tesi A. Caggiano.pdf - EleA@UniSA - Università degli Studi di Salerno

4.3. Elasto-plastic joint/interface model with isotropic linear softeningFigure 4.3: Schematic components of pull-out analysis for the analytical solution.matrix interface. According to the plasticity model described in section 4.3, the contactlaw (τ − s) presents a bilinear form, featuring an initial linear ascending branch, withthe k E initial slope, followed, when the elastic limit τ y,0 is reached, by a linear softeningbranch whose slope is now defined as k S = k E(1 − k Ek E +k H). The model is completedconsidering an ultimate slip, s u , at which the bond transferred stress is considered null.The full analytical solution is applied to a single fiber, as schematized in Figure 4.3.Based on the assumption that the fiber diameter d f and the local bond-slip relationshipkeep unchanged throughout the fiber bond length, l emb , the following infinitesimalequilibrium condition can be formulateddσ f [z]d z= − 4τ[z]d f(4.7)where τ[z] is the shear stress transferred at the interface and σ f [z] the axial steel stress.Assuming that bond failure occurs for fiber stresses lower than the corresponding yieldlimit (as generally observed in experimental investigations), the following constitutivelaws to model both the mechanical response of fiber and the interface adherences,respectively, can be writtenσ f [z] = E fd s[z]d z(4.8)73