. a) b) Figure 8 : Results in terms of applied load vs. slip: comparison between the approach 2 and the case with softening. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 shear stress [MPa] slip [mm] bi‐linear step‐function 0 2 4 6 8 0 1 2 3 4 applied load P [kN] slip s i (x=L) [mm] D'Antino et al., 2015 ‐ b p =60mm approach 2 softening 0 2 4 6 8 10 0 1 2 3 4 applied load P [kN] slip s i (x=L) [mm] D'Antino et al., 2015 ‐ b p =80mm approach 2 softening