Issue 47

E. Grande et alii, Frattura ed Integrità Strutturale, 47 (2019) 321-333; DOI: 10.3221/IGF-ESIS.47.24 330 - zone 3: 2 3 1 3 3 2 2 2 3 3 2 3 2 2 0 - 0 i e e i e e e d s K G s dx L b x L d s d s K G s dx dx                           (17) where 2  and 3  are the shear stress values identified by the steps approximating the descending branch in the phase 2. In this case, it is necessary to introduce twelve boundary conditions. Four boundary conditions concern the two end sections of the specimen where it is stated that: the stress is zero at the free end of the reinforcement; the stresses are zero at two ends of the upper mortar layer; the upper interface attains the slip * 1 s at the loaded end, i.e. the slip corresponding to the attainment of the tensile strength of the upper mortar layer, i.e.:         ,1 ,1 ,3 * 3 1 0 0 0 0 0 p e c e c e L s L s        (18) The other boundary conditions concern the continuity of normal stresses in the mortar layer and in the reinforcement, the continuity of the slip at the lower and upper layers at the section:                                                 1 2 1 2 2 3 2 3 1 2 1 2 1 2 1 2 e e e e c c p p e e e e c c p p i i e e i i e e L a b L a b L a b L a b L b L b L b L b s L a b s L a b s L a b s L a b s L b s L b s L b s L b                                         (19) Moreover, due to the introduction of the additional unknowns a and b, i.e. the length of the zone 2 and the zone 3 respectively, it is necessary to introduce the following two additional boundary conditions:     2 2 3 3 i i s L b s s L s    (20) where s 2 and s 3 are the slips identified by the two steps along the softening branch. The subsequent phase (Fig. 6.c) is characterized by both the interfaces in the post-peak stage. An increase of the number of equations is still due to the steps discretizing the descending branch of the shear stress-slip law of the lower interface. Moreover, some of the zones are also characterized by a null value of the shear stress at the upper interface. Indeed, considering the example shown in Fig. 6.c, the set of equations characterized by this condition are the ones related to the last two zones: - zone 4:   2 4 1 4 2 2 2 4 4 2 2 0 - 0 i i e d s K dx L c d x L d d s d s dx dx                       (21)